Midterm Examination 1

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Mariah Patterson
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1 CHEM 331 Physical Chemistry Fall 2013 Name: Answer Key Midterm Examination 1 1. A goat weighing 20 kg produces about 375 cm 3 gas per hour in his intestines. Assume that the gas is Methane; CH 4 with M = 16 g/mol. How long does it take the goat to produce an amount of intestinal gas equal to his own weight? Make appropriate approximations. Explicitly state your approximations g / (16g/mol) = 1250 mol Methane V = nrt/p = (1250 mol) ( Latm/Kmol) (300K) / ( 1atm) = L # hours = L / (0.375 L/hr) = hours Assume: Gas is Ideal and at 1 atm and 300K 2. A mixture of 1 mole H 2 and 2 mole O 2 is at 25 o C in a 20 L flask. Calculate P H2 and x H2. Provide a reasonable definition of the partial volume V i and use it to calculate V H2. P = nrt/v = (3 mol) ( Latm/Kmol) (298 K) / (20 L) = 3.67 mol x H2 = 1 mol / (1 mol + 2 mol) = Dalton's Law: P H2 = x H2 P = (0.333) (3.67 atm) = 1.22 atm V H2 = x H2 V = (0.333) (20 L) = 6.66 L

2 3. The Compressibility Factor Z for N 2 gas is 0.85 at a concentration of 10.0 mole/l at 200K. a) What Pressure would be exerted by this gas, under these conditions, if it is behaving Ideally? P = RT / = RTc = ( Latm/Kmol) (200 K) (10.0 mol/l) = 164 atm b) What Pressure is exerted by this gas, under these conditions? P = ZRT / = (0.85) ( Latm/Kmol) (200 K) (10.0 mol/l) = 140 atm c) What is the percentage error introduced into the Pressure calculation by assuming the gas is Ideal? % error = / 140 x 100 = 18%

3 4. Suppose that you have data giving the Compressibility Factor (Z) for a gas as a function of Temperature and Concentration (c); c = 1/. a) Derive an expression for calculating from this data. P = ZRT / = ZRTc b) The Virial expansion for a gas that can be modeled as a van der Waals gas is: Z = Develop an expression to determine first order in c. for a van der Waals gas that is good through c) Determine the value of this+ derivative for a van der Waals gas whose constants are: a = L 2 atm/mol 2 and b = L/mol. The temperature of the gas is K and its concentration is mol. = ( Latm/K) ( K) + 2 ( Latm/Kmol) + 2 ( mol/l) ( Latm/K mol\)( L/mol x ( L/mo L 2 atm/( Latm/Kmole)(273.15K) = L/mol L/mol = Lamt/ mol

4 5. The Compressibility Factor for a number of gases as a function of the reduced state variables is given as: The critical isotherm for CO 2 is as plotted below: Based on the form of this isotherm, explain why the curve for T R = 1.00 in the above Z vs. P R diagram is nearly vertical below P R ~ Along the critical isotherm; T R = 1.00 and P R ~ 1.00 at. You should notice that near, the isotherm is very flat. This means P/ V ~ 0. Along the isotherms of the Z vs P plot will have a slope of ~ (PV)/ P ~ V/ P ~ 1 / 0 =.

5 6. For 1 kg of Water between 0 o C and 40 o C, the volume can be represented as: V = t + ( x 10-3 ) t 2 - (6.79 x 10-5 ) t 3 Calculate the Isothermal Compressibility for Water at 3 o C. Recall: = Do you consider this result unusual? Comment Briefly. V = ( )(3) + ( x 10-3 ) (3) 2 - (6.79 x 10-5 ) (3) 3 = So, = ( x 10-3 ) t - 3 (6.79 x 10-5 ) t 2 = ( x 10-3 ) (3) - 3 (6.79 x 10-5 ) (3) 2 = = / = x 10-5 K -1 This value is unusual in that it is negative. This means the Water is contracting when heated.

6 7. A resistor is immersed in a bath of crushed Ice in a Dewar flask. A current of 2 Amperes passed through the resistor for 300 sec (5 min) results in the melting of some of the Ice. The resistance is 18. (Recall, the electrical work done on a resistor in passing a current through it is given by W = I 2 Rt.) a) Find Q, W and U for the System. Take the System to be the Ice-Water. Q Water = - Q Resistor = (2 Amperes) 2 (18 ) (300 sec) = J W ~ 0 J U = Q + W = J + 0 J = J b) Suppose all the Ice melts before the heating is complete. Will that affect your calculations above? Explain. If the Ice melts before the heating is complete, then the Water will warm. This will leave the resistor in a different state than it started in; meaning U is no longer zero for the resistor. Thus, some of the work on the resistor will be used in changing U. Hence we do not know how much heat is delivered to the Ice-Water. Hence we cannot calculate Q or U for the Ice-Water.

7 8. One mole of an Ideal Gas at 2 atm & 0 o C undergoes reversible Isobaric heating until it is at 2 atm & 50 o C. This then undergoes a reversible Isothermal compression to 2.1 atm. Calculate W for each leg of the path in going from state A to state B. Clearly identify, for each leg of the path, whether work is being done on the system by the surroundings, or vice versa. V B = nrt/p = (1 mol) ( Latm/Kmol) (323 K) / (2.1 atm) = 12.6 L Along Leg #1 of the Path: W = - = - = - P = - P V = - (2 atm) (13.3 L L) = Latm Work is being done by the system on the surroundings. Along Leg #2 of the Path: W = - = - = - = - nrt = - nrt

8 = - (1 mol) ( Latm/Kmol) (323 K) = Latm Work is being done by the surroundings on the system.

1. What is the value of the quantity PV for one mole of an ideal gas at 25.0 C and one atm?

1. What is the value of the quantity PV for one mole of an ideal gas at 25.0 C and one atm? Real Gases Thought Question: How does the volume of one mole of methane gas (CH4) at 300 Torr and 298 K compare to the volume of one mole of an ideal gas at 300 Torr and 298 K? a) the volume of methane