CLEARLY SHOW THE METHOD USED AND THE STEPS INVOLVED IN ARRIVING AT YOUR ANSWERS. It is to your advantaged to do this, since you may obtain partial credit if you do and will receive little or no credit if you do not. 1. A student is given the task of determining the specific heat capacity of a chunk of metal of unknown composition. The following materials are available. Distilled water Aluminum foil Beakers Gloves Goggles Hot plate/stirrers Lab coat Metal pieces/chunks Scale (0.01-‐g precision) Stirring rod Styrofoam cups Thermometer (+/-‐ 0.1°C) a. Explain how, on a microscopic level, thermal energy (heat) is transferred from a hot chunk of metal to liquid water (at a lower temperature than the metal) in a confined place. The heated metal contains metals atoms that vibrate in fixed positions. When a heated metal comes into contact with water at a lower temperature the energy of the metal atoms is transferred to the water until they come into thermal equilibrium (equal temperature). b. From an experimental design standpoint, explain how the student can heat the metal chunk to an observable/measurable (with a thermometer) temperature given the equipment available? Explain. The student should add distilled water to a beaker and boil the water using the hot plate. The student should place the metal chunk in the boiling water for a reasonable period of time so that the metal is assumed to have the same temperature as the water. Page 1 of 5 c. The student measures the temperature of 35.00 g of distilled water as being 24.2°C. The student then places the 2.33 g chunk of meal, heated to 100.2°C, into the 35.00 g of distilled water. i. Given the equipment available, what should the student use to contain the metal/water mixture? Justify your answer. The student should minimize heat lost to the atmosphere by using a Styrofoam container and the aluminum foil for the top. ii. At some point, following immersion of the hot metal into the room temperature water, a thermal equilibrium between the metal and water is established. How does the student determine the point at which thermal equilibrium is established? Thermal equilibrium will be established when the temperature of the water (the surroundings) is at its maximum. After this point heat will be lost to the Styrofoam cup and the atmosphere. iii. The student stirred the mixture as it approached its maximum temperature. Why is this a good idea, from an experimental design perspective? Stirring the mixture is a good idea because more of the heat (thermal energy) of the metal can be transferred to the water. d. Calculate the experimental value for the specific heat capacity of the unknown metal assuming that the metal-‐water mixture was found to be 44.5°C and that the specific heat of water is 4.18 J×g-‐1×°C-‐1. This is a conservation of energy problem. The energy gained by the water plus the energy lost by the metal must equal 0. The energy can be calculated using q = mCΔt. qmetal +(qwater =(0
(2.33(g)(C metal )(44.5(6(100.2(°C)(+((35.00(g)(4.18
C metal =(22.8
J
g × °C
Page 2 of 5 J
)(44.5(6(24.2(°C)(=(0 g × °C
e. The student’s calculated value in (d) was lower than the accepted value. Provide one reason to account for the difference. Justify your answer. Any thermal energy (heat) lost to the environment would lower the temperature change and thus the specific heat of the metal. The heat loss could come from a Styrofoam container that absorbs heat from the water or a top that is not completely sealed to the environment. 2. Hydrogen gas burns in air according to the equation below. 2H2(g) + O2(g) → 2H2O(l) a. Calculate the standard enthalpy change, ΔH°298, for the reaction represented by the equation above. (The molar enthalpy of formation, ΔH°f, for H2O(l) is -‐285.8 kJ mol-‐1 at 298 K). ΔH°#=#ΣΔH° f (products)0#ΣΔH° f (reactants)
ΔH°#=#(2 × 0285.8)#0#0#=#0571.6#
kJ
mole
b. Calculate the amount of heat, in kJ, that is released when 10.0 g of H2(g) is burned in air. 10.0$g$H 2 1$mole$H 2 ,571.6$kJ
=$1415$kJ 2.02$g$H 2 2$mole$H 2
c. Given that the molar enthalpy of vaporization, ΔH°vap, for H2O(l) is 44.0 kJ mol-‐1 at 298 K, what is the standard enthalpy change, ΔH°298, for the reaction 2H2(g) + O2(g) → 2H2O(g)? Given: H2O(l) → H2O(g) ΔH° vap = 44.0 kJ mol-‐1 2H2(g) + O2(g) → 2H2O(l) ΔH° = -‐571.6 kJ mol-‐1 Hess’s Law! Multiply first equation by 2. Add first two equations together… 2H2(g) + O2(g) → 2H2O(g) Page 3 of 5 ΔH° = -‐483.6 kJ mol-‐1 A fuel cell is an electrochemical cell that converts the chemical energy stored in a fuel into electrical energy. A cell that uses H2 as the fuel cell can be constructed based on the following half-‐reactions. d. Write the equation for the overall cell reaction. Note that problem states that H2 is a fuel…H2 is a reactant! Second half reaction must be flipped and run as the oxidation half reaction. H2(g) + 2OH-‐(aq) → 2H2O(l) + 2e-‐ E° = 0.83 V The other half reaction is the reduction reaction. 2H2O(l) + O2(g) + 4e-‐ → 4OH-‐(aq) E° = 0.40 V 2H2(g) + O2(g) → 2H2O(l) e. Calculate the standard potential for the cell at 298 K. E° cell = 0.83 V + 0.40 V = 1.23 V f. Assume that 0.93 mol of H2(g) is consumed as the cell operates for 600. seconds. i. Calculate the number of moles of electrons that pass through the cell. 0.93%mole%H 2 2%mole%e ,
=%1.86%mole%e , 1%mole%H 2
ii. Calculate the average current, in amperes, that passes through the cell. 1.86%mole%e * 96,485%C
=%179,462%C 1%mole%e *
q 179,462"C
I"=" ="
="299"A t
600."s
Page 4 of 5 g. Some fuel cells use butane gas, C4H10, rather than hydrogen gas. The overall reaction that occurs in a butane fuel cell is 2C4H10(g) + 13O2(g) → 8CO2(g) + 10H2O(l). What is one environmental advantage of using fuel cells that are based on hydrogen rather than on hydrocarbons such as butane? One environmental advantage of using fuel cells is that fuel cells limit dependence on fossil fuels. Fossil fuels are non-‐renewable resources and the byproducts are suspected to play a role in global warming. Page 5 of 5