The most important characteristic of a solution is its concentration. Concentration is sometimes referred to in general terms. A dilute solution is one that contains a relatively small amount of solute per volume of solvent. A concentrated solution is one that contains a relatively large amount of solute per volume of solvent. A saturated solution is one that contains the maximum amount of solute that the volume of solvent is capable of dissolving at a specified temperature. (A supersaturated solution contains more solute than the solvent is capable of dissolving; see Laboratory 6.3: Recrystallization: Purify Copper Sulfate.)
For many applications, it’s important to have a specific value for concentration. Chemists specify concentration in numerous ways, using the mass, volume, and/or number of moles of solute and solvent. Some ways, such as parts per million (ppm) are used primarily in specialized applications, such as trace metal analysis or environmental science. Others are obsolescent or seldom used.
Here are the primary methods chemists use to specify concentrations:
Molarity
Molarity, abbreviated mol/L or M, specifies the number of moles of solute per liter of solution (not per liter of solvent). Molarity is the most commonly used way to specify concentration. Technically, the word “molarity” and the unit symbol M are obsolete. The official replacements are amount-of-substance concentration and mol/dm3, neither of which anyone actually uses. The advantage of using molarity to specify concentration is that it makes it very easy to work with mole relationships. The disadvantages are that it is much more difficult to measure volumes accurately than it is to measure masses accurately, which makes it difficult to prepare solutions of exact molarities, and that the molarity of a solution changes with temperature because the mass of solute remains the same while the volume of the solution changes with temperature.
Expressing concentration as ppm or wt/wt percentage is common in industry. As an example, biocides and preservatives are added to paint, adhesives, wash water, cosmetics, oil, metal working fluids, and sizing baths in ppm. Additionally, the components that form a synthetic latex or plastics are measured in ppm. The pharmaceutical industry is, of course, different.
Molality
Molality, abbreviated mol/kg or m, specifies the number of moles of solute per kilogram of solvent (not per kilogram of solution). The primary advantage of using molality to specify concentration is that, unlike its volume, the mass of the solvent does not change with changes of temperature or pressure, so molality remains constant under changing environment conditions. Molality is used primarily in tasks that involve the colligative properties of solutions, which are covered in the following chapter. For the dilute aqueous solutions typically used in laboratories, molarity and molality are nearly the same, because nearly all of the mass of these solutions is accounted for by the solvent (water) and the mass of water at room temperature is almost exactly one kilogram per liter.
Normality
Normality, abbreviated N, specifies the number of gram equivalents of solute per liter of solution (not per liter of solvent). The concept of gram equivalents takes into account the dissolution of ionic salts in solution. For example, a 1.0 M solution of calcium chloride (CaCl2) can be made by dissolving one mole (111.0 g) of anhydrous calcium chloride in water and bringing the volume up to 1.0 liter. The calcium chloride dissociates in solution into one mole of calcium ions and two moles of chloride ions. That solution is 1.0 N with respect to calcium ions, but 2.0 N with respect to chloride ions. Accordingly, it is nonsensical to label such a solution of calcium chloride as 1.0 N or 2.0 N, unless you specify the ion species to which the normality refers.
Acids and bases are often labeled with their normalities, the assumption being that normality for an acid always refers to the hydronium (H3O+) ion concentration and the normality for a base to the hydroxide (OH-) ion concentration. For monoprotic acids such as hydrochloric acid (HCl) and nitric acid (HNO3), normality and molarity are the same, because these acids dissociate in solution to yield only one mole of hydronium ions per mole of acid. For diprotic acids such as sulfuric acid (H2SO4), the normality is twice the molarity, because one mole of these acids dissociates in solution to form two moles of hydronium ions. For triprotic acids such as phosphoric acid (H3PO4), normality is three times molarity, because in solution these acids yield three hydronium ions per acid molecule. Similarly, dibasic molecules such as barium hydroxide, Ba(OH)2, dissociate in solution to yield two moles of hydroxide per mole of compound, so for solutions of these compounds the normality is twice the molarity.
Mass percentage
Mass percentage, also called weight-weight percentage or w/w, specifies the mass of the solute as a percentage of the total mass of the solution. For example, dissolving 20.0 g of sucrose in 80.0 g of water yields 100 g of a 20% w/w sucrose solution. Mass percentage is often used to specify concentration for concentrated acids. For example, a bottle of reagent-grade hydrochloric acid may specify the contents as 37% HCl, which means that 100 g of that solution contains 37 g of dissolved HCl. (Such solutions are often also labeled with the density of the solution, which allows them to be measured volumetrically rather than requiring weighing to transfer an accurate amount of solute.)
Mass-volume percentage
Mass-volume percentage, also called weight-volume percentage or w/v, specifies the mass of the solute as a percentage of the total volume of the solution. For example, dissolving 5.0 g of iodine in ethanol and making up the final volume to 100.0 mL yields 100 mL of a 5% w/v iodine solution. Mass-volume percentage is often used to specify concentration for indicators such as phenolphthalein and other reagents that are typically used dropwise.
Volume-volume percentage
Volume-volume percentage, abbreviated v/v, specifies the volume of the solute as a percentage of the total volume of the solution, and is often used when mixing two liquids. For example, a 40% v/v solution of ethanol in water can be made by measuring 40 mL of 100% ethanol and adding water until the final volume is 100 mL. I phrased that last sentence very carefully, because volumes are not necessarily additive. For example, adding 60.0 mL of water to 40.0 mL of ethanol yields something less than 100.0 mL of solution.
Keep significant digits in mind when you make up and label solutions. The necessary accuracy of concentration depends on the purpose of the solution.
Bench solutions
Bench solutions specify concentration to only one, two, or three significant figures (e.g., 1 M, 1.0 M, or 1.02 M). For example, you might make up 500 mL of of a 1 M bench solution of dilute hydrochloric acid using a graduated cylinder to measure the concentrated acid and a large beaker to make up the solution to about 500 mL. The advantage of bench solutions is that they can be prepared quickly and can be used when the exact concentration doesn’t matter.
Standard solutions are used in quantitative analyses and are made up to whatever level of accuracy is required. Typically, standard solutions are accurate to four or five significant figures (e.g., 1.002 M or 1.0008 M) and are standardized against a reference standard (a solution of which the concentration is known very accurately).
For example, to make up 1 L of a nominal 1.0000 M solution of sodium carbonate requires one mole (105.99 g) of sodium carbonate. You begin by weighing an amount of sodium carbonate as close to 105.99 g as possible, but the exact amount is less important than recording the actual mass to within 0.01 g. You might, for example, end up with 106.48 g of sodium carbonate in the balance pan (or 104.37 g) but the important thing is that you know the mass to within 0.01 g. After recording the actual mass, you transfer the sodium carbonate to a 1 L volumetric flask that contains perhaps 800 mL of distilled water and swirl or shake the flask to dissolve the solute. You then rinse any small amount of sodium carbonate that remains in the weighing boat into the flask, fill the flask to within a centimeter of the reference line, and mix the contents again by swirling or shaking the flask. Finally, you fill the flask exactly to the reference line using a dropper.
At this point, you have 1 L of sodium carbonate solution with the concentration known to a high degree of accuracy. Depending on how much sodium carbonate you actually used, that concentration may be (for example) 1.0046 M, and the storage container can be labeled accordingly. To verify the exact concentration, you can titrate the solution against a reference standard.
Stock solutions
Stock solutions are concentrated solutions of stable chemicals, often saturated or nearly saturated, that are normally diluted before use. Stock solutions may be purchased or made up. The most common examples of purchased stock solutions are concentrated acids (such as acetic, hydrochloric, nitric, and sulfuric acids), some bases (such as aqueous ammonia), and other common liquid laboratory chemicals, such as concentrated hydrogen peroxide and formalin.
Many chemists keep on hand a variety of made-up stock solutions of solid chemicals that they use frequently. Stock solutions minimize required storage space and make it easy and convenient to produce more dilute bench solutions simply by diluting the stock solution in some proportion. For example, a 12 M stock solution of hydrochloric acid can easily be diluted with an equal part of water to provide 6 M HCl, with three parts of water to provide 3 M HCl, or with 11 parts of water to provide 1 M HCl. Stock solutions can also be standardized and diluted more accurately to provide more dilute standard solutions.
When you’re making up solutions, it’s important to consider the solubility of the solute, which specifies the maximum amount of solute that dissolves in the solvent at a particular temperature. For example, you might decide to make up 100 mL of a 1.00 M potassium permanganate stock solution. You look up the formula weight of potassium permanganate and find that it is 158.04 g/mol, which means you need 15.8 g to make up 100 mL of 1.00 M solution. So far, so good.
But if you start weighing and dissolving without further checking, you’re going to have an uh-oh moment. Why? Because, according to the CRC Handbook, at 20°C, 100 mL of water dissolves only 6.38 g of potassium permanganate and the other 9.42 g of potassium permanganate will remain undissolved in the bottom of your 100 mL volumetric flask. Oops. Time for a bit more figuring.
If the solubility of potassium permanganate in water at 20°C is 63.8 g per liter and the formula weight of potassium permanganate is 158.04 g/mol, that means that a saturated solution of potassium permanganate is [63.8 g] / [158.04 g/mol] = 0.40+ M. Because you don’t want potassium permanganate crystallizing out of the stock solution if the temperature in your lab happens to fall below 20°C, make up your potassium permanganate stock solution to 0.3 M by dissolving 4.74 g of potassium permanganate and making the solution up to 100 mL.
In this laboratory, we make up 100 mL of a stock solution of copper (II) sulfate, which is used in many of the other labs in this book. Although we won’t standardize the solution, we will make every effort to achieve an accurate concentration by weighing masses carefully and measuring volumes carefully.
The first question we need to answer is what the concentration of the stock solution should be. Ideally, we want the concentration to be as high as possible without quite being saturated. (We don’t want copper sulfate crystallizing out of solution if one day the lab happens to be a bit cooler than usual or if some of the solvent evaporates.) So, the first thing we need to determine is the molarity of a saturated solution of copper sulfate at room temperature. From that, we can decide what the molarity of our stock solution should be, and calculate how much copper sulfate is required to make up 100 mL of stock solution at that molarity. We proceed as follows:
Looking up copper sulfate pentahydrate in a reference book, we find that its its solubility at 20°C is 317 g/L and its formula weight is 249.7 g/mol.
Dividing 317 g/L by 249.7 g/mol tells us that a saturated solution of copper sulfate contains about 1.27 mol/L, which is 1.27 M.
To give us a safety margin against the solution crystallizing at lower temperatures, we decided to make our stock solution 1.00 M, or 1.00 mol/L.
Because we’re making up 100 mL (0.1 L) of solution, we need 0.1 moles of copper sulfate pentahydrate.
The formula weight of copper sulfate pentahydrate is 249.7 g/mol, so we need 24.97 g of copper sulfate pentahydrate for our 100 mL of solution.
The assay on the bottle of copper sulfate pentahydrate lists the contents as 99.0% copper sulfate pentahydrate, which means that this substance contains 1.0% of something other than copper sulfate pentahydrate (probably mostly metallic copper, copper oxide, and other insoluble copper salts). Dividing 24.97 g by 0.99 (99%) tells us that we need to weigh out 25.22 g of the substance in the bottle to get 24.97 g of copper sulfate pentahydrate. With the calculations complete, it’s time to head into the lab and actually make up the stock solution of copper sulfate pentahydrate.
If you have not already done so, put on your splash goggles, gloves, and protective clothing.
Place a weighing paper or boat on the balance and tare the balance to read 0.00 g.
Transfer copper sulfate pentahydrate crystals to the weighing paper until the balance reads as close as possible to 25.22 g. Read the mass to 0.01 g and record it. (It’s not important to have exactly 25.22 g of copper sulfate on the weighing paper, but it is important to know the mass as exactly as possible.)
Use the graduated cylinder to measure about 85 mL of distilled water, and transfer it to the beaker.
Transfer the copper sulfate pentahydrate from the weighing paper to the beaker, making sure that all of the crystals are added to the beaker.
Swirl the beaker gently until all of the copper sulfate has dissolved. This may take a few minutes, because this solution is nearly saturated.
Place the funnel in the mouth of the volumetric flask, and carefully pour the copper sulfate solution into the volumetric flask.
Use the wash bottle to rinse the inside of the beaker with 2 or 3 mL of water, and add the rinse water to the volumetric flask, rinsing the funnel as you do so. (Be careful not to use too much rinse water; the volumetric flask already contains about 85 mL of solution, and we can’t go over 100 mL.)
Repeat the rinse with another 2 or 3 mL of water. This procedure is called a quantitative transfer, and the goal is to make sure that all of the copper sulfate has been transferred to the volumetric flask.
Remove the funnel from the mouth of the volumetric flask, and use the dropper to add water dropwise until the level of solution in the flask reaches the reference line.
Insert the stopper in the volumetric flask and invert the flask several times to mix the solution thoroughly.
Using the funnel, transfer the solution from the volumetric flask to the labeled storage bottle.
Using the exact mass you recorded in step 3, calculate the molarity to the correct number of significant figures and record that molarity on the label. Also, record the date on the label.
Rinse the beaker, funnel, and volumetric flask and stopper with tap water and then with distilled water, and set them aside to dry.
Copper sulfate is moderately toxic by ingestion, inhalation, or skin contact. Wear splash goggles, gloves, and protective clothing at all times.
Compound | Formula | Formula Weight | Nominal M | Volume | Calculated Mass | Actual Mass | Actual M | |
cupric sulfate pentahydrate | CuSO4·5H2O | 249.68 g/mol | 1.0 M | 100 mL | 25.22 g | 25.34 g | 1.005 M | |
aluminum nitrate | _______.____ g/mol | ___.__ M | 100 mL | _______.____ g | _______.____ g | ___.______ M | ||
ammonium acetate | _______.____ g/mol | ___.__ M | 100 mL | _______.____ g | _______.____ g | ___.______ M | ||
ammonium chloride | _______.____ g/mol | ___.__ M | 100 mL | _______.____ g | _______.____ g | ___.______ M | ||
ammonium molybdate | _______.____ g/mol | ___.__ M | 100 mL | _______.____ g | _______.____ g | ___.______ M | ||
ammonium nitrate | _______.____ g/mol | ___.__ M | 100 mL | _______.____ g | _______.____ g | ___.______ M | ||
ammonium oxalate | _______.____ g/mol | ___.__ M | 100 mL | _______.____ g | _______.____ g | ___.______ M | ||
barium chloride | _______.____ g/mol | ___.__ M | 100 mL | _______.____ g | _______.____ g | ___.______ M | ||
barium nitrate | _______.____ g/mol | ___.__ M | 100 mL | _______.____ g | _______.____ g | ___.______ M | ||
calcium nitrate | _______.____ g/mol | ___.__ M | 100 mL | _______.____ g | _______.____ g | ___.______ M | ||
chromium (III) nitrate | _______.____ g/mol | ___.__ M | 100 mL | _______.____ g | _______.____ g | ___.______ M | ||
cobalt (II) nitrate | _______.____ g/mol | ___.__ M | 100 mL | _______.____ g | _______.____ g | ___.______ M | ||
copper (II) nitrate | _______.____ g/mol | ___.__ M | 100 mL | _______.____ g | _______.____ g | ___.______ M | ||
iron(III) nitrate | _______.____ g/mol | ___.__ M | 100 mL | _______.____ g | _______.____ g | ___.______ M | ||
iron (II) sulfate | _______.____ g/mol | ___.__ M | 100 mL | _______.____ g | _______.____ g | ___.______ M | ||
lead nitrate | _______.____ g/mol | ___.__ M | 100 mL | _______.____ g | _______.____ g | ___.______ M | ||
magnesium sulfate | _______.____ g/mol | ___.__ M | 100 mL | _______.____ g | _______.____ g | ___.______ M | ||
manganese(II) sulfate | _______.____ g/mol | ___.__ M | 100 mL | _______.____ g | _______.____ g | ___.______ M | ||
nickel(II) nitrate | _______.____ g/mol | ___.__ M | 100 mL | _______.____ g | _______.____ g | ___.______ M | ||
potassium bromide | _______.____ g/mol | ___.__ M | 100 mL | _______.____ g | _______.____ g | ___.______ M | ||
potassium chromate | _______.____ g/mol | ___.__ M | 100 mL | _______.____ g | _______.____ g | ___.______ M | ||
potassium ferrocyanide | _______.____ g/mol | ___.__ M | 100 mL | _______.____ g | _______.____ g | ___.______ M | ||
potassium hydrogen tartrate | _______.____ g/mol | ___.__ M | 100 mL | _______.____ g | _______.____ g | ___.______ M | ||
potassium iodide | _______.____ g/mol | ___.__ M | 100 mL | _______.____ g | _______.____ g | ___.______ M | ||
potassium nitrate | _______.____ g/mol | ___.__ M | 100 mL | _______.____ g | _______.____ g | ___.______ M | ||
potassium permanganate | _______.____ g/mol | ___.__ M | 100 mL | _______.____ g | _______.____ g | ___.______ M | ||
potassium thiocyanate | _______.____ g/mol | ___.__ M | 100 mL | _______.____ g | _______.____ g | ___.______ M | ||
silver nitrate | _______.____ g/mol | ___.__ M | 100 mL | _______.____ g | _______.____ g | ___.______ M | ||
sodium acetate | _______.____ g/mol | ___.__ M | 100 mL | _______.____ g | _______.____ g | ___.______ M | ||
sodium bicarbonate | _______.____ g/mol | ___.__ M | 100 mL | _______.____ g | _______.____ g | ___.______ M | ||
sodium bisulfite | _______.____ g/mol | ___.__ M | 100 mL | _______.____ g | _______.____ g | ___.______ M | ||
sodium borate | _______.____ g/mol | ___.__ M | 100 mL | _______.____ g | _______.____ g | ___.______ M | ||
sodium carbonate | _______.____ g/mol | ___.__ M | 100 mL | _______.____ g | _______.____ g | ___.______ M | ||
sodium hydroxide | _______.____ g/mol | ___.__ M | 100 mL | _______.____ g | _______.____ g | ___.______ M | ||
sodium nitrite | _______.____ g/mol | ___.__ M | 100 mL | _______.____ g | _______.____ g | ___.______ M | ||
sodium phosphate, tribasic | _______.____ g/mol | ___.__ M | 100 mL | _______.____ g | _______.____ g | ___.______ M | ||
sodium sulfate | _______.____ g/mol | ___.__ M | 100 mL | _______.____ g | _______.____ g | ___.______ M | ||
sodium sulfite | _______.____ g/mol | ___.__ M | 100 mL | _______.____ g | _______.____ g | ___.______ M | ||
sodium thiosulfate | _______.____ g/mol | ___.__ M | 100 mL | _______.____ g | _______.____ g | ___.______ M | ||
strontium nitrate | _______.____ g/mol | ___.__ M | 100 mL | _______.____ g | _______.____ g | ___.______ M | ||
zinc nitrate | _______.____ g/mol | ___.__ M | 100 mL | _______.____ g | _______.____ g | ___.______ M |
Q: | Q1: The molarity of a solution can never be more than a close approximation. List at least five factors that may cause the actual molarity of a solution to differ from the calculated molarity of that solution. __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ |
Q: | Q2: Although Table 7-1 assumes 100 mL of each solution, there are some solutions (such as silver nitrate) that you may want to make up in smaller batches, because the chemical is expensive or because you expect to use smaller amounts of the solution. Similarly, there are some solutions that you may want to make up in larger batches (such as sodium chloride), either because the chemical is inexpensive or because you expect to use larger amounts of the solution. For what other reasons might you decide to make up a smaller or larger batch of a particular solution? __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ |
Q: | Q3: What characteristic or characteristics of a particular chemical make it easier to obtain a known mass of that chemical by measuring a known volume of a solution of known concentration of that chemical rather than by weighing the solid chemical? __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ |
In this laboratory, we make up 100 mL of a 0.5 molal stock solution of potassium hexacyanoferrate(III) (potassium ferricyanide), which is used in several of the other labs in this book. Although we won’t standardize the solution, we will make every effort to achieve an accurate concentration by weighing the masses of the solute and solvent carefully.
As always when making up a solution, the first thing to determine is the concentration of a saturated solution of the chemical to make sure the chemical is soluble enough to make up a solution of the desired concentration. From that information, we can calculate how much potassium ferricyanide is required. Proceed as follows:
Looking up potassium ferricyanide in a reference book, we find that its room-temperature solubility is about 330 g/L and its formula weight is 329.24 g/mol.
Dividing 330 g/L by 329.24 g/mol tells us that a saturated solution of potassium ferricyanide contains about 1.00 mol/L, which is to say 1.00 M. (In dilute solutions, molality and molarity are nearly equal, so this calculation is valid even though we’re making up the solution to a specified molality.)
To give us a safety margin against the solution crystallizing at lower temperatures, we decide to make our stock solution 0.50 M, or 0.50 mol/L. We could make up the solution to 0.60, 0.75, or some other molality (0.90 m would be pushing it), but round numbers are easier to handle when you’re calculating equivalents and measuring solutions for use in other tasks.
A one molal (1 m) solution is defined as one mole of solute dissolved in one kilogram of solvent. Because we’re making up a 0.50 molal solution with 100 g of water as the solvent, we need 0.05 moles of potassium ferricyanide.
The formula weight of potassium ferricyanide is 329.24 g/mol, so we need 16.46 g of potassium ferricyanide for our solution.
The assay on our bottle of reagent grade potassium ferricyanide lists the contents as 99% potassium ferricyanide, meaning that this substance may contain up to 1% of something other than potassium ferricyanide. Dividing 16.46 g by 0.99 (99%) tells us that we need to weigh out 16.63 g of the substance in the bottle to get 16.46 g (0.0500 mol) of potassium ferricyanide.
With the calculations complete, we’re ready to prepare the solution.
If you have not already done so, put on your splash goggles, gloves, and protective clothing.
Place a weighing paper or boat on the balance and tare the balance to read 0.00 g.
Transfer potassium ferricyanide crystals to the weighing paper until the balance reads as closely as possible to 16.63 g. Read the mass to 0.01 g and record it. (It’s not important to have exactly 16.63 g of potassium ferricyanide on the weighing paper, but it is important to know the mass as exactly as possible.)
Transfer the potassium ferricyanide to the beaker, place the beaker on the balance pan, and tare the balance to read 0.00 g.
Use the wash bottle to transfer distilled water to the beaker until the balance reads close to 100.00 g. Use the dropper to add distilled water dropwise until the balance reads as closely as possible to 100.00 g (Figure 7-2). Depending on the dropper, one drop of water may weigh from about 0.05 g to about 0.02 g. When you have 100.00 g of water in the beaker, or as close to that as you can get, read the mass to 0.01 g and record it.
Swirl the beaker gently until all of the potassium ferricyanide has dissolved.
Place the funnel in the mouth of the labeled storage bottle, and carefully pour the potassium ferricyanide solution into the bottle.
Using the exact masses you recorded in steps 3 and 5, calculate the molality to the correct number of significant figures and record that molality on the label. Also record the date on the label.
Rinse the beaker, funnel, and volumetric flask and stopper with tap water and then with distilled water, and set them aside to dry.
Some common laboratory chemicals, such as sulfuric acid, are liquid at standard temperature and pressure. Many other chemicals, such as ammonia and hydrochloric acid, are gases, but are ordinarily stored and handled in the form of concentrated aqueous solutions. Whether the chemical is actually a liquid or is supplied in the form of a concentrated aqueous solution, the same principles apply to diluting the chemical to make up working solutions of known molarities.
In this laboratory, we make up 100 mL of 1.00 M hydrochloric acid, which is a common bench solution. (I actually make this stuff up 500 mL at a time, but not everyone has a 500 mL volumetric flask.) We’ll make up this solution by diluting concentrated hydrochloric acid. The label on the bottle of reagent-grade hydrochloric acid gives us several pieces of information about its concentration:
The mass percentage is specified as 36% to 38%, which means that 100 g of the concentrated acid contains between 36g and 38 g of dissolved HCl gas.
The density is specified as ranging between 1.179 g/mL and 1.189 g/mL, which tells us the mass of a specific volume of the concentrated acid. (The density is also specified as between 22° and 23° Baumé, which is an older and obsolescent method for specifying density or specific gravity.)
The molarity is specified as between 11.64 M and 12.39 M.
If they were mixing up a 1.0 M bench solution, most chemists would assume that the concentrated hydrochloric acid was 12.0 M, and add one part of concentrated acid to 11 parts water to make up the 1 M solution. To make up 100 mL of 1 M acid, we could measure 8.33 mL of the 12 M acid, add it to 70 mL or so of distilled water in a 100 mL volumetric flask, and make up the solution to 100 mL. In practice, that’s how it’s usually done.
But there are advantages to using mass percentage and density when making up dilute bench solutions, including higher accuracy and precision. Also, it’s important to know how to make up solutions based on mass percentage and density, because not all concentrated aqueous solutions list a molarity.
To make up solutions based on the mass percentage of a stock solution, begin by calculating the required number of moles of solute. For 100 mL (0.1 L) of 1 M hydrochloric acid, we need 0.1 moles of HCl. The formula weight of HCl is 36.46 g/mol, so we need 3.646 g of HCl. If the mass percentage of the concentrated acid is 37% (0.37), that means we need 3.646/0.37 = 9.854 g of the concentrated acid. To get that, we tare a small beaker or other container on our balance, and add concentrated acid to the beaker until the balance reads 9.854 g.
If we prefer to measure the concentrated acid volumetrically rather than gravimetrically, we also need to know the density of the solution to determine how many mL of the concentrated acid has a mass of 9.854 g. To calculate that value, we divide the required mass by the density of the solution. If the concentrated acid has a density of 1.183 g/mL, that means we need 9.854/1.183 = 8.330 mL.
Because the density and mass percentage of a solution are related, it’s possible to determine either of them, if the value of the other is known or can be determined. For example, the label on the bottle of reagent-grade concentrated hydrochloric acid may specify a fairly wide range for mass percentage (such as 36% to 38%) and density (such as 1.179 to 1.189 g/mL). To get a better value for actual concentration, I tared a 100 mL volumetric flask, filled it to the reference line with my concentrated hydrochloric acid, and determined the mass of the concentrated acid. That turned out to be 118.31 g, or 1.183 g/mL.
In this lab, we’ll make up 100 mL of 1.00 M hydrochloric acid, using our mass percentage calculations to determine how much concentrated acid to use. (If the values listed on your own bottle of concentrated hydrochloric acid differ significantly from these values, recalculate amounts based on the actual values of your concentrated hydrochloric acid.)
If you have not already done so, put on your splash goggles, gloves, and protective clothing.
Place a clean, dry 10 mL graduated cylinder on the balance and tare the balance to read 0.00 g.
Using the dropper, transfer concentrated hydrochloric acid into the graduated cylinder until the balance reads as closely as possible to 9.854 g, which it should when you have transferred just over 8.3 mL of acid to the graduated cylinder. Note the mass and volume of the concentrated HCl as accurately as possible and record them for future use.
Fill the 100 mL volumetric flask about two-thirds full with distilled water.
Place the funnel in the mouth of the volumetric flask, and carefully pour the concentrated acid into the volumetric flask.
Use the wash bottle to rinse the inside of the graduated cylinder with several mL of water, and add the rinse water to the volumetric flask, rinsing the funnel as you do so.
Repeat the rinse with another several mL of water to make sure that the transfer is quantitative.
Use the water bottle to rinse the funnel again, and bring the solution level in the volumetric flask up to within 1 cm of the reference line.
Remove the funnel from the mouth of the volumetric flask, and use the dropper to add water dropwise until the level of solution in the flask reaches the reference line.
Insert the stopper in the volumetric flask and invert the flask several times to mix the solution thoroughly.
Using the funnel, transfer the solution from the volumetric flask to the labeled storage bottle.
Calculate the molarity to the correct number of significant figures and record that molarity on the label. Also record the date on the label.
Rinse the beaker, funnel, and volumetric flask and stopper with tap water and then with distilled water, and set them aside to dry.
Concentrated hydrochloric acid is corrosive and emits toxic and irritating fumes. Wear splash goggles, gloves, and protective clothing at all times, and work in a well-ventilated area or under a fume hood.
Always add acid to water. Because most concentrated acids are denser than water, they will mix more readily when dropped into water. Water added on top of concentrated acid may sit on top of the acid, resulting in an interface that can generate a lot of heat and actually cause the water to boil.
Sulfuric and nitric acid solutions may require the donning of chemically impervious aprons. They eat through clothing, including lab coats. Even dilute solutions can ruin clothes (lots of tiny holes). I would recommend washing anything worn during this experiment separately from all other clothes. (Personal experience: in grad school, everything I owned was full of tiny holes.)
Mass-to-volume percentage solutions are more commonly used by pharmacists than by chemists, but these solutions still have a place in chemistry labs. The advantage of a mass-to-volume percentage solution is that it makes it easy to transfer a precise amount of solute by measuring the necessary volume of the solution. For example, a pharmacist may make up a solution that contains 3.00 g of a drug per 100 mL of solution. If the proper dosage of the drug is 150 mg, the pharmacist can direct the patient to take one teaspoon (5.0 mL). Similarly, if the proper dosage is 1.5 mg, the pharmacist can direct the patient to take one drop (0.05 mL).
The most common use of mass-to-volume solutions in chemistry labs is for indicators and similar solutions. For example, a chemist might keep on hand a 1% ethanol solution of phenolphthalein, a 0.2% aqueous solution of phenol red, and 0.4% aqueous solutions of bromocresol green and bromothymol blue. For most laboratory uses, the exact concentrations of these solutions is unimportant. For example, rather than weighing 1.000 g of phenolphthalein powder, dissolving it in ethanol, and making it up to 100 mL in a volumetric flask, most chemists would make up the solution by dissolving about a gram of the indicator powder in about 100 mL of ethanol, measured roughly in a beaker. We’ll take a bit more care in this lab, but not much more.
Although none of the chemicals used in this lab are hazardous, it’s good practice to 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 amounts used as an indicator solution are not ingested and are no cause for concern.)
If you have not already done so, put on your splash goggles, gloves, and protective clothing.
Place a weighing paper on the balance and tare the balance to read 0.00 g.
Weigh out about 1.0 g of phenolphthalein powder, and transfer it to the beaker.
Fill the 100 mL graduated cylinder to 100.0 mL with ethanol, and transfer the ethanol to the beaker.
Swirl or stir the contents of the beaker until the phenolphthalein powder is dissolved and the solution is mixed thoroughly.
Using the funnel, transfer the solution from the beaker to fill the small dropper bottle. Transfer the remaining solution into the larger storage bottle.
Record the date on the labels of the bottles.
Rinse the beaker and funnel with tap water and then with distilled water, and set them aside to dry.
Colorimetry is the study of color. As it applies to chemistry, colorimetry is used as a practical application of the Beer-Lambert Law (describing the relationship between chemical concentration and light transmitted; see your chemistry textbook) to determine the percentage of light that is transmitted by a solution that contains a colored solute, and from that to determine the concentration of the solute.
Nowadays, most colorimetry is done instrumentally, using one of the following instruments:
Colorimeter
A relatively inexpensive instrument—entry-level colorimeters are available for less than $1,000—that allows the light transmission of a solution to be tested with white light or with a limited number of discrete wavelengths. Older colorimeters use an incandescent white light source, which may be used as-is or may be filtered to allow testing transmission with colored light. Typically, such colorimeters are supplied with three filters: violet-blue, green-yellow, and orange-red. Newer calorimeters often substitute colored LEDs for the incandescent light source. Before use, a colorimeter is calibrated by filling the sample tube, called a cuvette, with distilled water and setting the colorimeter to read 100% transmission with that cuvette in place. The cuvette is then filled with the unknown solution and used to determine the percentage of light transmitted at one or several wavelengths. Colorimeters are widely used in industrial processes, such as wine making, where high accuracy and selectivity is not required.
Spectrophotometer
A spectrophotometer is a more sophisticated (and much more expensive) version of a colorimeter. Instead of using only white light or light at three or four discrete wavelengths, a spectrophotometer simultaneously tests a sample at many wavelengths. Inexpensive spectrophotometers may sample every 10 nanometers (nm) or 20 nm over the visible spectrum from 400 nm to 700 nm. Spectrophotometers used in university and industrial chemistry labs typically sample every nm (or better) over a range from 200 nm in the ultraviolet to 800 to 1,100 nm in the infrared. If a colorimeter is a meat-ax, a spectrophotometer is a scalpel. The many data points determined by a spectrophotometer can be plotted on a graph to yield a “fingerprint” of the transmission characteristics of a particular solution over a wide range of wavelengths. By comparing this fingerprint to the fingerprints of known compounds, spectrophotometry can be used to identify unknown compounds in solution, rather than just the concentration of a known compound.
Despite the ubiquity of colorimeters and spectrophotometers in modern laboratories, such instruments are not required to obtain useful data by colorimetry. Colorimetry was used long before such instruments became available, by employing one of the most sensitive instruments available for determining color: the Mark I human eyeball.
In this lab, we’ll use our eyes to determine the concentration of a solution of copper sulfate by colorimetry.
This laboratory has two parts. In Part I, we’ll make up solutions that contain known concentrations of copper sulfate. In Part II, we’ll make up a solution with an unknown concentration of copper sulfate and estimate the concentration of that unknown solution using visual colorimetry.
If you have not already done so, put on your splash goggles, gloves, and protective clothing.
Label six test tubes #1 through #6.
Use the 5.00 mL pipette to transfer 10.00 mL of distilled water into test tube #1, and 5.00 mL of distilled water into each of the other five test tubes.
Place a weighing paper on the balance and tare the balance to read 0.00 g.
Weigh out about 2.40 g of copper sulfate, record the mass to 0.01 g on line A of Table 7-2 under “Test tube #1,” and transfer the copper sulfate to test tube #1.
Swirl test tube #1 until all of the copper sulfate has dissolved.
Use the 5.00 mL pipette to transfer 5.00 mL of the copper sulfate solution from test tube #1 to test tube #2.
Swirl test tube #2 until the distilled water and copper sulfate solution is thoroughly mixed.
Repeat steps 7 and 8 for test tubes #3, #4, and #5. When you finish, each of the five test tubes should contain a solution of copper sulfate at half the concentration of the preceding tube. Test tube #1 should have an intense blue color, with each succeeding test tube a paler blue.
Calculate the mass of copper sulfate in each of the tubes #2 through #5 and the mass-to-volume percentage of tubes #1 through #5, and enter those values in lines A and B of Table 7-2.
Copper sulfate is moderately toxic by ingestion or inhalation and is irritating to eyes and skin. Wear splash goggles, gloves, and protective clothing at all times.
Copper sulfate solutions may be neutralized with sodium carbonate and the precipitate can then be disposed of with household waste. Alternatively, small amounts of copper sulfate solution may be flushed down the drain. (Copper sulfate is, after all, sold as root killer, for which purpose it is—you guessed it—flushed down the drain.)
Item | Test tube #1 | Test tube #2 | Test tube #3 | Test tube #4 | Test tube #5 |
A. mass of copper sulfate | ___._________ g | ___._________ g | ___._________ g | ___._________ g | ___._________ g |
B. mass-to-volume percentage | ____.________% | ____.________% | ____.________% | ____.________% | ____.________% |
If you have not already done so, put on your splash goggles, gloves, and protective clothing.
Use the 5.00 mL pipette to transfer 5.00 mL of distilled water into test tube #6.
Place a weighing paper on the balance and tare the balance to read 0.00 g.
Weigh out 2 to 3 g of copper sulfate and record the mass to 0.01 g on line A of Table 7-3.
Using the spatula, transfer about one quarter of the copper sulfate to test tube #6, and swirl the test tube until all of the copper sulfate has dissolved.
Compare the color of the solution in test tube #6 against the colors of the solutions in test tubes #1 through #5. You’ll find it easiest to get an accurate comparison if you place a well-lit sheet of white paper behind the test tubes.
Estimate the concentration of the unknown solution in test tube #6 by judging how its color compares to the known sample solutions in test tubes #1 through #5. For example, you might judge that the color of your unknown solution is a bit more than halfway between the colors of test tubes # 3 and #4. By interpolation, estimate the mass-volume percentage of copper sulfate in test tube #6 as closely as possible, and enter that value on line B of Table 7-3.
Weigh the remaining copper sulfate and record the mass to 0.01 g on line C of Table 7-3.
Determine the mass of the copper sulfate sample that you dissolved in test tube #6 and enter the value to 0.01 g on line D of Table 7-3.
Calculate the actual mass-to-volume percentage for test tube #6, and enter that value on line E of Table 7-3.
Calculate the percentage error and enter that value on line F of Table 7-3.
Item | Data |
A. initial mass of copper sulfate | ____.____ g |
B. interpolated mass-to-volume percentage estimate | _________% |
C. mass of remaining copper sulfate | ____.____ g |
D. mass of copper sulfate sample (A–C) | ____.____ g |
E. actual mass-to-volume percentage | ____.____% |
F. percentage error | ffl___.___% |