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.
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:
$$ k_\text{obs} = k \times [\text{bleach}] \Leftrightarrow k = \frac{k_\text{obs}}{[\text{bleach}]} = 0.0299~\mathrm{s^{-1}\; M^{-1}}$$