# Calculation of the specific rate constant (k)

Suppose we found that the reaction of Red#3 with bleach is 1st order in hypochlorite. The observed rate constant ($k_\mathrm{obs}$) for one of the trials was measured to be $\pu{0.00400 s^{-1}}$. If the concentration of hypochlorite was fixed at $\pu{0.134 M}$, calculate the specific rate constant ($k$) for that trial.

I am very confused in which equation I should use to solve this problem. Am I to use this equation? $$\mathrm{Rate} = k[A]^m[B]^n$$

If that is the case, for trial #1:

$$\mathrm{Rate} = \pu{0.00400 s^{-1}} \times \pu{0.134 M} = \pu{5.36e-4 mol L^{-1} s^{-1}}$$

But then what should I do next? This does not sound right. Please point out my mistakes.

• use the correct equation for first order kinetics. Yours does not fit. – ssavec Feb 26 '14 at 9:00

We assume 1st order kinetics in hypochlorite and 1st order kinetics in the color. Putting this in the equation we get the following: $$\frac{\text{d}[\text{Red}]}{\text{d}t} = -k\, [\text{Red}]^1 \, [\text{bleach}]^1$$

Because you keep the concentration of bleach the same throughout the trial, you can write $$k_\text{obs} = k\times [\text{bleach}]$$

Now, we can continue onwards as follows: $$k_\text{obs} = k \times [\text{bleach}] \Leftrightarrow k = \frac{k_\text{obs}}{[\text{bleach}]} = 0.0299~\mathrm{s^{-1}\; M^{-1}}$$

• Thank you very much for the clear explanation! :) I get it now. – Jesse Mar 2 '14 at 2:23