Question

The oxidation of certain metals is found to obey the equation $m^2=at+b$ where m is the thickness of the oxide film at time t, a and b are constants. What is the order of this reaction?

• A. First order
• B. Second order
• C. Third order
• D. None of these

Answer 1

The correct option is D None of these

Given that the thickness of oxide film is $m$, the oxidation of certain metal obeys the equation

$m^2=a{t}_b$ $-\left(i\right)$; $a$ and $b$ are constants differentiating $e{q}^n\left(i\right)$ $w.r.t$ $t$:-

$\Rightarrow 2m\frac{dm}{dt}=a$

$\Rightarrow \frac{dm}{dt}=\frac{a}{2}\left(\frac{1}{m}\right)$

$\Rightarrow \frac{dm}{dt}\propto \left(\frac{1}{m}\right)$

$\Rightarrow$ Rate of oxidation is inversely proportional to thickness of oxide film i.e. $m^{-1}$ so the order of this reaction is $-1$