CHEM 3351 Physical Chemistry I, Fall 2017

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1 CHEM 3351 Physical Chemistry I, Fall 2017 Problem set 1 Due 9/15/2017 (Friday) 1. An automobile tire was inflated to a pressure of 24 lb in -2 (1.00 atm = 14.7 lb in -2 ) on a winter s day when the temperature was 5 o C. What pressure will be found assuming no leaks have occurred and that the volume is constant, on a subsequent summer s day when the temperature is 35 o C? What complications should be taken into account in practice? 2. A mixture of oxygen and hydrogen is analyzed by passing it over hot copper oxide and through a drying tube. Hydrogen reduces the CuO to metallic Cu. Oxygen then reoxidizes the copper back to CuO. We know that 100 cm 3 of the mixture measured at 25 o C and 750 mm yields 84.5 cm 3 of dry oxygen measured at at 25 o C and 750mm after passage over CuO and the drying agent. What is the original composition of the mixture? (Hint: First write balanced chemical equation for the reactions.) 3. For a gas mixture in a gravity field, it can be shown that each of the gases obeys the distribution law independent of the others. For each gas, p i = p i0 exp[-m i gz/rt] where p i is the partial pressure of the ith gas in the mixture at the height z, p i0 is the partial pressure of the gas at ground level, and M i is the molecular weight of the gas. The approximate composition of the atmosphere at sea level is given in the table below Gas p i (atm) at 50km at 50km p i (atm) at 100km at 100km Nitrogen Oxygen Argon 0.93 Carbon Dioxide 0.03 Neon Helium Krypton Hydrogen Xenon Ozone Total Ignoring the last four components, compute the partial pressure of the others, the total pressure, and the composition of the atmosphere in mole, at altitudes of 50 and 100 km (assuming t=25 C). Check out the oxygen! 4. Calculate the pressure at 10 km above the sea level, and at 10 km below the sea level (10 km below the water surface). (Hints: the derivation done in class should be helpful;

2 assume T=25 C; assume the (ideal) gas atmosphere has only the first two components given in the table in problem 3). 5. The coefficient of thermal expansion is defined as =(1/V)( V/ T) p. Using the equation of state, compute the value of for an ideal gas. The coefficient of compressibility is define by = -(1/V)( V/ p) T.Compute the value of for an ideal gas. For an ideal gas, express the derivative ( p/ T) v in terms of and. (Check the end of the homework set for mathematics reference) 6. Solve problem Q1.13 from the textbook (pg. 13) 7. Solve problem Q1.14 from the textbook (pg. 13). Please note that average velocity of gas particles is directly related to gas temperature, according to the equation 1.10 in the textbook (pg. 4). 8. The ideal-gas constant is obtained by measuring P-V data for a real gas at a fixed temperature. The ratio PV/T is then computed at each measured pressure. The result is fitted by an appropriate least-squares procedure and extrapolated to zero pressure, at which point the gas will behave ideally. This problem illustrates the procedure. An investigator measures the pressure of 1 mole of real gas at various volumes at a fixed temperature of 300 K. The data are shown below. Use the data to solve the following: a) Compute the apparent value of R at each of the data points. b) How does computed R (V=20L) compare to the R (V=40L). Why? c) Calculate pressure of ideal gas at each volume given in the table. How does p ideal compare to p real at each volume; when are the two most different? Why? d) Use the last six data points (at volumes V=27 liters to V = 40 liters) to execute a least squares fit of the computed value of R to a linear function of the pressure. That is, fit the function R = a 0 + a 1 P to the computed values of R at the six lowest pressures. (Hint: do this in Excel, using its existing functions) e) Using the fitted function, obtain the limit of R as P 0; f) Plot the fitted function and compare your curve with the measured data points. Volume (liters) Pressure (atm)

3 A passenger flying in an airplane at 11 km above sea level tightly closes the empty water bottle. Upon landing in Miami, near the beach, he notices that the bottle shrunk, and its inside volume is only 2/3 of its original volume. What was the pressure of the plane cabin when the bottle was closed? What was the pressure just outside of the plane in flight? If the pressures inside and outside the flying plane are different, how do you think the pressure difference in the plane is obtained and maintained? Assume that T=25 C and remains constant. To determine the composition of air at 11 km above sea level and the total pressure outside the plane flying at 11 km above sea level, use the information given in problem

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