Help!

[JoD]

Hey so I'm trying to get an assignment done and I was wondering if anyone could send some suggestions my way on how to tackle #1 parts b and c, #5 and #6. Thanks!

 

1.

a) Derive the expression for the most probable speed in a gas.

 

b) Another way to characterize the width of a probability distribution is to compute the standard

deviation, sigma. Calculate sigma for the speed distribution; i.e.,

 

sigma = sqrt( < (c- < c >)^2 >).

 

(HINT: you may find the calculation easier if you first show that

< (c- < c >)2 >=< c2 > - < c >2).

 

c) In order to decide whether the speed distribution narrow or wide, consider sigma/ < c >. What is it?

 

 

5.

The reaction

 

A + B --> AB

 

proceeds using a surface catalyst via the following mechanism:

 

A + S -ks-> A* + S

A* + B -kAB-> AB,

 

where A* is a gas-phase intermediate and where the rate constants can be estimated using thecollision theory developed in class.

 

a) Write down the kinetic equations for the overall rates of change of A, A*, B, and AB (you should leave your answers in terms of ks and k AB).

 

b) It is often difficult to measure small concentrations of intermediates. Nonetheless, the fact that the concentration of A* is very small can be used to simplify your answer in a). Make the so-called steady-state approximation, which, here, assumes that the net rate of change of the intermediate A* is zero (usually the rate will be very small if the concentration of the intermidate is). This allows you to explicitly solve for [A*] and substitute your answer

into the remaining kinetic equations. What do you get? How would you tell an experimentalist to plot their data in order to confirm your result? (HINT: remember how the integrated rate laws are tested).

 

 

6.

An interference pattern is created using lasers in a gas of molecules that are photoreactive.The lasers are adjusted to give an initial periodic concentration profile of the photoreactive products of the form:

 

n(x, t = 0) = n0(1 + A sin(kx)), (1)

 

where k is the wavevector of the interference pattern and A is its amplitude. At t=0 the laser is switched off and the pattern starts to dissipate. Assume that Eq. (1) is valid for t > 0 (with a time dependent amplitude A(t)) and use the diffusion equation we derived in class to obtain an equation

for dA(t)/dt. What is the solution to this equation and what does it predict for the 1/e-life of the pattern (i.e., where the amplitude falls to 1/e of its initial value)? Finally, evalutate your 1/e-lives for methane at 1 atm pressure and 298.15K, assuming that k = 1. 0, 100. 0, and 106 cm-1. Use 0.4 nm for the diameter of methane.