AP Chemistry Unit 6

Chapter 6 Thermochemistry

Thermochemistry and Hess’s Law

In this experiment you will determine the empathy change that occurs when sodium hydroxide and hydrochloric acid solutions are mixed. Next, the enthalpy change for the reaction between sodium hydroxide and ammonium chloride will be measured. Lastly, you will determine the enthalpy change for the reaction between ammonia and hydrochloric acid. An algebraic combination of the first two equations can lead to the third equation. Therefore, according to Hess’s law, an algebraic combination of the enthalpy changes of the first two should lead to the enthalpy of the third reaction.

The molecular equations for the reactions are as follows:

(1) NaOH(aq) + HCl(aq) à NaCl(aq) + H₂O(l)

(3) 2NaHCO₃(aq) + HC₂H₃O₂(aq) à Na₂CO₃(aq) + H₂O + CO₂

There is no single instrument that can directly measure heat in the way a balance measures mass or a thermometer measures temperature. However, it is possible to determine the heat change when a chemical reaction occurs. The change in heat is calculated from the mass, temperature change, and specific heat of the substance which gains or loses heat.

The equation that is used to calculate heat gain or loss is:

Q = m C ΔT

Q = (grams of substance) x (specific heat) x (change in temp)

Where Q = the heat energy gained or lost and ΔT is the change in temperature. Since ΔT = (final temperature after minus initial temperature), an increase in temperature will result in a positive value for both ΔT and Q, and a loss of heat will give a negative value. A positive value for Q means a heat gain, while a negative value means a heat loss.

Acid-base neutralization is an exothermic process. Combining solutions containing an acid and a base will result in a rise of solution temperature. The heat given off by the reaction (which will cause the solution temperature to rise) can be calculated from the specific heat of the solution, the mass of the solution, and the temperature change. This heat quantity can then be converted to the enthalpy change for the reaction in terms of kJ/mole by using the concentrations of the reactants.

According the Hess, if a reaction can be carried in a series of steps, the sum of the enthalpies for each step should equal the enthalpy change for the total reaction. Another way of stating “Hess’s Law” is: If two chemical equations can algebraically be combined to give a third equation, the values ΔH for the two equations can be combined in the same manner to give ΔH for the third equation. An examination of the acid-base equations above shows that if equation 2 is subtracted from equation 1, equation 3 will result. Therefore, if the value of ΔH for equation 2 is subtracted from equation 1, the enthalpy change for equation 3 should result. We will test this idea in this experiment.

Chemicals

Hydrochloric acid, HCl, 2.0 M (11.6M) Sodium hydroxide, NaOH 2 M

Baking soda, NaHCO₃(s), Vinegar,2 M (17.4M) HC₂H₃O₂(aq)

Equipment

Magnetic stirrer and stirring bar Graduated Cylinder, 25 or 50 mL Ring, ring stand, wire gauze Beaker Bunsen burner

Calorimeter made of two nested Styrofoam cups and a cover

Thermometer (preferably one that is calibrated 0.1 degrees C)

Fume hood

Procedure

1. Find the heat capacity of the thermometer

Construct a calorimeter of two nested Styrofoam cups with a cover which has a hole in it to accept a thermometer. Measure 50.0 mL of distilled water at room temperature into the calorimeter. Place the assembly on a magnetic stirring motor, add a magnet and turn on the motor so the stirring bar spins slowly. (Alternatively, gently stir the solution with you thermometer.) Heat a second sample of 50 ml of water in a beaker to a temperature greater than 60°C. Allow its temperature to stabilize and record this value. Mix these two samples. Now record the temperature as precisely as you can. Use this data to determine the value of C for the cup.

2. Find the heat of the reactions

Determine the temperature change that occurs when 50.0 mL of 2.0 M HCl solution reacts with 50.0 mL of 2.0 M NaOH. First, measure the temperature of both the solutions. Be sure to rinse and dry the thermometer each time. The solution temperature should agree plus or minus 0.2 degreed Celsius. If they do not agree, you should use the average temperature as your initial temperature.

Measure out 50.0 mL of 2.0 M HCl and put it in the calorimeter. Put a stirring magnet in the solution, and set it moving gently (or stir with your thermometer). Measure out 50.0 mL of 2.0 M NaOH, add it to the acid, quickly cover and insert the thermometer. Record the temperature to the nearest 0.1 degree Celsius after 20 seconds, and every 20 seconds for three minuets.

Repeat the procedure, with the other solutions. Be sure that containers and thermometers are rinsed and dried between reactions.

Calculations

1. Calculate the Heat Capacity of the Calorimeter

a. When equal volumes of hot and cold water are combined, if there is no heat loss the new temperature should be the average of the two starting temperatures. In actual practice, the new temperature will be slightly less than the average because of the heat loss to the calorimeter assembly.

Additionally, when two solutions are mixed the thermometer cannot instantaneously record the temperature of the combined solutions. The solutions require some time to become completely mixed, and the thermometer needs time to come to temperature equilibrium with the solution. The theoretical temperature that the mixture would have if the process occurred instantaneously can be found from a graph.

Plot the data with temperature on the vertical axis versus time on the horizontal axis. The first few points may be erratic because of incomplete mixing and lack of temperature equilibrium with the thermometer. The points that follow should occur in a straight line as the temperature slowly drops while heat is lost to the calorimeter and to the surroundings. Draw a straight line through these points, and extend it back to fine the temperature at time zero, the theoretical instantaneous temperature of mixing, T_mix.

b. The difference between the average temperature, T_avg , and the instantaneous temperature, T_mix, is due to the fact that some heat was lost by water and absorbed by the calorimeter. Calculate q_lost, the heat lost by the water:

q_lost= (grams of water) x (specific heat of water) x (T_{mix -} T_avg)

where q_lost = heat lost by water and the specific heat of water is 4.18 J/(g·degrees C).

The heat absorbed by the calorimeter, q_calorimeter, will be equal to that lost by the water but opposite in sign.

q_calorimeter = -q_lost

c. Calculate the heat capacity of the calorimeter, C_calorimeter, which is the heat that the calorimeter absorbs each time the temperature of the solution changes 1˚C:

2. Calculate ΔH for each reaction.

a. Graph the temperature versus time for each of the three reactions tested. Extrapolate the line back to fond the theoretical instantaneous mixing temperature, T_mix, as you did above.

b. Calculate the amount of heat evolved in each reaction, q_rxn, by assuming that all of the heat is absorbed by the solutions and the calorimeter:

q_rxn=-[heat absorbed by solution + heat absorbed by calorimeter]

q_rxn=-[(grams of solution x specific heat of solution x ΔT_solution ) + (C_calirometer x ΔT_solution)]

where ΔT_solution = (T_{mix -} T_inital) for each reaction mixture. Assume that the density of the solution is 1.03 g/mL, and that the specific heat of the solution is the same as that of the water, 4.18 J/(g·˚C)

c. Calculate the value of the enthalpy change, ΔH, in terms of kJ/mole for each of the reactions.

3. Verify Hess’s law

a. Write net ionic equations for the three reactions involved.

b. Demonstrate calculating the value of ΔH for the three reactions using the product – reactant process

c. Demonstrate calculating the value of ΔH for the three reactions using the additive process

Disposal

The solutions can be flushed down the drain with a 20-fold excess of water. Consult the Flinn Chemical Catalog/Reference Manual, suggested disposal method #26b. See the appendix.

Questions

1. What is meant by ΔH?

2. Define specific heat.

3. The specific heat of a solution is 4.18 J/(g·˚C) and its density is 1.02 g/mL. The solution is formed by combining 20.0 mL of solution A with 20.0 mL of solution B, both initially at 21.4˚C. The final temperature is 25.3˚C. Calculate the heat of reaction assuming no heat os lost to the calorimeter. Use correct significant digits.

4. In problem 3 above, the calorimeter used has a heat capacity of 8.20 J/˚C. If you include a correction for the heat absorbed by the calorimeter, what is the heat of the reaction?

5. State Hess’s Law.

6. What is meant by calorimetry?

7. How does the graphical temperature analysis improve the accuracy of you data?

8. The equation used to find the heat evolved in each reaction is q_rxn= - [(grams of solution x specific heat of solution x ΔT_solution ) + ( C_calirometer x ΔT_solution)]. What is the meaning of the negative sign in the front of the bracket?

9. Do your values support Hess’s Law?

10. How could you modify the method to achieve greater accuracy?

11. Find a table listing standard heats of formation for the species included in your net ionic equations. Use them to calculate ΔH for each of these net ionic equations. Do these values support Hess’s Law?