If the reaction is first order in A and second order in B, what is the rate constant if [A] = "0.40 M" and [B] = "0.14 M"?

Nov 25, 2015

Well, I can't figure out what all your numbers are, but I can give you a general idea of what to do.

You know that the reaction is first order in $A$ and second order in $B$, so you can write the rate law as:

$r \left(t\right) = k \left[A\right] {\left[B\right]}^{2}$

You know that $\left[A\right] = \text{0.40 M}$ and $\left[B\right] = \text{0.14 M}$, and that you want the rate constant $k$. You apparently have $r \left(t\right)$ already, so you don't need to realize that the concentrations given are initial concentrations (they are).

There's nothing much you need to do here but plug things in and solve using some simple algebra.

$\textcolor{b l u e}{k = \frac{r \left(t\right)}{\left[A\right] {\left[B\right]}^{2}}}$

Since $r \left(t\right)$ is in $\text{M/s}$, and your concentrations overall give ${\text{M"*"M"^2 = "M}}^{3}$, what you have in units is:

${\text{M/s" = ("k units")*"M}}^{3}$
$\text{k units" = 1"/""M"^2*"s}$