Forces and Bonding: Heat Capacity

• To understand the meaning of heat capacity
• To use heat capacity to relate heat flow to temperature change
• To determine relative heat capacities for a number of pure substances.

When heat is added to a quantity of a pure substance in a certain phase (that is, solid, liquid, or gas), the temperature of the sample increases by an amount that depends upon the size of the sample and the inherent "capacity for heat" that characterizes the substance. Thus addition of 10 J of heat to a gram of water raises the temperature of the water by 2.4 Kelvins. In contrast, addition of the same amount of heat to a gram of copper raises the temperature by a much larger a mount, 26 Kelvins. The quantity of heat (energy) required to raise the temperature of 1.00 g of a pure substance by 1.00 Kelvins is called the specific heat capacity, C_s, of the substance. Similarly, the quantity of heat required to raise the temperature of 1 mole of substance by 1 Kelvin is called the molar heat capacity, C_m. These two quantities are related through the molar mass of the substance:

The relationship between heat added to a substance, heat capacity, and temperature change can be expressed as follows:

or

Both equations say that the amount of heat that must be added increases as the amount of substance increases and as the desired temperature change increases. This is quite reasonable.

Because heat added under conditions of constant pressure corresponds to the change in enthalpy of the system, we may substitute DH for q above. Then

This gives us the enthalpy change of a sample of substance when its temperature is changed by an amount DT.

The purpose of this experiment is to explore the relative molar heat capacities of a number of pure substances by measuring temperature changes.

• energy gained by calorimeter and water = energy lost by added hot water
  (C_cal + C_wM_w,cal)DT_cal = -C_wM_w,hotDT_water (5)

• energy gained by calorimeter and contents = energy lost by added hot water
  (C_cal + C_wM_w,cal + C_subM_sub,cal)DT_cal = -C_wM_w,hotDT_water (6)

In these equations,

1. In calorimetry with distilled water, do the final temperatures agree with what you would predict? Why not?
2. Use the class data from calorimetry with distilled water to determine the heat capacity of the calorimeter.
3. Using the observed temperature changes, determine the heat capacities of your assigned unknowns relative to that of water.

• analytical balance
• Calorimeter with stirrer
• 2 thermometers
• plastic powder funnel
• 50-mL graduated cylinder
• Nested styrofoam cups
• Foam cover for cups
• Hot water reservoir (thermos)
• Cold water reservoir (thermos)
• distilled water
• copper (pre-1981 pennies will do)
• lead shot
• sand
• glass beads
• acetone
• ethanol

Safety glasses must be worn at all times in the laboratory. You will work with hot water; exercise due caution. Acetone and ethanol should be measured out in a fume hood.

Record all data in your notebook. Your instructor will assign you a pure substance other than distilled water to study, and three target temperature differentials. Please write these down in your notebook. Suggested target differentials are 15-55 ^oC in 5-degree intervals.

Initial Activities. Obtain a calorimeter equipped with a stirrer, two thermometers, a 50-mL graduated cylinder, 2 nested styrofoam cups, a foam cover for the cups, a 50-mL beaker, and a 250-mL beaker. Into the small beaker, weigh 100 grams of your assigned substance. Fill the large beaker halfway with room temperature distilled water, and place both thermometers in it. Wait at least 1 minute, then read the temperature on both thermometers. They should agree to within 0.5 ^oC. If they do not, write down the temperature difference to use as a correction.

Calorimetry with Distilled Water. You will find in the lab two thermos bottles, one containing hot water and the other cold. Carefully measure 50.0 mL of cold distilled water using the graduated cylinder, and transfer it to the calorimeter thru the funnel. Quickly measure exactly 50 mL of hot water using the graduated cylinder and transfer it to the nested styrofoam cups. Cover the cups and insert the second thermometer. When the hot water has cooled sufficiently to give the desired temperature differential, start timing and record the hot water temperature (to the nearest 0.1 ^oC). After 30 seconds, record the temperature of the water in the calorimeter. Alternately read the hot and cold water temperatures at 30 second intervals for 3 minutes. At the 3.5 minute mark, quickly pour the hot water into the calorimeter thru the funnel. Stir the calorimeter contents completely, and monitor the temperature of the calorimeter contents at 1-minute intervals for at least 5 minutes. A recommended time-temperature protocol is outlined below.

Empty the calorimeter.

Repeat this procedure twice more for your other assigned temperature differentials. Carefully record temperature-time data.

When finished, plot T versus time for all three runs on the same sheet of graph paper (if you have a computer and want to use a spreadsheet, great). The zero of time should be taken as the time of addition of hot water to the calorimeter. From the graph for each run, determine, 1), the temperature of the hot water at t = 0; the temperature in the calorimeter at t =0 before addition of hot water; and the temperature in the calorimeter at t = 0 after addition of hot water. Calculate temperature changes for the calorimeter and the hot water as follows:

DT_cal = T_{cal,final at t = 0} - T_{cal,initial at t = 0}

DT_hot = T_{hot at t = 0} - T_{cal, final at t = 0}

Pool your DT data with that of the class, and construct a collective plot of DT_hot versus DT_cal. Determine the best-fit slope.

Calorimetry with Pure Substances. Prepare the calorimeter by loading it with the pure-substance sample prepared above. Pour exactly 50 mL of cold water into the graduated cylinder, and transfer to the calorimeter thru the funnel. Measure exactly 50 mL of hot water with the graduate, and quickly transfer it to the nested styrofoam cups. When the hot water has cooled sufficiently to give the first temperature differential, begin timing and monitor both the temperature inside the calorimeter and the temperature of the water in the cups in the same manner as above, recording data. At the 3.5 minute mark, quickly add the hot water to the calorimeter. Measure the temperature of the calorimeter contents at 1-minute intervals for at least 5 minutes.

Repeat the procedure for the remaining 2 target temperature differentials. Plot all temperature time data. The zero of time should be taken as the time of addition of hot water to the calorimeter. From the graph for each run, determine, 1), the temperature of the hot water at t = 0; the temperature in the calorimeter at t =0 before addition of hot water; and the temperature in the calorimeter at t = 0 after addition of hot water.

Return all equipment to the instructor. Return all solid samples; they will be reused.

Preparation Questions