The heat capacity of a substance is the amount of heat required to raise the temperature of a certain amount of substance by 1° C. Heat capacities may be expressed on a molar basis or a gram basis; in the later case, the heat capacity is known as the specific heat, Cp.
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(1) |
where m is mass, q is heat absorbed, and T is the change of Celsius temperature. The specific heat of a metal sample will be determined in this experiment using calorimetry techniques. Rearrangement of equation (1) shows that the temperature rise in a substance is directly proportional to the amount of heat absorbed:
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(2) |
A calorimeter is a device used to measure the amount of heat transferred during a process. A Dewar flask (vacuum bottle) is used as the calorimeter in this experiment. The insulation of the bottle largely prevents any heat exchange with the surroundings. In a hypothetical ideal case where there is no heat exchange with the surroundings, if a hot object and a cold object are placed in contact with each other inside a calorimeter, heat would flow from the hot object to the cold object until the two are at the same temperature (they are in thermal equilibrium). The amount of heat lost by the hot object would be equal to the amount of heat gained by the cold object. However, in reality the inside of the calorimeter also absorbs some heat. The calorimeter constant, Ccal, is the heat capacity of the calorimeter (units of J/°C). This amount of heat, qcal, absorbed or released by the calorimeter for each one degree change in temperature of the calorimeter.
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(3) |
The calorimeter constant must be determined experimentally for each calorimeter used. There are several ways to do this. In this experiment, hot water will be added to a calorimeter containing cold water:
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(4) |
The heat gained or lost by the water samples may be calculated using the measured temperature change, the mass, and the specific heat, Cp:
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(5) |
The specific heat of water is 4.1814 J/g°C. Equation (5) may be used to determine the calorimeter constant, since all other quantities in the equation are constant or experimentally measurable values. The temperature changes will be determined by a graphical procedure.
Essentially the same technique is used to determine the specific
heat of an unknown metal. The metal sample is heated and added to
cold water in the calorimeter. Time-temperature data are recorded
and graphed to determine the 
values. A heat balance equation similar to (5) is applied, except
that the hot sample is the metal rather than water.
Piere Dulong and Alexis Petit discovered in 1819 that the molar heat capacities of most metals are approximately equal, with an average value of about 26 J/°Cmol. This discovery is called, surprisingly, the Law of Dulong and Petit. This molar heat capacity may be used in combination with the experimentally determined specific heat to estimate the atomic mass of a metal (look at the ration between the two heat capacities).
Calorimeter, 100 mL graduated bylinder, 150 and 400 mL beakers, 51°C and 100°C thermometers, stirring rod, large test tube and test tube clamp, timer, ring stand, ring, wire gauze, burner, jaw clamp, split one-hole stopper, lighter.
Place 100 mL of deionized water in the clean, dry calorimeter. Place the cover on the calorimeter with the wire stirrer in place through the glass tube which passes through the cover. Insert the 51°C thermometer through the other opening in the cover of the calorimeter. Use a small piece of rubber tubing to support the thermometer at a height such that the tip is slightly above the bottom of the calorimeter. Measure and record the temperature of the water to the nearest 0.1°C.
Place another 100 mL sample of deionized water in a clean, dry 150 mL beaker. Heat with occasional stirring to approximately 40°C (remove the burner a little before the target temperature is reached) Place the beaker on an insulating surface (e.g. a book) and suspend the 51°C thermometer in the water such that it does not touch the bottom of the beaker (a split rubber stopper may be placed on the upper end of the thermometer and clamped to the ring stand). Verify that the temperature of the hot water is no longer rising, then start the timer, Record the temperature of the warm water sample to the nearest 0.1°C at 30 second intervals for five minutes.
With the timer still running, rapidly pour the entire hot water sample into the calorimeter and quickly replace the cover. Transfer the 51°C thermometer back to the calorimeter. Record the timer reading at the point of mixing and stir the mixture well. Continue to record time-temperature data at one-minute intervals from the sixth through the fifteenth minute. The mixture should be stirred constantly. When finished, do a second determination.
B. SPECIFIC HEAT DETERMINATIONFill a 400 mL beaker two-thirds full of water and heat to boiling over a burner. Add 50.0 mL of deionized water to a clean, dry calorimeter and record the temperature of the water.
Record the identification number of your unknown metal sample. Remove the cap from the vial and weigh the vial with the metal on the analytical balance. Pour the metal sample into a large, dry test tube and loosely stopper the tube with a piece of rolled paper towel. Reweigh the empty vial.
Suspend the test tube in the water bath so that the tube does not touch the beaker. When the water returns to a boil, heat for at least five minutes. Record the water temperature to the nearest 0.1°C using the 100°C thermometer.
Start a timer and record the temperature of the water in the calorimeter to the nearest 0.01°C (use the 51°C thermometer) at 30 second intervals for five minutes. Quickly remove the test tube from the water bath, wipe the outside dry, and add the metal to the calorimeter. Record the timer reading at the point of mixing and replace the cover. Continue to record time-temperature data at 30 second intervals from the sixth through the fifteenth minute. Stir the contents of the calorimeter continuously.
Pour the contents of the calorimeter into the waste beaker indicated by the instructor. Clean and dry the calorimeter. Obtain a second sample of the metal and carry out a second determination.
For each trial, plot the data on a graph with temperature on the y-axis and time on the x-axis. Use an interrupted temperature scale as in Figure 1 in order to make the size of a degree interval as large as possible. Draw a vertical line at the time of mixing. Draw the best straight lines or smooth curves through each set of points and extrapolate each line to the time of mixing. The intersection of each data line with the vertical line gives the respective initial or final temperature (the assumption is made that the heat transfer occurs instantaneously at the time of mixing, although this is not really true). Determine DThot and DTcold from the graph (as many significant figures as possible). The temperature change for the calorimeter is the same as that for the cold water.
Calculate the mass of each water sample by using the density of water at the temperature at which the volume was measured (initial temperature of the cold water sample). Look up the absolute density of water at the temperature in question in a chemistry handbook; be sure to reference your source.
Calculate the average calorimeter constant for your two trials.
B. Specific HeatDetermine the temperature changes of the metal, water, and calorimeter using graphical techniques for the water temperature as you did in part A. Look up the density of the initial water samples and calculate their masses. Calculate the specific heat of your metal for each trial and the average value. Use the law of Dulong and Petit to calculate the atomic mass of your unknown metal.
Identify your unknown metal in the discussion section of your report. Look up literature values of these quantities.
Figure 1
Determination of Temperature Changes