Determining the rate equation from a reaction where one reactant is in excess

Question

Lets say rate = k[A][B]ⁿ
(A is in excess, lets say at a concentration of 50mM)

My data includes the initial concentration of B, and the initial rate of reaction at that concentration

I can rewrite the rate equation as as:
rate = k^app[B]ⁿ

I then take the natural logarithm of this equation and plot a graph of ln(rate) against ln[B], the gradient will give me the value of n.

Am I right in thinking that the y intercept will give a value of k^app? And if it does, to determine the true rate constant do I just divide k^app by 50? If not, how do you determine the true rate constant?

Answer 1

There is no real need to invoke a "$k^{app}$".

Let the rate be $r$, so:

$$r=k[\ce{A}][\ce{B}]^n$$

Since as $\ce{A}$ is in large excess:

$$[\ce{A}]=C(A)\gg[\ce{B}] \implies r=kC(A)[\ce{B}]^n$$

So $[\ce{A}]$ doesn't vary perceptibly during the rate measurement interval.

Plot the value of $\ln r$ versus $\ln [\ce{B}]$ in the knowledge that:

$$\ln r=\ln k + \ln C(A) + n\ln [\ce{B}]$$

So the gradient of that graph is $n$.

And the intercept of that graph is $\ln k + \ln C(A)$. Since as $C(A)$ is known, $\ln k$, and thus $k$, is also known.