# EXPERIMENT 14: CALORIMETRY

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1 EXPERIMENT 14: CALORIMETRY Introduction: You will calculate the specific heat constant of a metal, c, by measuring the heat exchanged in a calorimeter. Once c is determined, use the Law of Dulong and Petit to calculate the approximate atomic mass of an unknown metal. Background: Heat energy can be gained or lost by an object when it warms or cools. One unit of heat energy is the joule, J, a derived unit representing kg-m 2 /s joules = 1 calorie (the amount of heat required to change the temperature of 1 g of water by 1 o C (or K) say from 4 o C to 5 o C). Although calories are much more familiar to most of you, the SI uses joules. In the US, and especially in health science, calories are more commonly used. The nutritional calorie is actually a kilocalorie (kcal) or 1000 cal. Heat flow, Q, measured in joules or calories, is proportional to the mass of the object, its change in temperature, and the specific heat constant c. Q = m x c x T c is specific heat in joules per gram per degree, or J/g- C, and T = Tfinal Tinitial. Specific heat is a property of a pure substance. The specific heat of water is J/g- C When two objects at different temperatures come into contact, heat flows from the hotter to the colder object until the two objects reach the same temperature (Tf). The double Styrofoam cups in this experiment serve as a calorimeter, an insulated device where there is no loss of heat to the outside. In this experiment, you will measure the specific heat of two metals, one known, Fe, and the other unknown. Iron has a specific heat of J/g-C o. Your value may differ and you will calculate the % error. The same method will be used to find the specific heat of the unknown metal. The hot metal is placed into the calorimeter, with water and the final temperature reached by both the metal and water is recorded Thus the heat lost by the metal (Qm) is equal to the heat gained by the water (Qw) Qw = Qm thus, mw x cw x Tw = - (mm x cm x Tm) All the values are known except cm. Note the negative sign on the right side of the equation. This cancels out since Tm is a negative quantity (Tf Ti is negative). The specific heat of the unknown metal will be used to estimate its atomic mass. The identity of the metal can be guessed from the Law of Dulong and Petit, stating that the atomic mass of a solid element equals 26 divided by the specific heat, ± 10%. Atomic mass = 26 / (specific heat) Safety No hazardous chemicals are used but you will be working with fairly large quantities of boiling water, pouring from one container to another, and dropping pieces of metal into boiling water. If you have long hair, be sure to tie it back. Materials Needed Equipment calorimeter (double Styrofoam cups), thermometer, thermometer clamp, stirring rod, utility clamp, burner 600 ml beaker, crucible tongs, iron ring, wire gauze Chemicals Iron metal Unknown metal

3 Specific Heat Values of Elements ( Joules / g-k ) (for elements at 300K) Li Be B C Na Mg Al Si P S K Ca Sc Ti V Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Rb Sr Y Zr Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb Te I Cs Ba La Hf Ta W Re Os Ir Pt Au Hg Tl Pb Bi Note: if you have a very large metal object, you may want to use up to (but not more than) 100 ml of water. Immersing the entire object is not critical, since heat flow between metal and water is much more efficient than between metal and air.

4 EXPERIMENT 14: REPORT CALORIMETRY Name: Section 1. Data Table for Iron: Mass of iron T of boiling water ( Ti(m) ) (initial T of metal) Mass of Calorimeter Mass of calorimeter & water Initial T (Ti(w)) of calorimeter water Final temperature of metal and water (calorimeter) Calculations and results: Mass of water in calorimeter T of water (Tf Ti(w)) T of metal ( Tf Ti(m)) Heat (J) gained by the water * Qw = m x cw x w Specific Heat of iron (cm) * (calculate from equation) Qm = mm x cm x metal Note: Q lost by water = Q gained by metal Percent error * (Compare your value of c with value from a table) Average specific heat of iron: Specific heat of iron from a table: ***Note on the three starred items show a complete setup for each calculation, neat and organized on an attached piece of paper!! Show similar calculations for the unknown metal on the same sheet of paper. Indicate formulas and all units clearly.

5 2. Data Table for Unknown Metal: Code # of metal: Mass of metal Temperature of boiling water Mass of calorimeter Mass of calorimeter with water Initial temperature of calorimeter water Final temperature of calorimeter, water & metal Calculations and results: Mass of water T of water T of metal * Heat (J) * Qw = mw x cw x Tw C w = J/mol-K Specific Heat ( cm) * Qm = mm x cm x Tm Average specific heat of unknown metal: Average Atomic mass ± (Calculate the range from the high & low values allowed by the uncertainty in the Law of Dulong & Petit) Unknown element (based on the value calculated from the Law of Dulong & Petit) Unknown element based on comparison with a table of actual c values. Note: some tables are given in calories/g- o C; other tables are in joules/g- o C. Use the factor J = 1 cal to convert. * As with the iron, show your calculations on a separate sheet of paper attached after this page, along with the calculations on the iron. Also show a reference value of cm from a table (see pg 71) or other source such as the CRC Handbook. Cite your reference!

6 Questions Some of these should be done before coming to lab, as preparation, to save time, and increase your understanding of the complex calculations involved in this experiment. 1) A student places 138 g of an unknown metal at 99.6 C into g of water at 22.1 C. The entire system reaches a uniform temperature of 31.6 C. Calculate the specific heat of the metal. 2) If the correct specific heat of the metal in Problem 1 is 0.25 J/g- C, calculate the percentage error. 3) While transferring the piece of unknown metal to the calorimeter, the student drops the metal into the calorimeter roughly, and some water splashes out of the calorimeter. Why must this be avoided? Be specific how would the loss of water from the calorimeter affect the calculated value of specific heat for the metal?

7 4) The calorimeter used in this experiment has no lid. Is this a potential source of error in this experiment? Explain how this could affect your determination of the specific heat. Be specific. Would the value of cm be high or low? Why? 5) This experiment has several potential sources of error. Discuss two more possible systematic errors, (besides the errors covered in the previous questions), which may cause the calculations to be in error. Again be specific as to how the calculated value of specific heat would be affected. (Note student errors such as weighing the samples wrongly are not systematic errors. Assume the student follows directions as well as possible).

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