146 
A problem that is often done in General Chemistry courses. Note that v_{rms}
is the rootmeansquare speed, which means it is the square root of the
average value of the squared speed.
(First the square, then the average, finally the square root). 
147 
Another problem that could be done in a General Chemistry course. 
1415 
Calculation of the ratio of the distribution functions G(v) for v = 500 m/s and v = 1500 m/s if the gas is O_{2}
at 25° C. The speed may increase by a
factor of only three, but the ratio of the probabilities drops
precipitously. Remember that 
1421 
A somewhat messy derivation of a formula that turns out to be simple. What is needed is the right starting equation (15.44) and basic calculus. It is necessary to be careful taking the (somewhat complicated) derivative and to recognize that exponential functions can never equal 0 (unless the argument is negative and infinite). Don't worry about the normalization factor because it is a constant that cannot be zero. 
1430 
Another problem that could be given to students in General Chemistry. What is needed is Graham’s Law of Diffusion, which says that the ratio of the rates of diffusion of two gases is inversely proportional to the square root of their molar masses. Levine doesn't ask that the formula of the gas be determined, but doing so is not difficult. 
1442 
How far do gas molecules travel between collisions (assuming a container large enough that collisions with the walls do not happen first)? A good exercise in cancelling units. The necessary equation is 14.67. Please do not memorize the equation but please do think about the numerical values calculated. 


1420 
Straightforward computation of rms, average, and most probable speeds for CO_{2}(g) at 500 K. The formulas can be found in the chapter (top of pg. 458); it is not necessary to memorize them. Please do, however, look at the values. Also, what are the values in miles per hour? 
1443 
A problem based on the barometric formula, which is P = P_{0}exp(M_{r}gh/RT),
where P_{0} is the barometric pressure at sea level and M_{r}gh is the gravitational potential energy (g
= 9.81 m/s^{2}).. Since R will
probably be in J the molar mass M_{r} will
need to be in kg/mol rather than in g/mol. 
1444 
The barometric formula applied to daily life. How much does the pressure fall per story of a standard building? (The answer, of course, is not very much.) This problem will be easier if an intermediate result from problem 1443 is used. 
1448 
An exercise in the prediction of a heat capacity. Look up C_{p} for CH_{4} at 298 K in Levine's Appendix and compare with the predicted value. Remember that CH_{4}, which has 5 atoms, has 3(5)6 = 9 vibrations, each of which would be predicted to add R to C_{v,m}. And it has three rotations (not two) because it is not linear. 