q (heat) mass x T SpHt (or s)

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1 General Chemistry I CHEM-1030 Laboratory Experiment No. 10 (Revised 10/30/2016) Specific Heat Introduction The specific heat of a substance, symbolized s or SpHt, is the quantity of heat needed to change the temperature of a gram of the substance by one degree Celsius. A given quantity of heat will produce different temperature changes in equal masses of different substances. For instance, it takes less heat to raise the temperature of 1 g of iron by 1 ºC than it does for 1 g of water. In other words, different amounts of heat are required to heat the same mass of different substances through the same temperature range. Specific heat is an intensive property. It is characteristic of the substance being studied and does not depend on the amount of matter present. (Specific heat of some substances may change very slightly with temperature, but that variation is unimportant in most cases.) The specific heat of one physical state of a substance has little relationship to its specific heat in another state. For instance, as Table 1 shows, the specific heat of liquid water is very different from that of water vapor. The equation for specific heat is: SpHt (or s) q (heat) mass x T (Equation 1) When heat in SI joule units, specific heat units are J g -1 ºC -1. In older work, heat was measured in calories and specific heat was expressed with the units cal g -1 ºC -1. Specific Heats of some selected substances, metals and nonmetals, are given in Table 1. Note that the specific heat of liquid water is higher than that of all but one other listed substance. Note also that the two metals listed have specific heats considerably smaller than those of the chemical compounds. Table 1 Substance Specific Heat (J g -1 ºC -1 ) water (gas) water (liquid) water (solid) ammonia (liquid) 4.39 ammonia (solid) 2.09 ethanol (liquid) 2.43 iron(solid) 0.44 gold(solid) 0.14 Table 2 lists specific heat values and other identifying characteristics of the metal unknowns in this experiment. You will identify a sample of an unknown metal in Question 3 of the report from your measured specific heat and the metal s density and appearance. Examine your metal and compare its appearance and your specific heat and density results with the information in Table 2 to identify the metal by name. Note: What we take for the appearance of a metal is sometimes the appearance of an oxide coating. For instance, polished aluminum has a high luster, but weathered aluminum, coated with aluminum oxide, is gray in appearance. 1

2 Table 2, Selected Metal Properties Metal Density (g/ml) Specific Heat (J g -1 ºC -1 ) Physical Appearance Al white with bluish tint Ba silvery-yellow Bi silvery white Co grayish tint Cu lustrous red-brown Fe silvery white (possible rust coating) Mg silvery-white Mn silvery (possible brown oxide coating) Ni lustrous white Sn lustrous silver-white Sr silvery-white Zn lustrous blue-white In this experiment, you will determine the specific heat of an unknown metal in a constant-pressure calorimeter, a simple insulated container open to the air. (Even though the container is open, consider it to be an isolated system. Assume no heat transfer occurs in or out of the system.) You will mix a hot metal sample of known mass and temperature with water also of known mass and temperature. The metal will lose heat to the water and the water will gain heat from the metal. After mixing, the temperature of the water and metal will be the same. The Zeroth Law of Thermodynamics states that in any heat transfer process, heat lost by one part of an isolated system equals heat gained by the rest of the system. This may be expressed as: q1 = - q2 (Equation 2) Equation 2 is the starting point for determining specific heats of many substances since heat gained by one part of a system of known specific heat is the same as heat lost by another part of the system whose specific heat is not known. Rearranging Equation 1 gives Equation 3, the expression for q, heat absorbed by a substance, where m is the sample mass in grams and ΔT is the change in temperature give by ΔT = Tfinal - Tinitial. q = s m ΔT (Equation 3) During the experiment, heat will flow from the hot metal to the room temperature water and to the calorimeter. The following equation relates the three system components. -qmetal = (qwater + qcal) (Equation 4) The quantity qcal, the heat absorbed by the calorimeter is usually much smaller than qwater. The quantity qcal is obtained by multiplying the calorimeter constant Ccal, which has units J/ºC (obtained in a separate experiment) by the water temperature change, ΔTwater. Ccal represents the amount of heat absorbed by the calorimeter for every degree Celsius temperature increase of the water (and therefore the calorimeter). 2

3 To simplify this type of experiment, we sometimes assume that the heat absorbed by the calorimeter is negligibly small. This leaves the equation, -qmetal = qwater (Equation 5) For the heat absorbed by the water in the calorimeter: qwater = swater mwater ΔTwater (Equation 6) The specific heat of water is known to be J g -1 ºC -1. The mass and ΔT of the water are easily measured. Heat lost by the metal is given by: qmetal = smetal mmetal ΔTmetal (Equation 7) According to Equation 5, the two heat quantities (q) have the same magnitude but different signs. Substituting Equations 6 and 7 into Equation 5 gives Equation 8. Since the masses of the metal and water and the ΔT values of the metal and water are easily measured, the specific heat of the metal can be determined by solving Equation 8 for the quantity smetal. (The negative sign in the equation will cancel out in calculations because one of the temperature changes has a negative value.) - smetal mmetal ΔTmetal = swater mwater ΔTwater (Equation 8) Experimental: Density Before you measure the metal density, start heating a beaker of water as described on the next page. Measure your metal density while the water is heating, using no more than one-quarter of the unknown metal. This density determination is essentially the same procedure you did in an earlier experiment. 1. Fill a 50 ml graduated cylinder about halfway with water. 2. Record the water volume on the data sheet. 3. Obtain an unknown metal sample vial and record its number on the data page. Weigh the vial of metal on a hanging pan balance to g. 4. Pour about one fourth of the metal into the graduated cylinder and weigh the vial on the same balance as before. The difference between the two masses is the mass of metal now in the graduated cylinder. 5. Read the total volume of water plus metal in the graduated cylinder. 6. Use the remainder of the metal in the vial for the two specific heat trials. (Do not use the wet metal from the density determination for your specific heat trials.) In your report, calculate the density of the metal showing the proper setup. 3

4 Experimental: Specific Heat 1. Obtain a 600 ml beaker and carefully inspect it, especially on the bottom, for cracks. Never heat water in any container with cracks or defects. Put no more than 400 ml of tap water in the beaker and place the beaker on a hotplate with a high setting. (If you overfill the beaker, some boiling water could splash out and burn you.) Place a Celsius thermometer in the water. Turn down the hotplate setting when the water begins boiling so that the water simmers gently. 2. Copy the average mass of the vial and metal after removal of unknown metal you entered on page 5 into the first data space on page 6*. This will be the initial mass of metal and vial for the first specific heat trial. 3. Pour about one third of the metal remaining in the vial into a large test tube, designated test tube Weigh the vial again three times on the same balance. Enter the average of the three measurements as the final mass for the first trial and the initial mass for the second trial**. 5. Pour all the remaining metal into a second large test tube (#2) and weigh the empty vial. The empty vial mass is the final mass for the second trial. 6. Place both test tubes in the beaker of hot water. Leave the test tubes in boiling water for at least 10 min so the metal reaches the same temperature as the hot water. 7. While the metal samples are heating, weigh two calorimeters, labeled 1 and 2 on a platform balance to 0.01 g. (A calorimeter may consist of a single Styrofoam cup or an insulated plastic coffee cup.) Pour close to 50 ml of distilled or deionized water from a laboratory carboy into each calorimeter. (Water stored in a laboratory container for some time is preferable to tap water, because the stored water temperature will be in equilibrium with that of the laboratory air.) Weigh the calorimeters again on the same platform balance to obtain the total mass of calorimeter and water. Cover the calorimeters and place them away from heat sources such as your hotplate. 8. Insert a Celsius thermometer into calorimeter 1. (Do not use the same thermometer you used for the hot water.) Stir the water in the cup with the thermometer for 10 s and measure the initial water temperature to 0.1 ºC. Assume this initial water temperature is the same for both calorimeters. 9. After both metal samples have been in the gently boiling water bath for at least ten minutes, read the hot water temperature to 0.1 ºC. Assume that the measured water temperature is the same as the metal temperature. This value is the initial metal temperature for both trials. 10. Carefully remove test tube 1 of hot metal from the boiling water bath. Pour the metal quickly into the water in calorimeter With the thermometer in the calorimeter, swirl the water for 10 s. (Do not allow the thermometer bulb to strike the metal pieces.) Read the final temperature of the metal and water. 12. Repeat the experiment in the second calorimeter with the metal sample from the second test tube. 13. Put your wet metal samples back into the vial and return the vial to the laboratory supply cart. Safety The principal hazard in this experiment is the risk of burns from the boiling water. Inspect the 600 ml beaker for cracks before you use it and handle the beaker with care at all times. Chemical splash goggles and a waterproof apron must be worn at all times during this and all chemistry experiments, from the very beginning to the very end of the time you spend in the laboratory. Do not sit in front of the beaker of boiling water in case it breaks. Cleanup Turn off the hotplate switch, and with dry hands, unplug the hotplate power cord. Return one thermometer to the laboratory supply area. Wipe down your work area with a damp sponge before you leave the laboratory. 4

5 General Chemistry I CHEM-1030 Laboratory Experiment No. 10 Specific Heat Data Page for Density Determination Unknown Metal Number: Physical Appearance of Metal: Mass of Vial and Unknown Metal (at least three times) Average Mass of Vial and Unknown Metal Mass of Vial after Removal of Unknown Metal (at least three times) Average Mass of Vial after Removal of Unknown Metal. Calculated Mass of Unknown Metal *(On the next page, enter this value as the initial mass before removing metal from the vial for Specific Heat Trial 1. Volume of Water Alone in the Graduated Cylinder Volume of Water and Metal in the Graduated Cylinder Calculated Volume of Metal in the Graduated Cylinder 5

6 General Chemistry I CHEM-1030 Laboratory Experiment No. 10 Specific Heat Specific Heat Determination Data Page The average of the final mass values on the previous page is the mass of the vial before you remove metal for Specific Heat Trial 1*. The average mass of the vial after removing metal for Specific Heat Trial 1 is the same as the mass of the vial before removing metal for Specific Heat Trial 2.** Trial 1 Trial 2 Average Mass of Metal and Vial * ** before Removing Specific Heat Metal Sample Mass of Vial after Removal of Metal Sample (three times) Average Mass of Vial after Removal of Metal Sample Calculated Mass of Metal (mmetal) Empty Calorimeter Mass ** (three times) Average Empty Calorimeter Mass Calorimeter and Water Mass (three times) Avg Calorimeter and Water Mass Calculated Mass of Water in Calorimeter (mwater) Initial Temperature of Water in Calorimeter Initial Temperature of Hot Metal Final Temperature of Water and Metal in Calorimeter Calculated Change in Metal Temperature (ΔTmetal) Calculated Change in Water Temperature (ΔTwater) 6

7 General Chemistry I CHEM-1030 Laboratory Experiment No. 10 Specific Heat Report 1. Unknown Metal Number: Rearrange Equation 8 to calculate the specific heat of your unknown metal from each of your two trials. For full credit, show the equations and setups clearly. (10 points) 2. Calculate the density of your unknown metal from the density equation d = m/v. Show the setup clearly. (2 points) 3. Use your calculated density value, your calculated metal specific heat and the metal s physical appearance to match your unknown to a metal in Table 2. If more than one metal is a possible match, state so. For full credit, clearly explain the reasons for your choice(s). (4 points) 7

8 4. Calculate the percent error of your experimental specific heat value. Use the tabulated specific heat of the metal you chose in Question 3 for the accepted value. Use the average specific heat value from your two trials for the experimental value in Equation 9. (2 points) accepted value - experimental value % error = x 100% accepted value (Equation 9) 5. Combine Equations 4, 6 and 7 to recalculate the specific heat of your metal from your Trial 2 data only, taking into account the heat absorbed by the calorimeter. Use 37.0 J/ºC for the calorimeter constant, Ccal. Multiply Ccal by ΔTwater to get qcal. (2 points) 8

9 General Chemistry I CHEM-1030 Laboratory Experiment No. 10 Specific Heat Prestudy 1. Calculate the heat needed to raise the temperature of g of water from 23.8 ºC to 89.8 ºC. (2 points) 2. What is the specific heat of a metal if g of the metal requires joules for a 19.0 ºC temperature change? (2 points) 3. A g sample of an unknown metal at 99.9 ºC is mixed with g of water at 21.6 ºC. The resulting mixture reaches a temperature of 24.9 ºC. Calculate the specific heat of the metal by solving Equation 8 for smetal. Equation 8, which is derived from Equations 5, 6 and 7, assumes the heat gained by the container (calorimeter) is negligible in comparison to the heat gained by the water. (3 points) (Answer question #4 on the reverse side of this page.) 9

10 4. Use the measurements in problem 3 to recalculate the specific heat of the unknown metal. This time combine Equations 4, 6 and 7 and solve algebraically for smetal to account for the heat absorbed by the calorimeter. The heat gained by the calorimeter is the temperature change of the water times the calorimeter constant, Ccal. Use 42.8 J/ºC for Ccal. (3 points) 10

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