Reaction kinetics, relating half life to reaction rate

![enter image description here](https://i.stack.imgur.com/8fKfm.png)


How do I relate the half life to the overall rate of reaction? 


I argued that from the data, doubling the partial pressure of either reactant, keeping the other constant, will half the half life. 


So try t1/2 = 
$\frac{\ce{[1]}}{\ce{[k][PA\_0][PB\_0]}}$ and since pressure of A is always greater than B, so t1/2 = $\frac{\ce{[1]}}{\ce{[k'][PB\_0]}}$ ?


I then wrote:
$$\frac{-\mathrm{d}[PB]}{\mathrm{d}t} = k [P\_B]^m $$, where **k** = k[PA] 




Recall the meaning of the half life $t\_{1/2}$: At $t\_{1/2}$, a concentration (or partial pressure) is decreased to the half of its initial value.


**It is crucial to realize that this represents exactly the $\mathbf{-\frac{dp\_A}{dt}}$ in your rate equation!**


With other words, $-\frac{dp\_A}{dt} = k\cdot p\_A\cdot p\_B^2$ becomes $-\frac{54}{2\cdot100} = k\cdot54\cdot(1.0)^2$ for your first set of data. 


Solve for $k$ and do the same for the other data sets. What is the result?


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