Chapter 15. Laboratory: Thermochemistry and Calorimetry

Thermochemistry is the study of the heat evolved or absorbed during chemical reactions, physical transformations (such as mixing), and phase changes (such as melting). Calorimetry, from the Latin words calor for heat and metrum for measure, is a technique used to measure the heat changes that occur in such processes.

All of the laboratories in this chapter require a calorimeter, a device that thermally isolates the process being investigated, preventing gain or loss of heat from the external environment. We used an inexpensive purpose-built calorimeter, which is available from Home Science Tools (http://www.homesciencetools.com) and similar vendors for $15 or so. If you don’t want to buy a formal calorimeter, you can achieve results nearly as accurate with a home-built calorimeter. Both types of calorimeter are shown in Figure 15-1.

Figure 15-1. Store-bought (left) and homemade calorimeters

Heat versus Temperature

Heat and temperature are related but not identical concepts. A sample may contain a small amount of heat, but the temperature may be relatively high, or vice versa. For example, the sparks coming off a grinding wheel are tiny particles of burning metal. Their temperature is very high—perhaps 1,000°C or higher—but the particles contain little heat, because the mass of each is a fraction of a milligram. If one of those particles were to contact your skin, you might not even notice it. Conversely, a liter of boiling water is at a relatively low temperature, only 100°C, but the kilogram mass of water stores a considerable amount of heat. If that water comes into contact with your skin, you will be burned badly.

All you need for a homemade calorimeter are a couple of 8- or 16-ounce (250 or 500 mL) foam cups, a lid, and a beaker or similar heavy container to provide stability. Place one cup inside the other to provide better insulation. Insert your thermometer or temperature probe through the center hole in the lid, and use it both for measuring temperatures and as a stirring rod. You can significantly improve the accuracy of your homemade calorimeter by replacing the snap-on plastic lid with a lid constructed of foam. Using the top (smallest diameter part) of the plastic lid as a template, mark and cut a circular piece of foam just large enough to fit inside the mouth of the cup. Using the top of the cup as a template, mark and cut a second circle of foam just a bit too large to fit inside the mouth of the cup. Center the smaller circle of foam on the larger one, and glue the two pieces together. Poke a small hole through the center of the new lid assembly to allow the insertion of a stirring rod or thermometer.

Measuring temperature changes accurately and precisely is the foundation of thermochemistry. We used an inexpensive digital temperature probe (thermometer) to measure temperatures to 0.1°C. You can substitute a standard glass-tube thermometer with some loss of accuracy and precision. If you do use a glass-tube thermometer, try to interpolate your temperature measurements by estimating values between the markings. With a standard 300 mm glass-tube lab thermometer, it’s usually possible to interpolate values accurate to 0.2°C. With longer thermometers, or those with narrower ranges, it may be possible to interpolate to 0.1°C.

In this chapter, we’ll use calorimetry to examine several aspects of thermochemistry.

Everyday Thermochemistry and Calorimetry

• The chemical cold packs sold in drugstores illustrate heat of solution (as defined on the next page). These packs have two compartments. One contains water and the second a solid chemical (usually ammonium nitrate or sodium thiosulfate) with a positive (endothermic) heat of solution. When you break the divider between the compartments, the solid chemical dissolves, absorbing heat from the environment.

• The reusable chemical heat packs sold in drugstores illustrate a different aspect of heat of solution. These packs contain a very concentrated solution of sodium acetate. Placing the pack in boiling water or heating it in a microwave oven for a few minutes dissolves the solid sodium acetate. When the pack has cooled to room temperature, it contains a supersaturated, supercooled solution of sodium acetate. When the pack is initiated, normally by bending a the small embedded metal disc that contains tiny slots with microscopic crystals of sodium acetic, the sodium acetate immediately begins recrystallizing, producing heat as it does so.

• If you’ve ever made ice cream in an old-fashioned ice cream maker, you’ve used a practical example of the heat of fusion of ice (as defined in Laboratory 15.2: Determine the Heat of Fusion of Ice). Adding salt to water ice reduces the freezing point, converting some of the ice to liquid water. The heat of fusion required to melt the ice must come from somewhere, and the only available source of heat is the ice itself. As the salt dissolves, the temperature of the ice/salt bath decreases enough to freeze the milk and cream, producing ice cream.

Laboratory 15.1: Determine Heat of Solution

Heat of solution, also called enthalpy change of solution, is heat that is absorbed or released when a solute is dissolved in a solvent. Dissolution is a complex process that involves both absorption and release of energy. Energy is absorbed (endothermic energy) to break the attractions between the solute molecules and the attractions between the solvent molecules. Conversely, energy is released (exothermic energy) as new attractions form between solute molecules and solvent molecules. The net difference between the energy absorbed and the energy released per mole of solute is defined as the heat of solution for that solute.

For a particular solvent, some solutes have a positive heat of solution, because the energy that must be absorbed to break the solute-solute bonds and the solvent-solvent bonds is greater than the energy that is released by the formation of solute-solvent bonds. Dissolving such a solute reduces the temperature of the solution relative to the original temperature of the solvent. Other solutes have a negative heat of solution, because less energy is needed to break the solute-solute and solvent-solvent attractions than is released by the forming of solute-solvent bonds. (Remember, heat of solution is defined as endothermic energy minus exothermic energy, so dissolving a compound with negative heat of solution causes the temperature of the solution to increase.)

Heat of solution (represented as ΔH_solution) is properly quantified using SI units of kJ/mol (kiloJoules/mole), but many older sources (and many older chemists . . .) continue to use the old-style C/mol (kilocalories/mole), where one kJoule equals 2.390 x 10^–1 kilocalories (0.2390 C) and one kilocalorie (kcal or C) equals 4.1841 kJ. For any particular solute/solvent combination, a value for heat of solution can be determined experimentally from data derived by dissolving a known mass of the solute in a known mass of the solvent and measuring the temperature change. That’s what we do in this lab.

Required Equipment and Supplies

	goggles, gloves, and protective clothing
	balance and weighing papers
	calorimeter
	thermometer
	graduated cylinder, 100 mL
	ammonium nitrate (40.0 g = 0.5 mol)
	sodium chloride (29.2 g = 0.5 mol)
	sodium hydroxide (20.0 g = 0.5 mol)
	water (at room temperature)

Substitutions and Modifications

• At the risk of some loss of accuracy, you can run this lab on a semi-micro scale by reducing the quantities of solutes and water by a factor of 10 and substituting a test tube for the calorimeter. (This is not ideal, because the glass of the test tube has much higher thermal mass than a foam cup and is a poor insulator.)

• You may substitute pure ammonium nitrate fertilizer for laboratory- or reagent-grade ammonium nitrate.

• You may substitute table salt for sodium chloride.

• You may substitute crystal drain opener that lists its contents as 100% sodium hydroxide for laboratory- or reagent-grade sodium hydroxide.

• If you are using a calorimeter in which the solutions will come into contact with aluminum or glass, substitute calcium chloride for the sodium hydroxide. In areas that have snowy winters, relatively pure calcium chloride is sometimes available as ice-melt crystals, although many different formulations are used, so it’s necessary to check the label.

Procedure

To achieve the highest accuracy, it’s best to have the solutes, solvent (water), and calorimeter at room temperature. The temperature of cold tap water is usually lower than room temperature. If you have time to prepare beforehand, fill a two-liter soft drink bottle or similar container with tap water and allow it to sit for several hours to equilibrate to room temperature.

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

2. Weigh 40.0 g of ammonium nitrate and record the mass in Table 15-1.

3. Use the graduated cylinder to measure 100.0 mL (100.0 g) of water.

4. Add the water to the calorimeter and replace the cover.

5. Measure the temperature of the water in the calorimeter as accurately as possible and record the temperature in Table 15-1. See Figure 15-2.

6. Add the ammonium nitrate to the calorimeter and replace the cover.

7. Stir the solution (or swirl the calorimeter) to dissolve the ammonium nitrate.

8. Watch the thermometer. When the temperature change reaches its maximum, record that temperature in Table 15-1. Calculate the temperature difference and record it in Table 15-1.

9. Dispose of the spent solution and rinse out the calorimeter.

10. Repeat steps 1 through 9, substituting 29.2 g of sodium chloride for the 40.0 g of ammonium nitrate.

11. Repeat steps 1 through 9, substituting 20.0 g of sodium hydroxide for the 40.0 g of ammonium nitrate.

Optional Activities

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

• Repeat the experiment using 10.0 mL of concentrated (98%) sulfuric acid as the solute. (Caution: concentrated sulfuric acid is extremely corrosive.) Calculate the heat of solution for concentrated sulfuric acid.

• Repeat the experiment using 10.0 mL of 35% sulfuric acid (battery acid) as the solute. (Caution: 35% sulfuric acid is extremely corrosive.) Calculate the heat of solution for 35% sulfuric acid. Does this value differ from the value for concentrated sulfuric acid on a per mole basis? If so, propose an explanation.

Caution

Ammonium nitrate is a strong oxidizer, and may detonate if heated strongly. Sodium hydroxide is corrosive, reacts strongly with aluminum (some commercial calorimeters have aluminum bodies), and in high concentrations etches or dissolves glass. Wear splash goggles, gloves, and protective clothing at all times.

Figure 15-2. Measuring the temperature of the contents of the calorimeter

Disposal

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

Table 15-1. Heat of solution—observed and calculated data

Solute	Mass	Water temperature	Solution temperature	Temperature difference	Calculated heat of solution
A. Ammonium nitrate	________.___ g	________.__ °C	________.__ °C	(+/-) ________.__ °C	(+/–) ________.___ kJ/mol
B. Sodium chloride	________.___ g	________.__ °C	________.__ °C	(+/-) ________.__ °C	(+/–) ________.___ kJ/mol
C. Sodium hydroxide	________.___ g	________.__ °C	________.__ °C	(+/-) ________.__ °C	(+/–) ________.___ kJ/mol

Review Questions

Q:

Q1: Using your experimental data, calculate the heats of solution for ammonium nitrate, sodium chloride, and sodium hydroxide. Enter your calculated values in Table 15-1.

Q:

Q2: Look up published values for the heats of solution of those three compounds on the Internet or in a printed reference. How closely do the values that you obtained experimentally correspond to the published values? If your values are significantly different, propose possible explanations. _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________

Laboratory 15.2: Determine the Heat of Fusion of Ice

If you add heat to a mixed-phase system that comprises a substance in its solid and liquid phases, both at the melting point of the solid, the temperature of the system does not increase until all of the solid is converted to liquid. The additional heat energy that is absorbed without causing a temperature increase is required to give the atoms or molecules that make up the solid sufficient energy to break the attraction that holds them in solid form. The additional heat energy that is required to change a solid to a liquid at its melting point is called heat of fusion, enthalpy of fusion, or specific melting heat.

In this laboratory, we’ll measure the heat of fusion of ice, which has a high heat of fusion because of the strong intermolecular attraction of hydrogen atoms. Heat of fusion is (officially) expressed as Joules per mole (J/mol) in the SI system, but many older and alternate forms are still used. Among the most common of those are calories per gram (cal/g), kiloJoules per kilogram (kJ/kg), and even British Thermal Units per pound (BTU/lb). In particular, cal/g is still very widely used, and is the format we use in this laboratory.

Caution

Take care with the hot water and hotplate to avoid burns. Wear splash goggles, gloves, and protective clothing.

Substitutions and Modifications

• You may substitute a sauce pan or similar container for the 600 mL beaker.

• You may substitute any heat source for the hotplate.

Required Equipment and Supplies

	goggles, gloves, and protective clothing
	calorimeter
	thermometer
	graduated cylinder, 100 mL
	ice bucket or similar wide-mouth container
	beaker, 600 mL
	beaker tongs
	hotplate
	strainer
	ice, crushed or chipped
	hot tap water

Procedure

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

2. Fill one of the 600 mL beakers about half full of crushed or chipped ice and allow the ice to begin melting while you perform the following steps.

   Cold as Ice

   Ice in a typical home freezer is typically at a temperature of –15°C to –20°C, well below the melting point of ice. To determine the heat of fusion of ice accurately, we need to start with ice at 0°C. Otherwise, some of the heat absorbed will be needed to warm the ice to 0°C, giving a false high value for the heat of fusion of ice. You can avoid this by crushing or chipping the ice into small pieces, allowing it to melt partially into slush, and using the strainer to separate solid ice from the water.

3. Add about 400 mL of hot tap water to the second 600 mL beaker and heat the water to 65°C ± 5°C.

4. Using the beaker tongs, pour about 100 mL of the heated water into the 100 mL graduated cylinder to preheat it. Wait 30 seconds and then dump the water from the graduated cylinder into the sink.

5. Repeat the preceding step with another 100 mL of heated water from the large beaker. After 30 seconds, dump the water into the sink.

6. While you are preheating the graduated cylinder, use the strainer to separate solid ice from the ice-water slush mixture and fill the calorimeter about half full with ice. Replace the cover on the calorimeter to prevent the ice from absorbing heat from the room air.

7. Using the beaker tongs, add about 25 mL of the heated water to the graduated cylinder. Measure the volume of the water to 0.1 mL and record the volume on line A of Table 15-2.

8. Measure the temperature of the water in the graduated cylinder to 0.1 °C and record that temperature on line B of Table 15-2.

9. Carefully pour off any water that has accumulated in the calorimeter, and add the 25 mL of warm water from the graduated cylinder to the calorimeter. Replace the calorimeter cover and stir the ice-water mixture. (Some ice must remain in the calorimeter at the conclusion of this step. If all of the ice melts, remove the calorimeter cover and quickly add more ice.)

10. Measure the temperature of the ice-water mixture, and record the value to within 0.1°C on line C of Table 15-2. (Ideally, that temperature should closely approach 0°C, but under experimental conditions, a temperature of 2°C to 3°C is acceptable. Simply watch the temperature until it stabilizes at its lowest value and record it.)

11. Pour the contents of the calorimeter through the strainer and into the graduated cylinder. Try to make sure that all of the water in the calorimeter is transferred to the graduated cylinder without spillage and that none of the remaining ice is transferred to the graduated cylinder. Measure the volume of the water in the graduated cylinder and record that value to 0.1 mL on line D of Table 15-2.

12. Repeat steps 1 through 10 at least once, and record the observed values in Table 15-2. If your results are poor (that is, they vary widely), run additional trials with the same steps and record the observed values in Table 15-2.

Table 15-2. Heat of fusion of ice—observed and calculated data

Item	Trial #1	Trial #2	Trial #3	Trial #4	Trial #5
A. Volume, initial	____.__ mL	____.__ mL	____.__ mL	____.__ mL	____.__ mL
B. Temperature, initial	____.__ °C	____.__ °C	____.__ °C	____.__ °C	____.__ °C
C. Temperature, final	____.__ °C	____.__ °C	____.__ °C	____.__ °C	____.__ °C
D. Volume, final	____.__ mL	____.__ mL	____.__ mL	____.__ mL	____.__ mL
E. Temperature change (B – C)	____.__ °C	____.__ °C	____.__ °C	____.__ °C	____.__ °C
F. Volume change (D – A)	____.__ mL	____.__ mL	____.__ mL	____.__ mL	____.__ mL
G. Heat of fusion of ice	______.___ cal/g	______.___ cal/g	______.___ cal/g	______.___ cal/g	______.___ cal/g

Review Questions

Q:

Q1: Using your experimental data for each of the first two trials, calculate the heat of fusion of ice in cal/g and record your calculated values on line G of Table 15-2. The actual value for the heat of fusion of ice is 79.72 cal/g. If the value you obtained experimentally differs significantly, propose possible reasons for this variation. _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________

Laboratory 15.3: Determine the Specific Heat of a Metal

When material at one temperature comes into contact with material at another temperature, heat flows from the warmer material to the cooler material until thermal equilibrium is attained when both materials are at the same temperature. In a controlled environment, such as our calorimeter, no heat is gained from or lost to the environment, so the heat gained by the (originally) cooler material equals the heat lost by the hotter material. (In practice, of course, there are minor heat gains or losses, even with the calorimeter, but these gains or losses are quite minor relative to the large changes that we’ll measure in this laboratory.)

In this laboratory, we’ll determine the specific heat of two metals, lead and iron, by heating a known mass of each metal to a known temperature, and then adding the hot metal to a known mass of cooler water at a known temperature and allowing the system to come to thermal equilibrium. Heat flows from the hot metal, warming the cooler water. Because the amount of heat lost by the metal is equal to the amount of heat gained by the water, we can calculate the specific heat of the metal by measuring the temperature increase of the water.

When the unit quantity is specified in mass, the heat transfer equation is:

• Q = mcΔT

where Q is the amount of heat transferred, m is the mass of the sample, c is the specific heat of the substance, and ΔT is the change in temperature. Because the heat transfer for the metal and the water is equal—although with different signs, because heat is lost by the metal and gained by the water—we can express this equivalence as:

• Q_water = –Q_metal

or

• (mcΔT)_water = –(mcΔT)_metal

The specific heat of water is known to be 4.181 Joules per gram per Kelvin (J/g · K or J · g^–1 · K^–1). Because the masses and temperatures of the metals and water will be measured and are therefore known, the only unknown is the value for the specific heat of the metal samples. We can calculate that value by rearranging the preceding formula to:

Required Equipment and Supplies

	goggles, gloves, and protective clothing
	balance and weighing boat
	calorimeter
	thermometer
	graduated cylinder, 100 mL
	test tube (2)
	test tube holder
	beaker, 600 mL
	hotplate
	lead and iron shot (see Substitutions and Modifications)
	water

Substitutions and Modifications

• You may substitute a small Petri dish or similar container for the weighing boat.

• You may substitute a sauce pan or similar container for the 600 mL beaker.

• You may substitute any appropriate heat source for the hotplate.

• You may substitute other forms of lead and iron, as long as the samples fits inside the test tube. Lead shot may be obtained from laboratory supply houses or from sporting goods stores that sell shotgun reloading supplies. (Lead shot used in shotgun shells is an alloy, but contains a high percentage of lead; some shotgun shells use copper-plated steel shot instead of lead shot.) At the expense of some accuracy, you may substitute wheel weights or fishing sinkers for the lead shot. Because these items are often made from a lead alloy rather than pure lead, your experimental results may differ significantly from the values obtained with a pure lead sample. You may substitute small steel nuts or bolts for the iron shot. Sporting goods stores sell lead airgun pellets, which are almost pure lead, and BBs, which are copper-plated steel shot.

Caution

Take care with the hot water and hotplate to avoid burns. Wear splash goggles, gloves, and protective clothing.

Degrees Celsius Versus Kelvins

The SI unit of temperature is the kelvin—not the degree Kelvin, just the kelvin. For all practical purposes one kelvin, abbreviated K, equals one degree Celsius, or 1°C. (I’m so old that I still think of the “C” as meaning centigrade rather than Celsius, so please excuse me if “centigrade” slips in occasionally.) For our purposes, J/g · K and J/g · °C can be considered equivalent.

• c_metal = [(mcΔT)_water ÷ –(mΔT)_metal]

Plugging in the known and experimentally determined values on the right side of the equation gives us the unknown value for the specific heat of the metal on the left side. This works both ways. If we happened to have a known value for the metal but not a known value for the specific heat of water, we could rearrange the equation slightly and solve for the specific heat of water.

If you look up published values for specific heat, keep in mind that specific heat can be specified on a mass basis, as we are doing in this laboratory, or on a mole basis. Mass-based specific heat values are represented by a lowercase c; mole-based specific heat values are represented by an uppercase C. These values can differ greatly. For example, the C (mole-based) specific heats of lead and iron are quite similar, at 26.4 and 25.1 J/mol · K, respectively, while the mass-based specific heat of lead, at 0.127 J/g · K, is less than one third the mass-based specific heat of iron, at 0.450 J/g · K.

You may also see specific heat values represented as c_p, c_v, C_p, or C_v. The subscript indicates whether the specific heat value is specified at constant pressure or constant volume, which is particularly important if you are measuring the specific heat of a gas. The difference between specific heat values at constant pressure versus constant volume is small for solids and liquids, and can be ignored for our purposes.

Procedure

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

2. Fill the 600 mL beaker nearly full of hot tap water, add a boiling chip, place the beaker on the hotplate, and bring the water to a boil. Once the water boils, turn down the temperature of the hotplate until the water just maintains a gentle boil.

3. Pour lead shot into one test tube until it is about half full. We’ll be immersing the test tube in the boiling water, and it’s important that the level of the lead shot in the test tube be well below the surface of the boiling water bath.

4. Place the weighing boat on the balance and tare the balance to read 0.00 g.

5. Transfer the lead shot from the test tube into the weighing boat and determine its mass. Record the mass of the lead shot on line A of Table 15-3.

6. Transfer the lead shot back into the test tube and immerse the test tube in the boiling water bath, making sure that none of the water is transferred into the test tube. If necessary, clamp the test tube in place to secure it.

7. Repeat steps 3 through 6 with the iron shot.

8. Measure the temperature of the boiling water bath to 0.1°C and record that value on line B of Table 15-3.

9. Keep the test tubes in the boiling water bath for at least 10 to 15 minutes, by which time the lead and iron shot will have reached the temperature of the boiling water bath. While you wait for the shot in the two test tubes to equilibrate to the temperature of the boiling water bath, set up your calorimeter.

10. Use the graduated cylinder to measure about 50.0 mL of cold tap water to 0.1 mL, and add the water to the calorimeter. Record the volume on line C of Table 15-3.

11. Measure the temperature of the water in the calorimeter to 0.1°C and record that value on line D of Table 15-3.

12. Using the test tube holder, remove the test tube of lead shot from the boiling water bath, transfer the lead shot into the calorimeter, and replace the cover of the calorimeter.

13. Swirl or stir the contents of the calorimeter, and measure the temperature of the water inside it. When the temperature peaks, record that value to 0.1°C on line E of Table 15-3.

14. Empty the calorimeter, and repeat steps 10 through 13 with the steel shot.

Disposal

Dry the lead and iron shot and save them for future use.

Optional Activities

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

• Repeat the experiment using different types of metal shot, such as aluminum, copper, magnesium, tin, and zinc.

• Repeat the experiment using alloyed metals rather than pure metals. For example, you might try solder (lead/tin), brass (copper/zinc), nickel silver (copper/nickel), bronze (copper/tin), and so on. Solder is a good choice, because the label usually gives the percentages of lead and tin in the solder. Measure the specific heat for the alloy and compare it to the specific heats for the component metals to determine whether the specific heat of the alloy is directly proportional to the specific heats of the component metals.

• Repeat the experiment using mineral oil, vegetable oil, motor oil, or a similar liquid in place of water. Using either published or your experimental values for the specific heat of lead, calculate the specific heat of the liquid.

Review Questions

Q:

Q1: Using your experimental data for the lead shot and iron shot, calculate the specific heat of lead and iron in J/g · °C and record your calculated values on line G of Table 15-3.

_______________________________________________________________________________

Table 15-3. Determine the specific heat of a metal—observed and calculated data

Item	Lead	Iron
A. Mass of shot	_________.___ g	_________.___ g
B. Temperature of water bath	_________.___ °C	_________.___ °C
C. Volume of water	_________.___ mL	_________.___ mL
D. Temperature of water (initial)	_________.___ °C	_________.___ °C
E. Temperature of water (final)	_________.___ °C	_________.___ °C
F. Temperature change (E – D)	_________.___ °C	_________.___ °C
G. Specific heat	___._____ J/(g · °C)	___._____ J/(g · °C)

Q:

Q2: The actual values for the specific heat of lead and iron are 0.127 J/g · °C and 0.450 J/g · °C, respectively. Calculate the percent error of the value you obtained experimentally.

_______________________________________________________________________________

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Q:

Q3: Propose several possible explanations for experimental error.

_______________________________________________________________________________

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Q:

Q4: After completing this laboratory, a student learned that her digital thermometer consistently reads 0.8°C high. What effect did this error have on the specific heat values that she determined experimentally? Why?

_______________________________________________________________________________

_______________________________________________________________________________

_______________________________________________________________________________

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Q:

Q5: After completing this laboratory, a student learned that his graduated cylinder consistently delivered 5% less liquid than indicated. What effect did this error have on the specific heat values that he determined experimentally? Why?

_______________________________________________________________________________

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Laboratory 15.4: Determine the Enthalpy Change of a Reaction

Chemical reactions absorb or release energy, usually in the form of heat (also called thermal energy). Endothermic reactions absorb heat; exothermic reactions release heat. If the reaction occurs in a solution in a calorimeter, the heat absorbed (or released) by the reaction reduces (or increases) the temperature of the solvent. This heat transfer to or from the solvent can be quantified with the familiar formula:

• Q = mcΔT

or, if water is the solvent:

• Q = (mcΔT)_water

where Q is the amount of heat transferred, m is the mass of the water, c is the specific heat of water, and ΔT is the change in temperature of the water. With known values for the mass and specific heat of water and ΔT determined experimentally, the value of Q can be calculated. (Remember that Q for an exothermic reaction is a negative value.) Q may be expressed in the traditional units of calories (cal) or in SI units of joules (J). The calculation is the same in either case. Only the units for the specific heat of water (c) are different:

• c_water = 1.00 cal/(g · °C)

• c_water = 4.18 J/(g · °C)

In this laboratory, we neutralize 50.0 mL of 1.0 M sodium hydroxide solution with an equal volume of 1.2 M hydrochloric acid solution. (We use a slight excess of HCl to ensure that all of the sodium hydroxide is consumed by the reaction.) The balanced equation for this reaction is:

• HCl_(aq) + NaOH_(aq) → H₂O + NaCl_(aq)

This reaction is exothermic, so the final temperature of the solution is higher than the starting temperature, and the value of Q is negative. Because the starting and final solutions are dilute, we can as a working approximation assume that their density is the same as that of water, 1.00 g/mL, which simplifies calculations. Filling in the known values gives us:

• Q = [100 g] · [1.00 cal/(g · °C)] · [ΔT]

Required Equipment and Supplies

	goggles, gloves, and protective clothing
	calorimeter
	thermometer
	graduated cylinder, 100 mL
	sodium hydroxide (NaOH) solution, 1.0 M (50 mL)
	hydrochloric acid (HCl) solution, 1.2 M (50 mL)

Substitutions and Modifications

• You can prepare 50 mL of 1.0 M sodium hydroxide solution by dissolving 2.00 g of sodium hydroxide in about 40 mL of water in a small beaker and then making it up to 50.0 mL in your graduated cylinder. Allow the sodium hydroxide solution to cool to room temperature before using it.

• You can prepare 50 mL of 1.2 M hydrochloric acid solution by adding 5.0 mL of concentrated (37%, 12 M) hydrochloric acid to about 35 mL of water in a small beaker and then making it up to 50.0 mL in your graduated cylinder. If you use hardware-store muriatic acid (typically 31.45% or 10.3 M HCl), add 5.8 mL of the acid to about 35 mL of water in a small beaker and then make it up to 50.0 mL in your graduated cylinder. Sodium hydroxide is the limiting reagent in this experiment, so the exact molarity of the hydrochloric acid is not critical, as long as HCl is in excess. Allow the hydrochloric acid solution to cool to room temperature before using it.

• If you already have 1.0 M stock solutions of sodium hydroxide and hydrochloric acid made up, you can use them. Make sure the HCl is slightly in excess. For example, use 45.0 mL of 1.0 M sodium hydroxide and 55.0 mL of 1.0 M hydrochloric acid.

Once we determine ΔT experimentally, plugging that value into the equation gives us the value of Q—the amount of thermal energy transferred. Determining the enthalpy change requires one more step. Q is denominated in calories or Joules, and the enthalpy change of reaction, ΔH°_reaction, is denominated in calories per mole or Joules per mole. To determine the enthalpy change of reaction, ΔH°_reaction, we need to divide Q, the heat of reaction we observe experimentally, by the number of moles that yielded that value of Q. (If we had a large calorimeter and reacted 1.0 mole of sodium hydroxide, the values of Q and ΔH°_reaction would be equal. Because we’re reacting only a small fraction of a mole of sodium hydroxide, the absolute value of ΔH°_reaction will be much larger than Q.)

Caution

Sodium hydroxide and hydrochloric acid solutions are corrosive and toxic, including the dilute solutions used in this laboratory. Wear splash goggles, gloves, and protective clothing.

Procedure

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

2. If you have just made up the sodium hydroxide solution and/or the hydrochloric acid solution, make sure that both are at room temperature before proceeding.

3. Use a clean, dry graduated cylinder to accurately measure 50.0 mL of 1.2 M hydrochloric acid, transfer it to the calorimeter, and replace the lid of the calorimeter. Record the volume of HCl solution on line A of Table 15-4. (Although the exact molarity of the hydrochloric acid is unimportant, it is important to record the volume of the HCl solution that you use as accurately as possible.)

4. Measure the temperature of the HCl solution to 0.1°C and record the temperature on line B of Table 15-4.

5. Rinse and dry the graduated cylinder, and then use it to accurately measure 50.0 mL of 1.0 M sodium hydroxide solution. Record the volume on line C of Table 15-4.

6. Rinse and dry the thermometer and then use it to measure the temperature of the sodium hydroxide solution to 0.1°C. Record the temperature on line D of Table 15-4. (The temperature of both solutions should be the same, but if they are not, you can average the two temperatures to arrive at a valid initial temperature. For example, if you start with 50.0 mL of hydrochloric acid at 22.3°C and 50.0 mL of sodium hydroxide solution at 21.1°C, your actual starting point is 100.0 mL of solution at 21.7°C.)

7. Remove the lid of the calorimeter, quickly add the sodium hydroxide solution, and replace the lid.

8. Stir the contents (or swirl the calorimeter gently) to mix the solutions thoroughly. Observe the temperature of the mixed solutions for several minutes until the temperature reaches its highest point. Record that temperature to 0.1°C on line E of Table 15-4.

Optional Activities

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

• Repeat the experiment using 1.2 M sulfuric acid in place of the 1.2 M hydrochloric acid. Look up the published value for the enthalpy change of reaction in the CRC handbook or an online reference and compare the known value to your experimentally determined value.

• Repeat the experiment using 1.2 M acetic acid in place of the 1.2 M hydrochloric acid. Look up the published value for the enthalpy change of reaction in the CRC handbook or an online reference and compare the known value to your experimentally determined value.

Table 15-4. Determine the enthalpy change of a reaction—observed and calculated data

Item	Data
A. Volume of HCl solution	_________.___ mL
B. Temperature of HCl solution	_________.___ °C
C. Volume of NaOH solution	_________.___ mL
D. Temperature of NaOH solution	_________.___ °C
E. Temperature of solution (final)	_________.___ °C
F. Temperature change [E – (B+D)/2]	_________.___ °C
G. Heat of reaction	_________.___ cal
H. Moles of sodium hydroxide	____.________ mol
I. Enthalpy change of reaction	_________.___ cal/mol

Review Questions

Q:	Q1: Calculate the heat of reaction and enter the value on line G of Table 15-4. (Hint: remember to use the proper sign.)
Q:	Q2: Calculate the number of moles of sodium hydroxide that reacted and enter that value on line H of Table 15-4.
Q:	Q3: Calculate the enthalpy change of reaction and enter that value on line I of Table 15-4.
Q:	Q4: Using the known value for enthalpy of reaction, calculate the percent error in your experimental results. (Use the proper sign.) _______________________________________________________________________________ _______________________________________________________________________________
Q:	Q5: Propose several possible reasons for the experimental error that you calculated in the preceding question. _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________

Disposal

The waste solution in the calorimeter contains only sodium chloride (table salt) and a small amount of hydrochloric acid. Dump it down the sink and flush with plenty of water.