Chapter 11. Laboratory: Acid-Base Chemistry

Acids and bases are two of the most important classes of compounds in chemistry. Surprisingly, it took chemists many years to agree on just what made an acid an acid and a base a base.

From experience, we understand that acids and bases have certain characteristics. For example, acid solutions taste sour and base solutions bitter. (Obviously, you should never taste any laboratory chemical, but the sour taste of edible acids such as lemon juice and vinegar is familiar to most people, as is the bitter taste of edible bases such as baking soda and quinine water). Acid solutions generally have an astringent feel on the skin, and base solutions feel slimy. Acid solutions turn blue litmus paper red, and base solutions turn red litmus paper blue. Acids and bases combine to form salts. And so on.

But these characteristics are insufficient to define acids and bases. Around the turn of the nineteenth century, French and European chemists believed that all acids must contain oxygen. (They were wrong, but echoes of that error persist; for example, the German word for oxygen is Sauerstoff, which translates literally as “sour material.”) Davy and other English chemists were much closer to the mark. They believed that all acids must contain hydrogen. And, although that statement is not absolutely true for all substances considered to be acids by modern definitions, it is true that all acids known to be acids at that time do contain hydrogen.

The first good working definition of acids and bases was proposed in the late nineteenth century by the Swedish chemist Svante August Arrhenius, who defined an acid as a substance that when dissolved in water increases the concentration of the hydronium (H₃O⁺) ion and a base as a substance that when dissolved in water increases the concentration of the hydroxide (OH^–) ion. Although that definition limits acids and bases to compounds that are water-soluble, it was a pretty good definition for the time and remains a useful definition even today.

But not all compounds that behave chemically as acids can dissociate to produce hydrogen ions, and not all compounds that behave chemically as bases can dissociate to produce hydroxide ions. In 1923, the Danish chemist Johannes Nicolaus Brønsted and the English chemist Thomas Martin Lowry redefined an acid as a proton (hydrogen nucleus) donor, and a base as a proton acceptor. Under the Brønsted-Lowry definition of acids and bases, an acid and its corresponding base are referred to as a conjugate acid-base pair. The conjugate acid is the member of the pair that donates a proton, and the conjugate base the member of the pair that accepts a proton. For example, hydrochloric acid dissociates in water to form chloride ions and hydronium ions:

HCl + H₂O ⇔ H₃O⁺ + Cl^-

In the forward reaction, the acid reactant (HCl) and the base reactant (H₂O) form the acid product (H₃O⁺) and the base product (Cl^–). In the reverse reaction, the acid reactant (H₃O⁺) and the base reactant (Cl^–) form the acid product (HCl) and the base product (H₂O). If the conjugate acid (HCl on the left side of the equation and H₃O⁺ on the right side) is strong, the conjugate base (H₂O on the left side of the equation and Cl^– on the right side) is weak, and vice versa. At equilibrium, the weaker acid is favored.

For aqueous solutions, the Arrhenius definition and the Brønsted-Lowry definition are essentially the same. The value of the Brønsted-Lowry definition is that it extends the concept of acids and bases to compounds that are not soluble in water.

The same year that Brønsted and Lowry defined acids and bases as proton donors and proton acceptors, respectively, the American chemist Gilbert N. Lewis extended the definition of acids and bases to include compounds that behaved chemically as acids and bases without donating or accepting a proton. Under the Lewis definition of acids and bases, a Lewis acid (also called an electrophile) is a substance that accepts an electron pair, and a Lewis base (also called a nucleophile) is a substance that donates an electron pair. (For example, the compound ferric chloride, FeCl₃, behaves as an acid, although it has no proton to donate, and so is classified as a Lewis acid.) Lewis acids and bases are particularly important to organic chemists, who make use of them in many syntheses.

In this chapter, we’ll examine the properties of acids and bases.

Everyday Acid-Base Chemistry

Acid-base chemistry is inextricably tied with our everyday lives. Here are just a few examples:

• Without the hydrochloric acid in our stomachs, we could not digest our food. Most people are surprised to learn that the pH of gastric juice (see Laboratory 11.1: Determine the Effect of Concentration on PH) can be as low as 1, a very strong acid capable of “dissolving” some metals.

• Mineral (inorganic) acids, including hydrochloric, nitric, phosphoric, and sulfuric acids, are among the most important industrial chemicals. Millions of tons of these acids are produced worldwide, and they are critical to the manufacture of thousands of important compounds, including foods and food supplements, drugs, fertilizers, soaps and detergents, dyes and pigments, explosives, metals, and fuels.

• Bases react with fats by a process called saponification to produce soaps, a reaction that is used to produce commercial soap products. But we also use saponification directly every time we use a window cleaner or other cleaning product that contains ammonia. The basic ammonia reacts with greasy dirt to produce soluble compounds (soaps) that can be rinsed away.

Activity versus Concentration

Technically, the pH of a solution depends on the activity of the hydronium ions rather than their concentration, but it’s easy to measure concentration accurately and very difficult to measure activity accurately. (Activity can be thought of as the effective concentration of hydronium ions, which is lower than the actual concentration, because in solution some of the hydronium ions are “screened” by other ions present in the solution and therefore unable to participate in reactions.) In very concentrated solutions, activity may be considerably lower than the actual concentration. In dilute solutions, concentration and activity correlate very closely, so the concentration is typically used for calculations.

Dr. Paul Jones Comments

Most beginning students are aware of acids and their dangers but are more or less ignorant of the dangers of alkali (base). For instance, aqueous sodium hydroxide can blind you in a matter of minutes if not cleansed thoroughly and I’ve seen lots of kids who are quick to put on goggles to work with 0.01 M HCl but throw 6 M NaOH around like it’s candy. Aqueous bases are every bit as dangerous as aqueous acids, if not more so, but many students treat aqueous bases as though they were innocuous.

Laboratory 11.1: Determine the Effect of Concentration on PH

pH is a metric used to specify the acidity (or basicity, also called alkalinity) of an aqueous solution. The pH of a solution is determined by the relative activities of the hydronium (H₃O⁺) ions and the hydroxide (OH^–) ions in the solution. The pH of a solution in which the activities of these two ions are equal—such as pure water at 25°C—is 7.00. A solution in which the activity of the hydronium ions is higher than the activity of the hydroxide ions has a pH lower than 7 and is acidic. A solution in which the activity of the hydroxide ions is higher than the activity of the hydronium ions has a pH greater than 7, and is basic.

pH is specified on a log₁₀ scale, which allows a very wide range of activities (concentrations) to be specified using a small range of numbers. A difference of one pH number corresponds to a difference of ten times in acidity or basicity. For example, a solution with a pH of 5 is ten times (10¹) more acidic than a solution with a pH of 6, and a solution with a pH of 9 is ten times (10¹) more basic than a solution with a pH of 8. Similarly, a solution with a pH of 2 is 10,000 (10⁴) times more acidic than a solution with a pH of 6, and a solution with a pH of 12 is 10,000 (10⁴) times more basic than a solution with a pH of 8. Although the range of pH values is usually considered to be 0 through 14, an extremely acidic solution (such as a concentrated solution of hydrochloric acid) can have a pH lower than 0, and an extremely basic solution (such as a concentrated solution of sodium hydroxide) can have a pH greater than 14.

For relatively dilute solutions of strong acids and bases, you can estimate pH using the formula:

pH = –log₁₀[H₃O⁺]

where [H₃O⁺] is the concentration of the hydronium ion in mol/L. For example, hydrochloric acid dissolves in water according to the following equation:

HCl + H₂O → H₃O⁺ + Cl^–

Because HCl is a strong acid, the reaction proceeds to completion, which is to say that essentially all of the HCl reacts to form hydronium ions and chloride ions. The approximate pH of a 0.01 M solution of hydrochloric acid is:

pH = –log₁₀[0.01] = 2

Required Equipment and Supplies

	goggles, gloves, and protective clothing
	balance and weighing papers
	beaker, 150 mL (6)
	volumetric flask, 100 mL
	pipette, 10 mL
	pH meter
	hydrochloric acid, 1 M (100 mL)
	sulfuric acid, 1 M (100 mL)
	acetic acid, 1 M (100 mL)
	sodium hydroxide, 1 M (100 mL)
	sodium carbonate, 1 M (100 mL)
	distilled or deionized water (boil and cool before use)

In calculating that approximate pH, we assume that the hydrochloric acid fully dissociates in solution into H₃O⁺ ions and Cl^– ions. For strong acids like hydrochloric acid, that’s a reasonable assumption. For weak acids, such as acetic acid, that assumption is not valid, because weak acids dissociate only partially in solution. The concentration of hydronium ions in a solution of a weak acid is lower (perhaps much lower) than the concentration of the acid itself.

When acetic acid dissolves in water, the dissociation reaction looks like this:

CH₃COOH + H₂O ⇔ H₃O⁺ + CH₃COO^–

This reaction reaches an equilibrium, with reactants being converted to products and vice versa at the same rate. Therefore, in a 1.0 M solution of acetic acid (about the concentration of household vinegar), the actual concentration of the hydronium ion is something less than 1.0 M, because some of the acetic acid remains undissociated. Based on the previous calculation, we know that the pH of a 1.0 M solution would be about 0 if the acid had fully dissociated, so we know that the actual pH of the 1.0 M acetic acid will have some value higher than 0.

Substitutions and Modifications

• You may substitute foam cups or similar containers for the beakers.

• You may substitute a 100 mL graduated cylinder for the 100 mL volumetric flask and a 10 mL graduated cylinder for the 10 mL pipette, with some loss of accuracy. (Unless your pH meter is very accurate, instrumental error will be greater than volumetric error anyway.)

• You may substitute narrow-range pH testing paper for the pH meter, with some loss of accuracy. (Typical inexpensive pH meters are accurate to 0.1 or 0.2 pH, while typical narrow-range pH testing paper is accurate to 0.4 or 0.5 pH.)

• You may reduce the quantities of the acid and base solutions, depending on the size and type of probe used by your pH meter, and use smaller containers. If your meter has a very thin probe (or if you are using pH paper), you can reduce the quantities from 100 mL to 10 mL and use test tubes.

• If you don’t have a 1 M bench solution of hydrochloric acid available, you can make it up by diluting 8.33 mL of 12 M (37%) concentrated hydrochloric acid to 100 mL. If you have hardware-store muriatic acid that lists the contents as 31.45% HCl, you can make up a 1 M solution by diluting 9.71 mL of acid to 100 mL.

• If you don’t have a 1 M bench solution of sulfuric acid available, you can make it up by diluting 5.56 mL of 18 M (98%) concentrated sulfuric acid to 100 mL. If you have hardware-store battery acid that lists the contents as 35% sulfuric acid, you can make up a 1 M solution by diluting 15.57 mL of acid to 100 mL.

• If you don’t have a 1 M bench solution of acetic acid available, you can make it up by diluting 5.75 mL of 17.4 M (99.8%) concentrated (glacial) acetic acid to 100 mL. Alternatively, most distilled white vinegar contains 5% to 6% acetic acid, which is close enough to 1 M to use for this experiment.

• If you don’t have a 1 M bench solution of sodium hydroxide available, you can make it up by dissolving 4.00 g of sodium hydroxide in water and making up the solution to 100 mL.

• If you don’t have a 1 M bench solution of sodium carbonate available, you can make it up by dissolving 10.60 g of anhydrous sodium carbonate in water and making up the solution to 100 mL.

• I suggest boiling and cooling the distilled or deionized water before use to eliminate any dissolved carbon dioxide gas, which forms carbonic acid and lowers the pH below the 7.00 pH of pure water. Alternatively, you can use distilled or deionized water from a freshly opened container or one that has been kept tightly capped.

If we assume for a moment that at equilibrium only 10% of the acetic acid has dissociated, we can calculate the approximate pH of the solution. If only 10% of the acid has dissociated in a 1.0 M solution of acetic acid, the hydronium ion concentration is 0.1 M. Filling in the formula, we get:

pH = –log₁₀[0.1] = 1

But to estimate the pH of this solution accurately, we need a better value than our guesstimate of 10% dissociation. We get that value by looking up the equilibrium constant for the dissociation reaction shown above. In the context of pH, the equilibrium constant is referred to as the acidity constant, acid dissociation constant, or acid ionization constant, and is abbreviated K_a.

With the acid dissociation constant for acetic acid known to be 1.74·10^–5, and ignoring the tiny contribution to [H₃O⁺] made by the water, we can calculate the pH of a 1.0 M solution of acetic acid as follows:

K_a = 1.74·10^–5 = ([H₃O⁺]·[CH₃COO^–]/[CH₃COOH])

An unknown amount of the acetic acid has dissociated, which we’ll call x. That means that the concentration of the acetic acid, or [CH₃COOH] is (1.0 – x), while the concentrations of the dissociated ions, [H₃O⁺] and [CH₃COO^-], are both x. Filling in the formula gives us:

1.74 · 10^–5 = ([x] · [x]/[1.0 – x])

or

1.74 · 10^–5 = x²/(1.0 – x)

or

(1.74 · 10^–5) · (1.0 – x) = x²

or

1.74 · 10^–5– (1.74 · 10^–5 · x) = x²

K_a versus pK_a

The acidity constant may be specified directly as K_a or as the negative logarithm of K_a, which is abbreviated as pK_a. For example, at 25°C, the K_a of acetic acid is 1.74 · 10^–5 and the pK_a is 4.76. Either value can be used by adjusting your calculations accordingly.

Dr. Paul Jones Comments

I’d say that pK_a is used far more today than K_a. Also, you might mention that any compound with hydrogen can, plausibly, be an acid. However, if the pK_a of the compound is above 14, it essentially won’t dissociate at all in water. Also, when pH = pK_a, the acid is 50% dissociated; another good reason to use pK_a.

Solving for x gives us a value of about 4.17 · 10^–3 or about 0.00417. Our original estimate that 10% of the acetic acid would dissociate was wildly high. In fact, only about 0.417% of the acetic acid dissociates. Knowing that value tells us that the concentration of the hydronium ion in a 1 M acetic acid solution is 0.00417 M. Plugging that value into the formula allows us to calculate the approximate pH of the 1.0 M acetic acid solution:

pH = –log₁₀[0.00417] = 2.38

Although we’ve focused until now on acids rather than bases, remember that the concentrations of the hydronium ion and the hydroxide ion are related. We know that pure water at 25°C has a pH of 7.00 and that the concentrations of hydronium ions and hydroxide ions are equal. A pH of 7.00 tells us that the concentration of hydronium ions, [H₃O⁺], is 1.00 · 10^–7, which means that the concentration of hydroxide ions, [OH^–], must also be 1.00 · 10^–7. We know that hydronium ions and hydroxide ions react to form water:

H₃O⁺ + OH^– ⇔ H₂O

According to Le Chatelier’s Principle (see Chapter 13), in a system at equilibrium, increasing the concentration of one reactant forces the reaction to the right, producing more product. Increasing [H₃O⁺] reduces [OH^–] proportionately, and vice versa. Expressed as a formula, the equilibrium constant is:

K = [H₃O⁺] · [OH^–]

or

K = (1.00 · 10^–7) · (1.00 · 10^–7) = 1.00 · 10^–14

In other words, the product of the concentrations of the hydronium ions and the hydroxide ions always equals 1.00 · 10^–14.

Caution

All of the chemicals used in this laboratory can be hazardous, particularly in concentrated solutions. Check the MSDS for each of these chemicals before you proceed. Wear splash goggles, gloves, and protective clothing at all times.

If you increase the concentration of hydronium ions by a factor of 10 (or 10,000), the concentration of hydroxide ions decreases by a factor of 10 (or 10,000), and vice versa.

In this laboratory, we’ll determine the pH of solutions of two strong acids, a weak acid, a strong base, and a weak base at various concentrations.

Procedure

1. If you have not already done so, put on your splash goggles, gloves, and protective clothing.

2. Label six beakers #1 through #6.

3. Pour about 100 mL of 1 M hydrochloric acid into beaker #1.

4. Using the 10 mL pipette, transfer 10.00 mL of the 1 M hydrochloric acid to the 100 mL volumetric flask.

5. Fill the volumetric flask to the reference line with distilled water, mix thoroughly, and transfer the 0.1 M solution of hydrochloric acid to beaker #2.

6. Proceeding from beaker to beaker, repeat steps 4 and 5 until you have 0.01 M, 0.001 M, 0.0001 M, and 0.00001 M solutions of hydrochloric acid in beakers #3 through #6, respectively.

7. Read and follow the directions for your pH meter with respect to calibrating it, rinsing the electrode between measurements and so on. Use the pH meter to measure the pH of the solutions in beakers #1 through #6, and record those values on line A of Table 11-1.

8. Repeat steps 3 through 7 for the solutions of sulfuric acid, acetic acid, sodium hydroxide, and sodium carbonate.

9. Based on your observations, calculate the pK_a values for the acids and the pK_b values for the bases, and enter your calculated values in Table 11-1.

Disposal

Retain the 1.0 M acid and sodium hydroxide solutions for use in the following lab. Neutralize the other solutions, beginning with the most dilute samples, by pouring them into a bucket or similar container. The contents of the bucket can be flushed down the drain.

Figure 11-1. Using a pH meter to determine the pH of a solution

Table 11-1. Determine the effect of concentration on pH—observed and calculated data

Solute	Beaker #1 (1.0 M)	Beaker #2 (0.1 M)	Beaker #3 (0.01 M)	Beaker #4 (0.001 M)	Beaker #5 (0.0001 M)	Beaker #6 (0.00001 M)	pK
A. Hydrochloric acid	____.___ pH	____.___ pH	____.___ pH	____.___ pH	____.___ pH	____.___ pH	____.___
B. Sulfuric acid	____.___ pH	____.___ pH	____.___ pH	____.___ pH	____.___ pH	____.___ pH	____.___
C. Acetic acid	____.___ pH	____.___ pH	____.___ pH	____.___ pH	____.___ pH	____.___ pH	____.___
D. Sodium hydroxide	____.___ pH	____.___ pH	____.___ pH	____.___ pH	____.___ pH	____.___ pH	____.___
E. Sodium carbonate	____.___ pH	____.___ pH	____.___ pH	____.___ pH	____.___ pH	____.___ pH	____.___

Review Questions

Q:	Q1: Chart pH against concentration for all five compounds on one piece of graph paper. What do you conclude about the effect of concentration for a strong acid (hydrochloric acid or sulfuric acid) versus a weak acid (acetic acid) and for a strong base (sodium hydroxide) versus a weak base (sodium carbonate)? ____________________________________________________________________ ____________________________________________________________________ ____________________________________________________________________ ____________________________________________________________________ ____________________________________________________________________ ____________________________________________________________________ ____________________________________________________________________ ____________________________________________________________________
Q:	Q2: What pH values would you expect for 10 M solutions of hydrochloric acid and acetic acid? Why? ____________________________________________________________________ ____________________________________________________________________ ____________________________________________________________________ ____________________________________________________________________ ____________________________________________________________________ ____________________________________________________________________
Q:	Q3: If acids A and B have pKa values of –9.32 and 2.74, respectively, which is the stronger acid? Why? ____________________________________________________________________ ____________________________________________________________________ ____________________________________________________________________
Q:	Q4: The [H3O+] of a solution is known to be 0.000413 mol/L. What is the pH of the solution? ____________________________________________________________________ ____________________________________________________________________ ____________________________________________________________________
Q:	Q5: The [OH–] of a solution is known to be 0.000413 mol/L. What is the pH of the solution? ____________________________________________________________________ ____________________________________________________________________ ____________________________________________________________________
Q:	Q6: A 0.1 M solution of an acid is found to have a pH of 2.37. What is the pKa of that acid? ____________________________________________________________________ ____________________________________________________________________ ____________________________________________________________________
Q:	Q7: Knowing only the molarity and pH of an unknown acid solution, how might you identify the acid? ____________________________________________________________________ ____________________________________________________________________ ____________________________________________________________________

Laboratory 11.2: Determine the pH of Aqueous Salt Solutions

When an acid reacts with a base, it forms a salt and water. For example, reacting hydrochloric acid with sodium hydroxide produces the salt sodium chloride (common table salt) and water. Reacting nitric acid with potassium hydroxide produces potassium nitrate and water. Reacting acetic acid with aqueous ammonia produces ammonium acetate and water. And so on. Such reactions are referred to as neutralizing the acid with the base (or vice versa).

Unfortunately, the word “neutralize” is a common source of confusion among beginning chemists, many of whom assume that reacting equivalent amounts of an acid and base should yield a solution that contains only the “neutral” salt that is neither acidic nor basic, and therefore has a pH of 7.0. That’s not how it works.

The pH of a neutralized solution depends on the particular acid and base that are reacted. Reacting equivalents of a strong acid with a strong base in fact does produce a salt solution that has a pH at or near 7.0, as does reacting a weak acid with a weak base. But if the strengths of the acid and base are very different—as occurs, for example, if you react a strong acid with a weak base or vice versa—the pH of the neutralized solution will not be 7.0. The greater the difference in the strengths of the acid and base, the greater the difference in the pH of the neutralized solution from 7.0.

For example, if you neutralize hydrochloric acid (a very strong acid) with aqueous ammonia (a relatively weak base), the resulting solution of ammonium chloride will have a pH less than 7.0. Conversely, if you neutralize acetic acid (a relatively weak acid) with sodium hydroxide (a very strong base), the resulting neutralized solution of sodium acetate will have a pH greater than 7.0.

In this lab, we’ll determine the pH of aqueous solutions of various salts.

Substitutions and Modifications

• You may substitute a foam cup or similar container for the beaker.

Required Equipment and Supplies

	goggles, gloves, and protective clothing
	beaker, 150 mL
	pH meter
	ammonium acetate, 0.1 M (100 mL)
	ammonium chloride, 0.1 M (100 mL)
	sodium acetate, 0.1 M (100 mL)
	sodium chloride, 0.1 M (100 mL)

Substitutions and Modifications

• You may substitute narrow-range pH testing paper for the pH meter, with some loss of accuracy. (Typical inexpensive pH meters are accurate to 0.1 or 0.2 pH, while typical narrow-range pH testing paper is accurate to 0.4 or 0.5 pH.)

• You may reduce the quantities of the solutions, depending on the size and type of probe used by your pH meter, and use smaller containers. If your meter has a very thin probe (or if you are using pH paper), you can reduce the quantities from 100 mL to 10 mL and use test tubes.

• If you have bench solutions of any of the required chemicals, you can make up the required solutions by diluting the bench solutions appropriately.

• You can make 100 mL of 0.1 M ammonium acetate by mixing 10 mL of 1.0 M aqueous ammonia with 10 mL of 1.0 M acetic acid and 80 mL of water.

• You can make 100 mL of 0.1 M ammonium chloride by mixing 10 mL of 1.0 M aqueous ammonia with 10 mL of 1.0 M hydrochloric acid and 80 mL of water.

• You can make 100 mL of 0.1 M sodium acetate by mixing 10 mL of 1.0 M sodium hydroxide with 10 mL of 1.0 M acetic acid and 80 mL of water.

• You can make 100 mL of 0.1 M sodium chloride by mixing 10 mL of 1.0 M sodium hydroxide with 10 mL of 1.0 M hydrochloric acid and 80 mL of water.

Caution

Although none of the salts used in this lab are particularly hazardous, it’s good practice to wear splash goggles, gloves, and protective clothing at all times. If you make up the salt solutions from acid and base solutions as described in the Substitutions and Modifications section, use the normal precautions for working with acids and bases.

Disposal

All of the solutions used in this laboratory can be flushed down the drain with plenty of water.

Procedure

1. If you have not already done so, put on your splash goggles, gloves, and protective clothing.

2. Using what you know about strong and weak acids and bases, predict the approximate pH values for the solutions of the four chemicals and enter your predicted values in Table 11-2 by circling one of the pH numbers. If you are uncertain, circle a range of numbers.

3. Pour about 100 mL of 0.1 M ammonium acetate into the beaker.

4. Read and follow the directions for your pH meter with respect to calibrating it, rinsing the electrode between measurements and so on. Use the pH meter to measure the pH of the ammonium acetate solution, and record the observed value on the appropriate line of Table 11-2.

5. Repeat steps 3 and 4 for the solutions of ammonium chloride, sodium acetate, and sodium chloride.

Table 11-2. Determine the pH of aqueous salt solutions—observed and calculated data

Solute	Predicted pH	Observed pH
A. Ammonium acetate	0 1 2 3 4 5 6 7 8 9 10 11 12 13 14	____.___ pH
B. Ammonium chloride	0 1 2 3 4 5 6 7 8 9 10 11 12 13 14	____.___ pH
C. Sodium acetate	0 1 2 3 4 5 6 7 8 9 10 11 12 13 14	____.___ pH
D. Sodium chloride	0 1 2 3 4 5 6 7 8 9 10 11 12 13 14	____.___ pH

Review Questions

Q:

Q1: What general conclusions can you draw from the pH values that you observed for the four solutions? ____________________________________________________________________ ____________________________________________________________________ ____________________________________________________________________ ____________________________________________________________________ ____________________________________________________________________

Q:

Q2: If you mixed equal amounts of a 0.1 M ammonium chloride solution and a 0.1 M sodium acetate solution, would you expect the pH of the resulting solution to be strongly acidic, weakly acidic, about neutral, weakly basic, or strongly basic? Why? ____________________________________________________________________ ____________________________________________________________________

Laboratory 11.3: Observe the Characteristics of a Buffer Solution

A buffer solution is usually a solution of a weak acid and its conjugate base or, less commonly, a solution of a weak base and its conjugate acid. A buffer solution resists changes in the concentrations of the hydronium ion and hydroxide ion (and therefore pH) when the solution is diluted or when small amounts of an acid or base are added to it. The resistance of a buffer solution to pH change is based upon Le Chatelier’s Principle and the common ion effect.

One common example of a buffer solution is a solution of acetic acid (the weak acid) and sodium acetate (its conjugate base). In solution, acetic acid reaches an equilibrium illustrated by the following equation.

CH₃COOH(aq) + H₂O(l) ⇔ CH₃COO^– + H₃O⁺

As we learned earlier in this chapter, acetic acid does not dissociate completely in solution. For example, in a 1 M solution of acetic acid, only about 0.4% of the acetic acid molecules dissociate into hydronium and acetate ions, leaving most of the acetic acid in molecular form. Dissolving sodium acetate in the acetic acid solution forces the equilibrium to the left, reducing the hydronium ion concentration and therefore increasing the pH of the solution.

Consider what happens if you add a small amount of a strong acid or strong base to this buffer solution. Ordinarily, you would expect adding a small amount of a strong acid or base to cause a large change in the pH of a solution. But if you add hydrochloric acid (a strong acid) to the acetate/acetic acid buffer solution, the hydronium ions produced by the nearly complete dissociation of the hydrochloric acid react with the acetate ions to form molecular (non-dissociated) acetic acid. According to Le Chatelier’s Principle, the equilibrium is forced to the left, reducing the concentration of hydronium and acetate ions, and increasing the concentration of the molecular acetic acid in the solution.

The acid dissociation constant for this buffer is:

K_a = [H₃O⁺] · [CH₃COO^-]/[CH₃COOH]

If the buffer solution contains equal amounts of acetic acid and sodium acetate, we can assume that the sodium acetate is fully dissociated and that dissociation of the acetic acid is negligible (because the high concentration of acetate ions from the sodium acetate drives the dissociation equilibrium for acetic acid far to the left). We can therefore assume that the concentrations of CH₃COO^– and CH₃COOH are essentially identical, and simplify the equilibrium equation to:

Required Equipment and Supplies

	goggles, gloves, and protective clothing
	beaker, 150 mL (2)
	beaker, 250 mL
	graduated cylinder, 100 mL
	graduated cylinder, 10 mL
	pipette, 1.00 mL
	stirring rod
	pH meter
	acetic acid, 1.0 M (100 mL)
	sodium acetate, 1.0 M (100 mL)
	hydrochloric acid, 6.0 M (20 mL)
	sodium hydroxide, 6.0 M (20 mL)
	distilled or deionized water (boil and cool before use)

K_a = [H₃O⁺]

which means that the pH of this buffer solution is equal to the pK_a.

If we add hydrochloric acid to the buffer solution, the HCl ionizes completely in solution, yielding hydronium ions and chloride ions. According to Le Chatelier’s Principle, the increase in hydronium ions forces the acetic acid equilibrium to the left, decreasing the concentration of hydronium ions and increasing the concentration of molecular acetic acid. This equilibrium shift changes the effective number of moles of acetic acid and acetate ions, which can be calculated as follows:

final CH₃COO^– moles = initial CH₃COOH moles – initial HCl moles

final CH₃COOH moles = initial CH₃COO^– moles + initial HCl moles

Substitutions and Modifications

• You may substitute foam cups or similar containers for the beakers.

• You may substitute a calibrated beral pipette for the 1.00 mL transfer pipette. (To calibrate the beral pipette, count the number of drops required to reach 10.00 mL in a graduated cylinder, and then calculate the number of drops per mL.)

• You can make up 1.0 M acetic acid by diluting 5.7 mL of concentrated (glacial) acetic acid to 100 mL. Alternatively, you may use distilled white vinegar, which is close to 1 M straight out of the bottle.

• You can make 100 mL of 1.0 M sodium acetate by dissolving 8.20 g of anhydrous sodium acetate or 13.61 g of sodium acetate trihydrate in some distilled water and then making up the solution to 100 mL.

• You can make 20 mL of 6.0 M hydrochloric acid by mixing 10.00 mL of concentrated (37%, 12 M) hydrochloric acid with 10.00 mL of water. If you have hardware-store muriatic acid (31.45%, 10.3 M), mix 11.65 mL of the acid with 8.35 mL of water.

• You can make 20 mL of 6.0 M sodium hydroxide by dissolving 4.80 g of sodium hydroxide, stirring constantly, in 90 mL of water and making up the solution to 100 mL. (Caution: this reaction is extremely exothermic.)

Conversely, if we add sodium hydroxide to the buffer solution, the NaOH ionizes completely in solution, yielding hydroxide ions and sodium ions. According to Le Chatelier’s Principle, the increase in hydroxide ions forces the acetic acid equilibrium to the right, decreasing the concentration of hydroxide ions and increasing the concentration of acetate ions. This equilibrium shift changes the effective number of moles of acetic acid and acetate ions, which can be calculated as follows:

final CH₃COO^– moles = initial CH₃COOH moles + initial NaOH moles

final CH₃COOH moles = initial CH₃COO^– moles – initial NaOH moles

In either case, after you calculate the number of moles of acetic acid and acetate ions, you can use the final volume of the solution to determine the concentration of the acetic acid and acetate ions and plug those values into the Henderson-Hasselbalch equation to determine the new pH.

pH = pK_a + log₁₀([CH₃COO^–]/[CH₃COOH])

In this lab, we’ll make up a buffer solution of acetic acid and sodium acetate and examine the effects of adding hydrochloric acid and sodium hydroxide to this buffer solution.

Caution

Hydrochloric acid and sodium hydroxide are corrosive. Wear splash goggles, gloves, and protective clothing at all times.

Procedure

1. If you have not already done so, put on your splash goggles, gloves, and protective clothing.

2. Make up the buffer solution by mixing 100 mL of 1.0 M acetic acid and 100 mL of 1.0 M sodium acetate in the 250 mL beaker.

3. Transfer 100 mL of the buffer solution to one of the 150 mL beakers, and 100 mL of distilled water to the second 150 mL beaker.

4. Read and follow the directions for your pH meter with respect to calibrating it, rinsing the electrode between measurements and so on.

5. Use the pH meter to measure the pH of the buffer solution, and record the observed value on line A in the second and fourth columns of Table 11-3.

6. Use the pH meter to measure the pH of the distilled water, and record the observed value on line A in the third and fifth columns of Table 11-3.

7. Use the 1.00 mL pipette to transfer 1.00 mL of 6.0 M hydrochloric acid to the beaker that contains the buffer solution and another 1.00 mL of hydrochloric acid to the beaker that contains the distilled water. Stir or swirl the beakers to mix the solutions thoroughly. (If you use only one stirring rod, rinse it thoroughly before using it in the other beaker.)

8. Use the pH meter to determine the pH value for the buffer solution, and record that value on line B in the second column of Table 11-3.

9. Use the pH meter to determine the pH value for the water solution, and record that value on line B in the third column of Table 11-3.

10. Repeat steps 7 through 9, adding 1.00 mL of hydrochloric acid each time until you have added a total of 10.00 mL of hydrochloric acid to the buffer solution and water solution.

11. Rinse the beakers and pipette thoroughly.

12. Transfer the remaining 100 mL of buffer solution to one of the 150 mL beakers, and 100 mL of distilled water to the second 150 mL beaker.

13. Repeat steps 7 through 11 using the 6.0 M sodium hydroxide solution.

Table 11-3. Observe the characteristics of a buffer solution—observed data

Acid/base added	Buffer + HCl	Water + HCl	Buffer + NaOH	Water + NaOH
A. 0.00 mL	____.___ pH	____.___ pH	____.___ pH	____.___ pH
B. 1.00 mL	____.___ pH	____.___ pH	____.___ pH	____.___ pH
C. 2.00 mL	____.___ pH	____.___ pH	____.___ pH	____.___ pH
D. 3.00 mL	____.___ pH	____.___ pH	____.___ pH	____.___ pH
E. 4.00 mL	____.___ pH	____.___ pH	____.___ pH	____.___ pH
F. 5.00 mL	____.___ pH	____.___ pH	____.___ pH	____.___ pH
G. 6.00 mL	____.___ pH	____.___ pH	____.___ pH	____.___ pH
H. 7.00 mL	____.___ pH	____.___ pH	____.___ pH	____.___ pH
I. 8.00 mL	____.___ pH	____.___ pH	____.___ pH	____.___ pH
J. 9.00 mL	____.___ pH	____.___ pH	____.___ pH	____.___ pH
K. 10.00 mL	____.___ pH	____.___ pH	____.___ pH	____.___ pH

Disposal

All of the solutions used in this laboratory can be flushed down the drain with plenty of water.

Review Questions

Q:	Q1: How did the pH change compare in the buffer solution versus water? ____________________________________________________________________ ____________________________________________________________________ ____________________________________________________________________
Q:	Q2: Calculate the expected pH of the buffer solution. How does the calculated value correspond to the observed value? ____________________________________________________________________ ____________________________________________________________________ ____________________________________________________________________ ____________________________________________________________________ ____________________________________________________________________
Q:	Q3: Graph the amounts of added acid and base against the pH of the buffer solution. At what point does the buffer begin to lose effectiveness? Why? ____________________________________________________________________ ____________________________________________________________________ ____________________________________________________________________ ____________________________________________________________________
Q:	Q4: You have on hand 0.5 M solutions of acetic acid and sodium acetate. You want to make up 100 mL of a pH 5.0 buffer solution to calibrate your pH meter. Calculate the amounts of acetic acid solution and sodium acetate solution required to make up this buffer solution. ____________________________________________________________________ ____________________________________________________________________ ____________________________________________________________________ ____________________________________________________________________ ____________________________________________________________________ ____________________________________________________________________ ____________________________________________________________________ ____________________________________________________________________ ____________________________________________________________________ ____________________________________________________________________ ____________________________________________________________________ ____________________________________________________________________ ____________________________________________________________________ ____________________________________________________________________ ____________________________________________________________________ ____________________________________________________________________ ____________________________________________________________________ ____________________________________________________________________ ____________________________________________________________________ ____________________________________________________________________

Laboratory 11.4: Standardize a Hydrochloric Acid Solution by Titration

The process used to determine the concentration of a solution with very high accuracy is called standardizing a solution. To standardize an unknown solution, you react that solution with another solution whose concentration is already known very accurately.

For example, to standardize the hydrochloric acid solution that we made up in a preceding lab, we might very carefully measure a known quantity of that solution (called an aliquot) and neutralize that aliquot with a solution of sodium carbonate whose concentration is already known very accurately. Adding a few drops of an indicator, such as phenolphthalein or methyl orange, to the solution provides a visual indication (a color change) when an equivalence point is reached, when just enough of the standard solution has been added to the unknown solution to neutralize it exactly. By determining how much of the sodium carbonate solution is required to neutralize the hydrochloric acid, we can calculate a very accurate value for the concentration of the hydrochloric acid. This procedure is called titration.

Titration uses an apparatus called a burette (or buret), which is a very accurately graduated glass cylinder with a stopcock or pinchcock that allows the solution it contains to be delivered in anything from a rapid stream to drop-by-drop. Because titration is a volumetric procedure, the accuracy of the results depends on the concentration of the reagent used to do the titration. For example, if 5.00 mL of 1.0000 M sodium carbonate is required to neutralize a specific amount of the unknown acid, that same amount of acid would be neutralized by 50.00 mL of 0.10000 M sodium carbonate. If our titration apparatus is accurate to 0.1 mL, using the more dilute sodium carbonate reduces our level of error by a factor of 10, because 0.1 mL of 0.10000 M sodium carbonate contains only one tenth as much sodium carbonate as 0.1 mL of 1.0000 M sodium carbonate. For that reason, the most accurate titrations are those performed with a relatively large amount of a relatively dilute standard solution.

The obvious question is how to obtain an accurate reference solution. For work that requires extreme accuracy, the best answer is often to buy premade standard solutions, which are made to extremely high accuracy (and the more accurate, the more expensive). None of the work done in a home lab requires that level of accuracy, so the easiest and least expensive method is to make up your own standard solutions. (In fact, to illustrate the principles of standardization and titration, you don’t even need a truly accurate reference solution; you can simply pretend that a 1 M solution is actually 1.0000 M and proceed on that basis. Your results won’t be accurate, but the principles and calculations are the same.)

Required Equipment and Supplies

	goggles, gloves, and protective clothing
	balance and weighing papers
	beaker, 150 mL (2)
	volumetric flask, 100 mL
	funnel
	pipette, 10 mL
	burette, 50 mL
	ring stand
	burette clamp
	storage bottle, 100 mL (labeled “sodium carbonate, 1.500 M”)
	hydrochloric acid, 1 M bench solution (~10 mL)
	sodium carbonate, anhydrous (15.90 g)
	phenolphthalein indicator solution (a few drops)
	distilled or deionized water

When you make up a standard solution, take advantage of the difference between absolute errors and relative errors. For example, if your balance is accurate to 0.01 g, that means that any sample you weigh may have an absolute error of as much as 0.01 g. But that absolute error remains the same regardless of the mass of the sample. If you weigh a 1.00 g sample, the absolute error is 1% (0.01 g/1.00 g · 100). If you weigh a 100.00 g sample, the absolute error is 0.01% (0.01 g/100.00 g · 100). Similarly, volumetric errors are absolute, regardless of the volume you measure. For example, a 10.00 mL pipette may have an absolute error of 0.05 mL. If you use that pipette to measure 10.00 mL, the relative error is (0.05 mL/10.00 mL · 100) or 0.5%. If you measure only 1.00 mL, the relative error is ten times as large, (0.05 mL/1.00 mL · 100) or 5.0%.

Substitutions and Modifications

• You may substitute any suitable containers of similar size for the 150 mL beakers.

• You may substitute a 100 mL graduated cylinder for the 100 mL volumetric flask and/or a 10 mL graduated cylinder for the 10 mL pipette, with some loss in accuracy.

• If you do not have a burette, ring stand, and burette clamp, you may substitute a 100 mL graduated cylinder, with some loss in accuracy. To do so, fill the graduated cylinder with titrant and record the starting level. Transfer titrant to the reaction beaker by pouring carefully until the endpoint is near (evidenced by a nonpersistent color change in the indicator that disappears when you swirl the beaker). Then use a dropper or beral pipette to transfer titrant dropwise until the end point is reached. Transfer any remaining titrant from the dropper or beral pipette back into the graduated cylinder, record the ending level, and subtract to determine how much titrant was required to reach the endpoint.

• If you do not have anhydrous sodium carbonate, you may substitute equivalent weights of the monohydrate, heptahydrate, or decahydrate.

• You may substitute cresol red, thymol blue, or a similar indicator for the phenolphthalein indicator.

One way to minimize the scale of errors is to use a relatively large amount of solute to make a starting solution and then use serial dilution to make a dilute standard solution to use as the titrant. Serial dilution simply means repeatedly diluting small aliquots of known volume. For example, we might start with a 1.5 M solution of a chemical. We use a pipette to take a 10.00 mL aliquot of that solution and dilute it to 100.0 mL in a volumetric flask to make a 0.15 M solution. We then take a 10.00 mL aliquot of the 0.15 M solution and dilute it again to 100.0 mL, yielding a 0.015 M solution.

For example, a reference book tells us that the formula weight of anhydrous sodium carbonate is 105.99 g/mol and its solubility at 20°C is about 200 g/L. A saturated solution of sodium carbonate is therefore about 1.9 M, because (200 g/L)/(105.99 g/mol) = 1.88+ M. In this lab, we’ll make up a 1.5 M solution of sodium carbonate and then use serial dilution to produce a 0.15 M solution to use as our titrant. We’ll titrate our unknown HCl solution once using phenolphthalein as the indicator, and a second time using methyl orange as the indicator. Why two passes with two separate indicators?

Caution

Hydrochloric acid is corrosive. Wear splash goggles, gloves, and protective clothing at all times. (Phenolphthalein, formerly widely used as a laxative, was withdrawn from the market because of concerns about possible links with cancer, but the small amount used in an indicator solution is not ingested and is no cause for concern.)

Figure 11-2. Methyl orange (left) and phenolphthalein at their equivalence points

As it happens, the neutralization of sodium carbonate by hydrochloric acid is a two-step process. In the first step, one mole of sodium carbonate reacts with one mole of hydrochloric acid to produce one mole of sodium hydrogen carbonate (sodium bicarbonate) and one mole of sodium chloride:

Na₂CO₃(aq) + HCl(aq) → NaHCO₃(aq) + NaCl(aq)

In the second step, a second mole of hydrochloric acid reacts with the sodium hydrogen carbonate formed in the first step:

NaHCO₃(aq) + HCl(aq) → NaCl(aq) + CO₂(g) + H₂O(l)

Each of these reactions has an equivalence point. The first occurs when the first mole of HCl has reacted with the sodium carbonate to form one mole each of sodium bicarbonate and sodium chloride. The pH at the equivalence point of this reaction happens to correspond very closely to the pH range where phenolphthalein changes color, but is well above the pH range of methyl orange. The second equivalence point occurs when the second mole of HCl has reacted with the sodium bicarbonate to form one mole each of sodium chloride, carbon dioxide, and water. The pH at the equivalence point of this reaction happens to correspond very closely to the pH range where methyl orange changes color, but is well below the pH range of phenolphthalein.

Because these reactions occur with exactly a 2:1 proportion of hydrochloric acid, the amount of titrant needed to reach the indicated equivalence point with methyl orange is exactly twice as much as the amount of titrant needed to reach the indicated equivalence point with phenolphthalein. In other words, if you use methyl orange, you miss the first equivalence point completely. If you use phenolphthalein, you are misled into believing that the first equivalence point is the final equivalence point. For this reason, the neutralization of sodium carbonate with hydrochloric acid is often used as a (literal) textbook example of the importance of choosing the proper indicator.

Note that for titrations with multiple equivalence points, it makes a difference which solution is used for the titrant. For example, if we titrate a solution of sodium carbonate by adding hydrochloric acid, we could observe the first (higher pH) equivalence point by using phenolphthalein as an indicator. When sufficient HCl has been added to convert the sodium carbonate to sodium bicarbonate, the phenolphthalein changes from pink to colorless. We could then add some methyl orange indicator to observe the color change from yellow to red at the second (lower pH) equivalence point, when the sodium bicarbonate is converted to sodium chloride. Conversely, if we titrate a solution of hydrochloric acid with sodium carbonate as the titrant, the acid is always in excess until sufficient sodium carbonate has been added to completely neutralize the acid. In this case, we use phenolphthalein as the indicator, because only one equivalence point exists for this reaction, and it is at the higher pH when sodium carbonate is in slight excess.

In this lab, we’ll standardize an approximately 1 M solution of hydrochloric acid by titrating a known volume of the acid with a sodium carbonate solution of known molarity.

Procedure

This laboratory has three parts. In Part I, you’ll make up a stock reference solution of 1.500 M sodium carbonate. In Part II, you’ll use serial dilution to make up a working reference solution of 0.1500 M sodium carbonate solution to use as a titrant. In Part III, you’ll use that tritrant to standardize an approximately 1 M bench solution of hydrochloric acid by titration.

Part I: Make Up a Stock Reference Solution of ~1.500 M Sodium Carbonate

1. If you have not already done so, put on your splash goggles, gloves, and protective clothing.

2. Place a weighing paper on the balance and tare the balance to read 0.00 g.

3. Weigh out about 15.90 g of anhydrous sodium carbonate powder, and record the mass to 0.01 g on line A of Table 11-4.

4. Using the funnel, transfer the sodium carbonate to the 100 mL volumetric flask.

5. Rinse the funnel with a few mL of distilled or deionized water to transfer any sodium carbonate that remains in the funnel into the volumetric flask.

6. Fill the volumetric flask with distilled or deionized water to a few cm below the reference line.

7. Stopper the flask and invert it repeatedly until all of the sodium carbonate dissolves.

8. Finish filling the volumetric flask with water until the bottom of the meniscus is just touching the reference line.

9. Stopper the flask and invert it several times to mix the solution thoroughly.

10. Transfer the sodium carbonate solution to the 100 mL storage bottle and cap the bottle.

11. Use the actual mass of sodium carbonate from step 3 to calculate the actual molarity of the sodium carbonate solution to the appropriate number of significant figures, and record that molarity on line B of Table 11-4.

12. Label the bottle with its contents, molarity, and the date.

Part II: Use Serial Dilution to Make Up a Working Reference Solution of ~0.1500 M Sodium Carbonate

1. If you have not already done so, put on your splash goggles, gloves, and protective clothing.

2. Rinse the 100 mL volumetric flask, first with tap water and then with distilled or deionized water.

3. Use the 10 mL pipette to transfer about 10 mL of the ~1.500 M sodium carbonate solution you made up in Part I to the volumetric flask. Record the volume to 0.01 mL on line C of Table 14-4.

4. Fill the volumetric flask with water until the bottom of the meniscus just touches the reference line.

5. Stopper the flask and invert it several times to mix the solution thoroughly.

6. Use the actual volume of sodium carbonate solution from step 3 to calculate the actual molarity of the working sodium carbonate solution to the appropriate number of significant figures, and record that molarity on line D of Table 11-4.

Part III: Standardize a Bench Solution of ~1 M Hydrochloric Acid

1. If you have not already done so, put on your splash goggles, gloves, and protective clothing.

2. Use the 10 mL pipette to transfer about 10 mL of the ~1.0 M hydrochloric acid bench solution to a 150 mL beaker. Record the volume to 0.01 mL on line E of Table 11-4.

3. Add about 25 mL of water to the beaker and swirl the beaker to mix the solution.

4. Add a drop or two of phenolphthalein indicator to the beaker and swirl to mix the solution.

5. Calculate the approximate amount of titrant you expect to need to neutralize the 10 mL of ~1.0 M hydrochloric acid solution, and enter that value on line F of Table 11-4.

6. Rinse the burette thoroughly, first with water and then with a few mL of the titrant solution.

7. Install the burette in the burette clamp and fill it to or above the top (0.00 mL) line with titrant solution.

8. Run a few mL of titrant through the burette, making sure that no air bubbles remain and that the level of titrant is at or below the top index line at 0.00 mL. (It’s not important that the initial reading be exactly 0.00 mL, but it is important to know the initial reading as closely as possible.) Record the initial reading as accurately as possible on line G of Table 11-4.

9. While swirling the beaker, use the burette to dispense into the beaker a few mL less of the titrant than you estimated in step 5 will be required to neutralize the hydrochloric acid.

10. Begin adding the titrant dropwise but quickly and with continuous swirling. As you approach the equivalence point, you’ll see the solution turn pink where the titrant is being added, but the pink color will disappear with swirling. This indicates that you are rapidly approaching the equivalence point. Using a sheet of white paper or other white background under or behind the beaker makes it easier to detect the first hint of a color change.

11. Continue adding titrant slowly dropwise, with swirling, until the solution in the beaker shows an overall very slightly pink color that does not disappear when the solution is swirled. A permanent slight pink coloration indicates that you’ve reached the equivalence point. All of the hydrochloric acid is neutralized, and there is a tiny excess of sodium carbonate. A dark pink color (or any color other than pale pink) indicates that the equivalence point has been met and exceeded, which means you need to redo the titration. If you use a different indicator, such as universal indicator, the indicative color change may be slightly different.

12. Record the final burette reading on line H of Table 11-4. Subtract line G from line H and record the difference on line I as the volume of titrant required to neutralize the aliquot of hydrochloric acid.

13. Calculate the number of moles of sodium carbonate contained in the volume of titrant you used, and record that value on line J of Table 11-4.

14. Calculate the number of moles of hydrochloric acid present in the aliquot (remember that two moles of hydrochloric acid react with one mole of sodium carbonate) and enter that value on line K of Table 11-4.

15. Calculate the molarity of the HCl bench solution, and enter that value on line L of Table 11-4.

Disposal

Retain the stock sodium carbonate solution and the standardized hydrochloric acid solution for later use. The other solutions can be flushed down the drain with plenty of water.

Optional Activities

If you have time and the required materials, consider performing these optional activities:

• Repeat the titration once or twice and compare these results with your initial results. If the results are not in close agreement, run additional titrations until you have an accurate value for the molarity of the hydrochloric acid bench solution.

• Use your standard sodium carbonate solution and your newly standardized hydrochloric acid solution to determine accurate concentrations for various household acids and bases. For example, you might use the sodium carbonate solution (after serial dilution) to titrate aliquots of distilled vinegar (acetic acid) and lemon juice (citric acid), and the standardized HCl solution to titrate aliquots of household ammonia and liquid drain cleaner (sodium hydroxide).

Table 11-4. Standardize a solution by titration—observed and calculated data

Item	Data
A. Mass of sodium carbonate	_______.____ g
B. Titrant stock solution molarity	____.______ mol/L
C. Volume of titrant stock solution	_____.____ mL
D. Titrant working solution molarity	____.______ mol/L
E. Volume of ~1.0 M HCl bench solution	_____.____ mL
F. Estimated volume of titrant required	_____.____ mL
G. Initial burette reading	_____.____ mL
H. Final burette reading	_____.____ mL
I. Actual volume of titrant used (H – G)	_____.____ mL
J. Moles of sodium carbonate required	___._______ moles
K. Moles of HCl present in aliquot	___._______ moles
L. Molarity of HCl bench solution	____.______ mol/L

Review Questions

Q:	Q1: Best practice when titrating an unknown is to do multiple titrations. Why? ____________________________________________________________________ ____________________________________________________________________ ____________________________________________________________________ ____________________________________________________________________ ____________________________________________________________________ ____________________________________________________________________ ____________________________________________________________________ ____________________________________________________________________ ____________________________________________________________________ ____________________________________________________________________
Q:	Q2: List at least five possible sources of error in the procedure you followed in this laboratory. ____________________________________________________________________ ____________________________________________________________________ ____________________________________________________________________ ____________________________________________________________________ ____________________________________________________________________ ____________________________________________________________________ ____________________________________________________________________ ____________________________________________________________________ ____________________________________________________________________ ____________________________________________________________________
Q:	Q3: You are titrating an unknown base solution and have standardized solutions of hydrochloric acid and acetic acid available. Is the acid you choose for the titration likely to affect the accuracy and/or precision of your results? If so, why? ____________________________________________________________________ ____________________________________________________________________ ____________________________________________________________________ ____________________________________________________________________ ____________________________________________________________________ ____________________________________________________________________ ____________________________________________________________________
Q:	Q4: Other than using an indicator solution, how might you determine the equivalence point(s) for a titration? ____________________________________________________________________ ____________________________________________________________________ ____________________________________________________________________ ____________________________________________________________________ ____________________________________________________________________ ____________________________________________________________________ ____________________________________________________________________