Find order of reaction 2A → B + C


> 
> Derive the integrated rate expression for a reaction of type:
> 
> 
> $$\ce{2A -> B + C}$$
> 
> 
> 


I first need to determine the order of the reaction in order to find integrated rate law of that particular order. How to find the order of above reaction? Please note that there is no extra data is provided, and the rate law expression is also not given.


It appears there is not enough data in the question to come to a conclusion. Normally, experimental data would be provided or at least the rate expression. I tried to search a lot, but it was all in vain.




If
$$
2\ce{A ->[$k$] B + C}
$$
is assumed to be an elementary step then the reaction is second order 
$$
-\frac{1}{2}\frac{\mathrm d[\ce{A}]}{\mathrm dt}=k[\ce{A}]^2
$$
because the sum of the exponents on the right-side of the equation is $2.$


The integrated rate expression is found by taking the rate of change, rearranging and integrating from an initial concentration $[\ce{A}]\_0$ at $t =0$ to $[\ce{A}]$ at time $t$:
$$
\int\_{[\ce{A}]\_0}^{[\ce{A}]}\frac{\mathrm d[\ce{A}]}{[\ce{A}]^2} = -2k \int\_0^t\mathrm dt
$$
to yield
$$
\frac{1}{[\ce{A}]} = \frac{1}{[\ce{A}]\_0} + 2kt
$$


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