The rate of a reaction increases sixteen times when the concentration of the reactant increases four times. The order of the reaction is
Assertion (A): The units of rate constant of a zero order reaction and rate of reaction are the same.
Reason (R): In zero order reaction, the rate of reaction is independent of the concentration of reactants.
The following experimental rate data were obtained for a reaction carried out at $$25^{\circ} \mathrm{C}$$
$$A_{(g)}+B_{(g)} \rightarrow C_{(g)}+D_{(g)}$$
| Initial $$\mathrm{[A_{(g)}]/mol~dm^{-3}}$$ | Initial $$\mathrm{[B_{(g)}]/mol~dm^{-3}}$$ | Initial rate/mol $$\mathrm{dm^{-3}s^{-1}}$$ |
|---|---|---|
| $$3.0 \times 10^{-2}$$ | $$2.0 \times 10^{-2}$$ | $$1.89 \times 10^{-4}$$ |
| $$3.0 \times 10^{-2}$$ | $$4.0 \times 10^{-2}$$ | $$1.89 \times 10^{-4}$$ |
| $$6.0 \times 10^{-2}$$ | $$4.0 \times 10^{-2}$$ | $$7.56 \times 10^{-4}$$ |
$$\text { What are the orders with respect to } \mathrm{A}_{(\mathrm{g})} \text { and } \mathrm{B}_{(\mathrm{g})} \text { ? }$$
Assertion (A): For a zero order reaction the unit of rate constant and rate of reaction are same.
Reason (R) : Rate of reaction for zero order reaction is independent of concentration of reactant.
Show that in case of a first order reaction, the time taken for completion of $99 \%$ reaction is twice the time required for $90 \%$ completion of the reaction. $(\log 10=1)$
The rate constant of a reaction quadruples when the temperature changes from 300 K to 320 K . Calculate the activation energy for this reaction. $\left[\log 2=0.30, \log 4=0.60,2.303 \mathrm{R}=19.15 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\right]$
What happens to the rate constant $$k$$ and activation energy $$E_a$$ as the temperature of a chemical reaction is increased? Justify.
(a) For the reaction
$$2 \mathrm{~N}_2 \mathrm{O}_{5(\mathrm{~g})} \rightarrow 4 \mathrm{NO}_{2(\mathrm{~g})}+\mathrm{O}_{2(\mathrm{~g})} \text { at } 318 \mathrm{~K}$$
Calculate the rate of reaction if rate of disappearance of $$\mathrm{N}_2 \mathrm{O}_{5(\mathrm{~g})}$$ is $$1.4 \times 10^{-3} \mathrm{~m} \mathrm{~s}^{-1}$$.
(b) For a first order reaction derive the relationship $$\mathbf{t}_{99 \%}=\mathbf{2} \mathbf{t}_{90 \%}$$