Answer Happy

INTRODUCTION Calorimetry is a technique commonly used to measure the flow of energy into or out of a system. In this experiment, a known amount of heated metal shot will be added to a carefully measured amount of room temperature water in a Styrofoam cup calorimeter. The amount of heat transferred to the water will be measured by monitoring the rise in temperature of the water. The change in temperature of both the water and the metal will be used to determine the heat capacity of the metal. While decidedly low-tech, Styrofoam has an incredibly low heat capacity and excellent insulation characteristics allowing all of the energy released by the hot metal to be transferred to the water with almost no energy lost to the surroundings. As described below, if the initial and equilibrium temperatures of the metal and water are known, along with the mass of the metal and water, the specific heat of the metal can be determined. This calorimetry experiment relies on the assumption that all of the energy lost by the metal as heat (qmetal) is gained by the water (qwater): qwater-metal (Eqn. 1-1) Here, the negative sign accounts for the fact that energy lost by the metal is gained by the = 4.184 and the mass of the water water. Given the specific heat of water (mwater) the energy gained by the water (qwater) can be determined by monitoring the change in temperature ATwoter: (Swater 9.k K 9 THE qwater = mwater X Cwater X ATwater F-I Similarly, the energy lost by the metal is given by: Mclar (Eqn. 1-2) 1. Ametal= mmetal X Cmetal X ATmetal (Eqn. 1-3) Note that ATwater will be positive making qwater positive while ATmetal will be negative making qmetal negative. Substituting equations 2 and 3 into equation 1, one may derive an expression for the specific heat of the metal. The temperature of solid metal is a direct measure of kinetic energy of the atoms which comprise the metal. Being solids, atoms in metals are not free to move around but they can vibrate and it is in these vibrations that metals store energy. Indeed, the only difference
between a red-hot iron rod and a cold iron rod is the degree to which the iron atoms are vibrating. By modeling metals as regular arrays of vibrating atoms, scientists have derived a very simple expression for the specific heat of any metal: Cmetal= 3R- MM where R is the gas constant (8.3145) and MM is the molar mass of the metal. Surprisingly, 100 years before this result was discovered two French scientists, Pierre Louis Dulong and Alexis Therese Petit, found the same relationship experimentally by measuring the heat capacities of a variety of metals. Their result is now known as the Dulong-Petit law and was used in the late 1800's to determine the molecular weight of several newly discovered metallic elements: (Eqn. 1-4) 5K-mol (MM) (Eqn. 1-5) Both of these equations imply that there i an inverse relationship between the heat capacities of metals and their molar mass. Cmetal 25- PROCEDURE PART A: Prepare the Heated Metal Samples 1. Place approximately 500 mL of deionized water in the 600 mL beaker and bring to a boil. You can add 5-6 boiling chips to the water to prevent violent bumping as the water boils. 2. Dry the first unknown metal sample with paper towels, if needed. Weigh out enough metal so it fills 1 to 2 inches of the test tube. Note the exact mass of the metal in your notebook. Place the metal in a dry test tube and, using a clamp and a ring-stand, suspend the test tube in the boiling water. Make sure the level of the metal in the test tube is below the level of the boiling water. Also, make sure the test tube is not in contact with the bottom of the beaker. 3. Place the digital thermometer (not attached to the computer) in the metal and allow the metal to thermally equilibrate for 15 minutes. You may want to note the time you began heating each sample in your notebook so that you ensure each sample has 15 minutes to reach thermal equilibrium with the boiling water. 4. Repeat steps 1 and 2 for the second metal sample so that it is warming up as you perform the experiment on the first metal sample, but leave the digital thermometer in the first sample. PART B: Prepare the Calorimeter 5. While the metal is heating, dry your Styrofoam cups with a paper towel and nest them one inside the other. Weigh the empty Styrofoam calorimeter, noting the exact mass in your notebook.
Unknown-ID Mass of metal Mass of calorimeter Mass of calorimeter and water Mass of water Ti,water Ti,metal Tfinal ATmetal ATwater Calculated Cmetal Identity of metal Trial 1 Di 43. 1569 Trial 2 D2 32.561g 7.460g 7466g 21.00 -941 1.4 49.553, 50-5389 35.093g 43.072 5 19.6°C 20.00 73.78-998888 671 8 alac 7676 21.1.2
METAL c (J/g.K) Pb 0.13 Sn 0.21 Rh Zn Ni 0.24 0.39 0.54 Table 1-1: Specific heats of several common metals Fe 0.45 Al 0.91 Na 1.21