How can you determine the rate law of the following reaction?
$$2 \mathrm{NO}(\mathrm{~g})+\mathrm{O}_2(\mathrm{~g}) \longrightarrow 2 \mathrm{NO}_2(\mathrm{~g})$$
We can determine the rate of this reaction as a function of initial concentrations either by keeping the concentration of one of the reactants constant and changing the concentration of the other reactant or by changing the concentration of both the reactants. e.g., for the given reaction,
(i) Keeping $\left[\mathrm{O}_2\right]$ constant, if the concentration of NO is doubled, rate is found to become four times. This shows that,
$$\text { Rate } \propto[\mathrm{NO}]^2$$
(ii) Keeping [NO] constant, if the concentration of $\left[\mathrm{O}_2\right]$ is doubled, rate is also found to become double. This shows that,
$$\text { Rate } \propto\left[\mathrm{O}_2\right]^2$$
Hence, overall rate law will be
$$\begin{aligned} \text { Rate } =k\left[\mathrm{NO}^2\left[\mathrm{O}_2\right]\right. \\ \text{Rate law expression}\quad -\frac{1}{2} \frac{\Delta[\mathrm{NO}]}{\Delta t} & =-\frac{\Delta\left[\mathrm{O}_2\right]}{\Delta t} \\ & =\frac{1}{2} \frac{\Delta\left[\mathrm{NO}_2\right]}{\Delta t} \end{aligned} $$
For which type of reactions, order and molecularity have the same value?
If the reaction is elementary reaction then order and molecularity have same value because elementary reaction proceeds in a single step.
In a reaction if the concentration of reactant $A$ is tripled, the rate of reaction becomes twenty seven times. What is the order of the reaction?
Rate of any elementary reaction can be represented as
$$r=k[A]^n$$
After changing concentration to its triple value $A=3 A, r$ becomes $27 r$
$$\begin{aligned} & 27 r=k[3 A]^n \\ & \frac{r}{27 r}=\frac{k[A]^n}{k[3 A]^n} \\ & \frac{1}{27}=\left[\frac{1}{3}\right]^n \Rightarrow\left[\frac{1}{3}\right]^3=\left[\frac{1}{3}\right]^n \end{aligned}$$
Hence, $n=3$
Order of reaction is three.
Derive an expression to calculate time required for completion of zero order reaction.
For zero order reaction $[R]=[R]_0-k t$
For completion of the reaction $[R]=0$
$$\therefore \quad t=\frac{[R]_0}{k}$$
For a reaction $A+B \longrightarrow$ Products, the rate law is - Rate $=k[A][B]^{3 / 2}$. Can the reaction be an elementary reaction? Explain.
During an elementary reaction, the number or atoms or ions colliding to react is referred to as molecularity. Had this been an elementary reaction, the order of reaction with respect to $B$ would have been 1, but in the given rate law it is $\frac{3}{2}$. This indicates that the reaction is not an elementary reaction. Hence, this reaction must be a complex reaction.