[Big-Daddy]

The reaction Cl + CH₄  HCl + CH₃ has been studied by forming Cl atoms with a laser pulse in excess methane, and observing the concentration of HCl as a function of time.

(a) Show that the HCl concentration, [itex]c_{HCl}[/itex], varies with time t as

[tex]c_{HCl} = c_{HCl,t=\infty} \cdot (1 - e^{-k_1 \cdot c_{CH_4} \cdot t})[/tex]

where [itex]c_{CH_4}[/itex] is the methane concentration, [itex]c_{HCl,t=\infty}[/itex] is the concentration of HCl at t=∞ and [itex]k_1[/itex] is the rate constant.

(b) The following data apply to the reaction at 298 K with [CH₄] = 10¹⁵ molecule cm^-3.

t / ms, [HCl] / 10¹⁰ molecule cm^-3
2, 0.57
4, 1.05
8, 1.74
12, 2.19
16, 2.46
∞, 3.00

Evaluate k1.

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I don't have a clue on the first part. Especially why there is no dependence on Cl's concentration.

On the second, I can obviously rearrange for k₁ and plug in the values for a certain set, but we've been given 5 sets of data in addition to the t=∞ result, which to me suggests that we should use more than one. I get either 1.08·10^-16 molecule^-1·cm³·s^-1 or 1.07·10^-16 molecule^-1·cm³·s^-1 depending on which set I use, but a more advanced method is unclear to me.

[Corribus]

Part (a):

There are some hints buried in there that tell you the way you should approach the problem.  For example:

where [itex]c_{CH_4}[/itex] is the methane concentration,

What approximation is this hinting at?

Your question here is really at the crux of the problem:

I don't have a clue on the first part. Especially why there is no dependence on Cl's concentration.

Who says there is no dependence?  Let me give you a hint by asking a question of my own to you.  What is the relationship between the Cl concentration and the HCl concentration at any point in time?

Part (b):

This is easy if you are allowed to access data processing software and can do a fit.  A program like Origin will allow you to do this with no sweat.  I'm not sure what tools are at your disposal for solving this problem, though.

[curiouscat]

This is easy if you are allowed to access data processing software and can do a fit.  A program like Origin will allow you to do this with no sweat.  I'm not sure what tools are at your disposal for solving this problem, though.

Even manually, not too hard. Just rearrange, take logs and plot  a straight line.