Calorimetry: Specific Heat of a Metal

EXPERIMENT IV

CALORIMETRY: SPECIFIC HEAT OF A METAL

OBJECTIVES

To learn about the operation of the Tirrill burner.

To determine the specific heat of a metal using calorimetry.

To then attempt to identify the metal using the Law of Dulong and Petit.

REFERENCE

Introductory Chemistry by Charles H. Corwin, pages 75-82.

INTRODUCTION

Heat is a form of energy (thermal energy) which flows spontaneously from a region of high temperature to a region of low temperature. Two objects that start out at different temperatures will reach the same temperature (equilibrium temperature) when brought into contact with one another. If the two objects are isolated from their surroundings, the amount of heat which flows from the hot object must equal the amount of heat which enters the cold object. The study of heat (or energy) flow is called thermodynamics.

Figure 4.1The Tirrill Burner.

Heat flow may be measured in a device called a calorimeter. A calorimeter is a vessel which has insulating walls: within the calorimeter, heat may move from one part of the calorimeter to another, but no heat flows into or out of the calorimeter. Inside this device, a sample of hot metal will be placed in thermal contact with a sample of cold water. Since the specific heat of water is known, the specific heat of the metal may be calculated. The Law of Dulong and Petit will provide an approximation to the molar mass of the metal and hence its identity. To raise the temperature of the metal sample, a Tirrill burner will be employed. Before its usage, the design and safe operation of this common and important laboratory instrument must be discussed.

The Tirrill Burner

The Tirrill Burner is a gas burner that has four main features (Figure 4.1). The barrel of the burner is supported by the base. In the barrel of the burner, natural gas and air are mixed for combustion. At the base of the barrel, openings are provided for air to enter. Turning the barrel clockwise closes the air intakes while counterclockwise turns open them. The gas inlet valve regulates the flow of gas into the barrel. Gas flow increases by turning the thumbscrew counterclockwise and decreases by turning clockwise (facing the knurled knob). By properly adjusting the air intake and the gas inlet, the proper ratio of air to gas can be maintained in the barrel so that the chemical reaction is most efficient.

The following equation represents a chemical reaction when the gas (methane, CH4) combines with oxygen (O2) from the air

CH4 + 2O2 → CO2 + 2H2O + heat

The products of this reaction are carbon dioxide (CO2), water (H2O), and heat. From the balanced equation, it is noted that one methane molecule combines with two oxygen molecules. For this to occur, the gas to air ratio must be properly adjusted. Then, the flame at the top of the barrel will have a characteristic blue color. If less oxygen is available in the barrel, the reaction may proceed as

CH4 + O2 → C + 2H2O + heat

There are two important aspects to this equation. First, the amount of heat produced is much less than that generated in the first reaction. Second, the change in the ratio of the combining reactants has changed which products are formed. The second reaction can be achieved by closing the air intakes completely. In this instance, the flame has the characteristic yellow color caused by the presence of carbon.

When lighting a burner, always use the procedure given as follows. First, connect the burner to the gas jet on the bench top with rubber tubing. Close the gas inlet valve on the burner by turning the screw clockwise as far as possible. Next, open the gas valve on the bench top completely. Note that the gas valve is completely open when the handle is parallel to the nozzle. It is completely closed when the handle is perpendicular to the nozzle. Open the gas inlet valve on the burner until gas is entering the barrel. The gas can be detected from the sound that the gas flow makes or by the odor (although methane is odorless, a small amount of a foul-smelling chemical has been added for your benefit). Light the burner with a striker at the top of the barrel. Adjust the air intakes until a blue flame is obtained. The height of the flame can be controlled by changing the gas and air content in the barrel. If the flame will not stay lit, there is likely too much air in the mixture, and it is “blowing itself out”. Partially close the air intake valves and reignite. When the flame is properly lit, its hottest point is located at the tip of its inner, lighter-blue cone.

Temperature

Temperature is the property of a system that determines the direction of heat flow and any temperature change must be accompanied by a flow of heat. At the molecular level, temperature is a measure of the average energy of individual particles of the system; at the macroscopic level, temperature is measured using a thermometer. Temperature measurements are particularly important in calorimetry experiments and the quality of your results will depend on your ability to accurately measure temperature to the correct number of significant figures. The markings on the thermometers in lab are based on the Celsius scale of temperature. Ice freezes at 0.0 oC, room temperature is often between 20.0 oC (which equals sixty-eight degrees Fahrenheit) and 25.0 oC (= 77 oF), and water normally boils at 100.0 oC (because of variations in atmospheric pressure, the temperature of boiling water may vary slightly). Before measurement, the temperature should be the same throughout the container. This may be accomplished by gentle swirling or stirring, but you must not use a thermometer as a stirrer. To obtain an accurate reading, the thermometer should not touch the sides or bottom of the container. Finally, please remember that these thermometers should not be shaken before use.

As stated earlier, heat flows from an object at high temperature to an object at low temperature spontaneously. When a sample of metal is heated to a high temperature thigh and placed in a calorimeter with a sample of water at a low temperature tlow, heat flows from the metal to the water. With the loss of heat, the temperature of the metal decreases. Conversely, with a gain of heat, the temperature of the water increases. The temperature of the metal keeps decreasing and the temperature of the water keeps increasing until the metal and the water are at the same temperature. When the two samples reach this equilibrium temperature teq, the net flow of heat ceases. The magnitude of the temperature change of the metal tmetal will be given by

tmetal = thigh - teq

Note that with this definition, tmetal is a positive quantity. The sample of water will have undergone a temperature change twater given by

twater = teq - tlow

While the metal and water both have the same final temperature, they do not necessarily undergo the same temperature change. Instead, the final temperature is determined by the requirement that the same amount of heat must leave the metal as enters the water. The temperature change produced by this transfer of heat depends on the mass of the substance and on the specific heat of the substance (somewhat like thermal inertia).

Specific Heat

Specific heat is defined as the amount of heat (energy) required to change the temperature of one gram of a substance by one degree Celsius. When the unit of heat is calories (cal), specific heat has the units of cal/g oC. Mathematically,

specific heat (sh) = heat transferred / (mass)(temperature change)

The mass of the metal can be measured using a balance, the temperature change of the metal can be measured using a thermometer, and the amount of heat can be measured using calorimetry.

Calorimetry

When the hot metal and the cold water are isolated in the calorimeter, the amount of heat entering the water qwater is the same as the amount of heat leaving the metal

qmetal = qwater

This is the fundamental equation of calorimetry (in practice, this relation is only approximate because a small amount of heat will be lost both to and through the calorimeter). By rearranging the equation above defining specific heat

heat transferred = mass x specific heat x temperature change

the heat entering the water can be calculated from

qwater = (mwater)(shwater)(∆twater)

where mwater is the mass of the water and shwater is the specific heat of water. The specific heat of water is 1.00 cal/g oC. This is not an accident. Initially, the specific heat of water was chosen to be exactly 1.00 cal/g oC. This defined the calorie as the amount of heat necessary to raise the temperature of one gram of water one Celsius degree.

Likewise, the amount of heat leaving the metal can be calculated from

qmetal = (mmetal)(shmetal)(∆tmetal)

where mmetalis the mass of the metal andshmetal is the specific heat of the metal.

Using the fundamental equation of calorimetry where it is stated that heat lost is equal to heat gained yields the following.

(mmetal)(shmetal)(∆tmetal) = (mwater)(shwater)(∆twater)

All quantities are known with the exception of the specific heat of the metal. Mathematical rearrangement gives the equation for the unknown specific heat.

Shmetal = ()(Shwater)()

The Law of Dulong and Petit

For metals, there is an old relationship called the Law of Dulong and Petit which relates the atomic mass of a metal to its specific heat

molar mass ≈ 6.2 cal/mol ºC / (specific heat)

When the specific heat has units of cal/g oC, the atomic mass will have units of g/mol. By comparing the experimental result to atomic masses listed in a periodic table (one is available at the back of your lab manual), it may be possible to tell which metal was used in the experiment. Of course, the identification is only tentative because of the approximate nature of the relation and the possibility of experimental error.

EXERCISES

1.A 125.0 g piece of metal with specific heat 0.219 cal/g oC is heated from an initial temperature of 18.00 oC to a final temperature of 27.00 oC. How much heat was absorbed? (ans: 246 cal)

2.How many grams of water can be heated from 28 oC to 73 oC with 500.0 calories of heat?

m = q / (sh)(Δt) = (500.0cal) / (1.00cal/gºC)(73ºC - 28ºC) = 11g

3.When 300.0 calories of heat are added to 32.5 g of copper (specific heat of 0.0920 cal/g oC), what is the temperature change?

∆t = q / (sh)(m) = (300.0cal) / (0.0920cal/gºC) X (32.5g) = 100.ºC

4.A sample of metal has a mass of 1.75 kg and a specific heat of 0.115 cal/g oC. What is the temperature change of the metal after 625 calories of heat are added? (ans: 3 oC)

5.If 120.0 g of copper at 100.0 oC is added to 28.6 grams of water at 26.5 oC, what is the final equilibrium temperature?

qmetal = qwater

(mmetal)(shmetal)(∆tmetal) = (mwater)(shwater)(∆twater)

(0.0920 cal/gºC) x (120.0 g) x (100.0 ºC - teq) = (1.00 cal/gºC) x (28.6 g) x (teq - 26.5 ºC)

1104 ºC - (11.04 teq) = (28.60 teq) - 757.9 ºC

1862 ºC = 39.64 teq

teq = 46.97 ºC = 47.0 ºC

6.If 74.7 grams of copper at 100 oC are added to 42.5 g of water at 18 oC, what is the final equilibrium temperature of the system? (ans: 29.4 oC)

PROCEDURE

SAFETY GOGGLES MUST BE WORN WHILE WORKING IN THE LABORATORY

1.Place a 400 mL beaker ½ full with water on the tripod with wire gauze under it. While doing the next two steps, heat to boiling with the Tirrill burner.

2.Place the calorimeter (2 nested Styrofoam cups) on the balance and tare the balance. Add about 30 g of distilled water with a wash bottle. Accurately record the mass of water on your data sheet.

Figure 4.2Test tube assembly.

3.Place a weighing boat on the balance and tare the balance. Add half of the metal sample to the boat (but no more than 75 g). Accurately record the weight of the metal and the unknown number on the data sheet. Transfer the metal to a large dry test tube. Tighten a clamp near the top of the test tube (Fig. 4.2).

4.Place the tube with metal into the boiling water in the 400 mL beaker. The level of the water should be 3 cm above that of the metal in the tube. Measure and record the temperature of the hot metal to the nearest 0.1 oC with the digital thermometer when the temperature has stabilized near 100 oC. The tip of the thermometer should be at least 2 cm below the surface of the metal.

5.Remove the thermometer from the metal, cool it with tap water, then dry the thermometer. Place the thermometer in the calorimeter cup through the hole in the lid (Fig. 4.3). Gently swirl the water (don't spill any!) around the thermometer. Measure and record this initial temperature value to the nearest 0.1 oC. Do not remove the thermometer.

6.Use the clamp to handle the hot test tube. Remove it from the boiling water, blot off any water. Open the lid with thermometer in place. Quickly but carefully (no splashing) pour the metal into the water in the calorimeter. Immediately replace the lid with thermometer and swirl gently. Observe the rise in temperature and record the maximum temperature attained by the water as the final (equilibrium) temperature.

7.WITHOUT LOSING ANY METAL PIECES, drain as much water as possible from the cup. Let the pieces of metal dry on a paper towel by your lab station, or place the metal as directed by your instructor Do NOT mix different metals under any circumstances. Dry the inside of the calorimeter with a paper towel.

Figure 4.3Calorimeter assembly.

8.Repeat steps 1-7 with the other half (no more than 75 g)of your metal sample and a fresh supply of water.

9.Turn off the gas supply. Calculate the specific heat of the metal. Use the Law of Dulong and Petit to determine the approximate molar mass of the metal employed in the experiment. Use the molar mass and the appearance of the metal to guess its identity.

LABORATORY DATA SHEET

Specific Heat of a MetalUnknown Number ______

Trial / I / II
Mass of water (mwater)
Mass of metal (mmetal)
Initial temperature of metal (thigh)
Initial temperature in calorimeter (tlow)
Final temperature in calorimeter (teq)
twater = teq - tlow
tmetal = thigh - teq
Specific heat of water (shwater) / 1.00 cal/g oC / 1.00 cal/g oC
Specific heat of metal (shmetal)
Molar mass of metal
Appearance of metal
Identity of metal

Calculations:

shmetal = ()(shwater)()

Mmetal =

LABORATORY REPORT SHEET

EXPERIMENT IV: CALORIMETRY

Name______

Date______

Partner______

Section______

Specific Heat of a MetalUnknown Number ______

Sample Calculations: