# EXPERIMENT 7:  DETERMINATION OF THE SPECIFIC HEAT OF A METAL

Lansing Community College General Chemistry Laboratory I

LEARNING OBJECTIVE

Determine the specific heat capacity of a metal using a coffee cup calorimeter.

## INTRODUCTION

Heat is a form of energy that is transferred between objects with different temperatures. Heat always flows from high temperature to low temperature. The amount of heat absorbed or released (q) by the object depends on its mass (m), specific heat (Cs), and the change in temperature (ΔT).

Specific heat can be defined as the amount of heat required (q) to raise the temperature of one gram of the substance by one degree Celsius.

Equation 1

Rearranging Equation 1:                                                                                                                                                   Equation 2

Each pure substance has a specific heat that is a characteristic physical property of that substance. The specific heats of some common substances are provided in Table 1.

Table 1. Specific Heat of Some Common Substances

 Substance Specific heat (J/g°•C) Water 4.184 Wood 1.76 Concrete 0.88 Mercury 0.14 Iron 0.451 Copper 0.385

The magnitude of specific heat varies greatly from large values like that of water (4.184 J/g°•C) to small values like that of mercury (0.14 J/g°•C). When equal masses of objects are heated to absorb an equal amount of heat, the object with smaller the specific heat value would cause the greatest increase in temperature.

Heat energy is either absorbed or evolved during nearly all chemical and physical changes. If heat is absorbed or enters the system, the process is endothermic and if heat is evolved or exits the system, the process is exothermic. In the laboratory, heat flow is measured in an apparatus called a calorimeter. A calorimeter is a device used to determine heat flow during a chemical or physical change. A doubled Styrofoam cup fitted with a cover in which a hole is bored to accommodate a thermometer can serve well as a calorimeter (See Figure 7.1.)

Figure 7.1 Coffee Cup Calorimeter

In this experiment you will heat a known mass of a metal to a known temperature and then transfer it to a calorimeter that contains a known amount of room temperature water (Tc). The maximum temperature reached by the water in the calorimeter (Tmax) will be recorded and the temperature change of the water (Tmax - Tc) and the temperature change of the metal (100.0°C - Tmax) calculated.

The flow of energy (heat) between a metal and its environment is described by Equations 3 and 4.

|qlost by metal|= qgained by water + qgained by calorimeter                                                                                                                                                 Equation 3

mmetal x Csmetal  x |Tmax – 100.0°C| = [mwater x Cswater  x (Tmax – Tc)] + [15.9  x  (Tmax – Tc)]

Equation 4

(Note: heat capacity of coffee cup is calorimeter = 15.9 J/°C)

Rearranging Equation 4 to solve for the specific heat of the metal:

Csmetal =                      Equation 5

### EXPERIMENTAL PROCEDURE

This experiment is done in a team of two. Place 200 mL of room temperature water from a carboy in a 250 mL beaker and set it aside for later use. Next place about 250 mL of tap water into a 400 mL beaker. Add 4-5 boiling chips into the tap water to prevent bumping. Bring the tap water to a gentle boil using a hot plate.  Obtain three clean dry 18 by 175 mm test tubes. Label them runs 1 – 3. Tare one of the test tubes in a beaker. Carefully add about 30 g of the metal sample to the test tube and record the mass of the metal in DATA TABLE I. While you are at the balance, mass two additional samples into the test tubes 2, and 3. Put all the three test tubes containing the unknown metal in the water bath. Heat to boiling, and then maintain the temperature for about 5 minutes. Assume that the temperature of the metal is 100.0°C after it has been in the boiling water bath for at least 5 minutes.

While the metal is being heated, obtain two Styrofoam cups, a lid, a thermometer and a timer. Using a graduated cylinder, measure 50.0 mL of the room temperature water and transfer into the double Styrofoam cup. Allow 5 minutes for this system to reach thermal equilibrium.  After 5 minutes, record the temperature of the water, Tc, in DATA TABLE I and in DATA TABLE II for time 0 seconds.

Using a test tube holder, lift the test tube containing the heated metal from the boiling water bath. Quickly remove the lid and pour the hot metal (labeled run 1) into the calorimeter. Make sure no hot water from the outside of the test tube drips into the calorimeter. Replace the lid of the calorimeter and the thermometer. Swirl the system gently. Record the temperature every 5 seconds for a minute and then every 15 seconds for about 2-3 minutes or until you observe a maximum temperature (Tmax) for about four consecutive readings. Continue to swirl the calorimeter gently while recording temperatures. Drain the metal and water into a large filter funnel in the hood. Repeat the above procedure using two additional samples. Dry the calorimeter between each trial.

Plot time (x- axis) vs. temperature time for each of the three runs using Excel. Please combine all three runs on one graph. Column A is time and columns B, C, and D will be temperatures for Runs 1-3. Give the graph a title and label the x and y axes. Determine the Tmax from the graph and label it on the graph by inserting a double headed arrow shape Figure 7.2.

Figure 7.2

Finally, calculate the specific heat of the metal using Equation 5.

#### Clean Up & Waste Disposal

1. Pour the metal sample and warm water into the labeled bottles fitted with funnels in the hood.
2. Wash the test tubes and place them in the tray next to the oven.
3. Please turn off the digital thermometers, and the timer. Return them to the side bench.
4. Shut down the laptop computer and return it to its numbered space in the Dry-Dock. Plug in the correct laptop charging cable.
5. Carefully unplug the hot plate and leave it out on the bench.
6. Please clean the bench top with a moist paper towel

### CALCULATIONS

1. Determine the change in temperature, Tmax – Tc for water.

Tc = Temperature of the cold water in the coffee cup before the metal was dropped

Tmax = Final temperature of the water after the metal was dropped into the coffee cup

1. Determine the absolute value for the change in temperature of the metal, |TMax – 100.0°C|.
2. Use Equation 5 to calculate the specific heat capacity of the unknown metal.

Csmetal =                  Equation 5

= mass of water in grams

= mass of metal in grams

## DATA SHEET FOR EXPERIMENT 7 – DETERMINATION OF THE SPECIFIC HEAT OF A METAL

Your Name: ______________________      Lab Partner Name: _______________________

DATA TABLE I (2 pts.)

(Record the measurements with units and the correct number of significant figures.)

 Quantity Run 1 Run 2 Run 3 Volume of water in the calorimeter 50.0 mL 50.0 mL 50.0 mL Mass of metal Temperature of metal 100.0 °C 100.0 °C 100.0 °C Temperature of water in calorimeter, Tc Maximum Temperature, Tmax Temperature change of the cold water, Tmax - Tc

DATA TABLE II (2 pts.)

 Time Seconds Temperature °C Run 1 Temperature °C Run 2 Temperature °C Run 3 0

Plot time (x-axis) vs. temperature for each of the three runs in DATA TABLE II using Excel. Give each graph a title and label the x and y axes.  Mark the ∆T’s (Tmax – Tc) on your graph. (2 pts.)

TABLE III – Tabulated Results (2 pts.)

 Quantity Run 1 Run 2 Run 3 Calculated specific heat Average specific heat Average deviation Known specific heat 0.222 J/g oC Relative % error for average specific heat

Calculations: Show your calculations below. Be sure to include units in your set up and report your answer to the correct number of significant figures.

1. Calculated Specific heat for Run 1: (2 pts.)

1. Average Specific heat: (1 pt.)

1. Average deviation: (2 pts.)

1. Relative % error for average specific heat: (1 pt.)

## POST LABORATORY for EXPERIMENT 7 - DETERMINATION of the SPECIFIC HEAT of a METAL

Name: _________________________________________

1. Discuss the precision and accuracy of your specific heat determination. Use your calculated average deviation and relative error in your discussion. (An average deviation of 0.02 J/g°C and a relative error of less than 10% are considered good in this experiment.) (4 pts.)

1. Explain clearly how the two errors below would increase or decrease your calculated value for specific heat by referring to the equation:

Error #1:  The student used 25.372 g for this experiment but recorded 23.372 g in the data table and used the incorrect value when calculating the specific heat. (Hint:  the error is using the 23.372 g data point.) (2 pts.)

Error #2:  The initial temperature of the metal was 98 °C, not 100 °C, as we have assumed.  (Hint:  The error is using the 100 °C.) (2 pts.)