A reactant $\ce{X}$ is converted into products $\ce{Y}$ and $\ce{Z}$ according to the following first order parallel reactions:



$\ce{[X]}$ has decreased from $\pu{1.00 M}$ at $t = 0$ to $\pu{0.549 M}$ after $\pu{10 min}$. Calculate the rate constants $k_1$ and $k_2$, knowing that the yields of $\ce{Y}$ and $\ce{Z}$ obtained are $25.0$ and $\pu{75.0 mol\%}$, respectively.

So far, I have the ratio between $k_1$ and $k_2$ $=0.33$, which I found from the yield ratio but I'm unsure what to do with this ratio.

I also have derived the equation $[A] = [A]_0 \cdot e^{-(k_1+ k_2)t}$


1 Answer 1


By some simple mathematics, you can reach the following equations (the first of which you have reached):

$[X]=[X]_0\cdot e^{-(k_1+k_2)t}$

$[Y]=\frac{k_1}{k_1+k_2}[X]_0\cdot e^{-k_1 t}$

$[Z]=\frac{k_2}{k_1+k_2}[X]_0\cdot e^{-k_2 t}$

The $1:3$ ratio that you have arrived at is correct, i.e. $\dfrac{k_1}{k_2}=\dfrac{1}{3}$.

Substituting this in the equation for $\ce{X}$, we get

$[X]=[X]_0\cdot e^{-4k_1 t}$

All that is left to do now is to substitute and solve, which leads to the answer:

$(k_1,k_2)\equiv(0.015\ (min)^{-1},0.045\ (min)^{-1})$

There you go!

PS: I've used $[X]_0$ for representing the initial concentration of $\ce{X}$.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.