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University of Waterloo Term Test 1 Chemistry 254: Thermodynamics Friday 29 May 2009 12:30-1:20 PM NAME .................................…………….................... I.D. ................................................……………..… T G A P H Instructions (1) (2) (3) Answer ALL the questions, and do the easy ones first. A standard, non-programmable calculator is allowed. Total time permitted for this examination is 50 minutes. V U S Equations and Constants R = 1.9872 cal mol-1 K-1 = 8.3145 J mol-1 K-1 = 0.082057 atm L mol-1 K-1 = 0.083145 bar L mol-1 K-1 = 8.3145 Pa m3 mol-1 K-1 = 62.364 torr L mol-1 K-1 Constants 0°C = 273.15 K General equations ⎛ ∂U ⎞ ⎛ ∂U ⎞ dU = ⎜ ⎟ dT + ⎜ ⎟ dV ⎝ ∂V ⎠ T ⎝ ∂T ⎠ V ⎛ ∂P ⎞ ⎛ ∂U ⎞ ⎜ ⎟ = T⎜ ⎟ − P ⎝ ∂T ⎠ V ⎝ ∂V ⎠ T For a monatomic ideal gas P= nRT V and CP 5 = R n 2 For a van der Waals gas P= and nRT n 2a − 2 V − nb V and ⎛ ∂U ⎞ ⎜ ⎟ =0 ⎝ ∂V ⎠ T CP CV − =R n n n 2a ⎛ ∂U ⎞ ⎜ ⎟ = 2 ⎝ ∂V ⎠ T V Score Q1 /5 Q3 /5 Q2 /5 Q4 /5 Total /20 Please hand in this exam paper. Be sure to PRINT your name and ID. WARNING: Cheating in exam is considered to be the most serious academic misconduct and is ground for expulsion at the University of Waterloo. Don’t do it! Page 1 of 5 INSTRUCTIONS: Attempt ALL the questions. Each question has equal weight. Please present your work logically and neatly, and cross-off any rough work that you do not want the marker to see. Marks will be deducted for messy, disorganized presentation. Use the back of the page for your rough work, if needed. 1. A vessel of volume 22.4 L contains 2.0 mol H2 and 1.0 mol N2 at 0°C initially. All of the H2 react completely with sufficient N2 to form NH3 in the following reaction: N2 + 3H2 → 2NH3 Calculate the partial pressures of N2, H2 and NH3, and the total pressure of the final mixture. Assume all the gases behave like an ideal gas. Express your answers in unit of atm. Page 2 of 5 2. When a system is taken from state A to state B along the path ACB shown in the following figure, 80 J of heat flows into the system and the system does 30 J of work. (a) How much heat flows into the system along the path ADB if the work done by the system is 10 J? (b) When the system is returned from state B to state A along the curved path BA, the work done on the system is 20 J. Does the system absorb or liberate heat, and how much? (c) If UD−UA = +40 J, find the heat absorbed in the processes AD and DB. Page 3 of 5 3. One mole of an ideal gas is subjected to two successive changes in states: (a) From 298 K and 100 kPa, the gas is expanded isothermally against a constant pressure of 20 kPa to twice the initial volume. (b) At the end of step (a), the gas is cooled at constant volume from 298 K to 248 K. Calculate q, w, ΔU, and ΔH for steps (a) and (b). Note that the molar heat capacity at constant V for a monatomic ideal gas is CV,m = Express your answers in unit of J. 3 2 R. Page 4 of 5 4. The isothermal compressibility κ is defined as: κ=− 1 ⎛ ∂V ⎞ ⎜ ⎟ V ⎜⎝ ∂P ⎟⎠ T where V is the molar volume. For an ideal gas, is κ = 1 or κ = V ? Show work. P Page 5 of 5