Which of the energy values marked as $\mathrm{I}, \mathrm{II}$ and $\mathrm{III}$ in the following diagram, will change by the addition of a suitable catalyst?

Urea, $\mathrm{CO}{\left({\mathrm{NH}}_2\right)}_2,$ decomposes at $90°\mathrm{C}$ as ${\left[\mathrm{CO}\left({\mathrm{NH}}_2\right)\right]}_2\left(\mathrm{aq}\right)\to {\mathrm{NH}}_4^{+}\left(\mathrm{aq}\right)+{\mathrm{OCN}}^{-}\left(\mathrm{aq}\right).$ Experimental data obtained for the reaction is given in the following plot;

From the graph it can be inferred that-

A simple mechanism for enzyme-catalyzed reaction is given by the following set of equations:

$\underset{\left(\mathrm{enzyme}\right)}{\mathrm{E}}+\underset{\left(\mathrm{reactant}\right)}{\mathrm{S}}\rightleftharpoons \underset{(\mathrm{intermediate}-1)}{\mathrm{ES}}$

$\underset{(\mathrm{intermediate}-1)}{\mathrm{ES}}\rightleftharpoons \underset{(\mathrm{intermediate}-2)}{\mathrm{EP}}$

$\underset{(\mathrm{intermediate}-2)}{\mathrm{EP}}\rightleftharpoons \underset{\left(\mathrm{enzyme}\right)}{\mathrm{E}}+\underset{\left(\mathrm{product}\right)}{\mathrm{P}}$

This is known as the Michaelis-Menten mechanism. The potential energy diagram is shown in the figure. Which of the following sets of identifications is correct? (Assume that the temperature and pressure are constant).

Consider the following reactions at $300 \mathrm{K}.$

$\mathrm{A}\to \mathrm{B}$ (uncatalysed reaction)

$\mathrm{A}\stackrel{\mathrm{catalyst}}{\to }\mathrm{B}$ (catalyst reaction)

The activation energy is lowered by $8.314 \mathrm{KJ} {\mathrm{mol}}^{-1}$ the catalysed reaction. How many times is the rate of this catalysed reaction greater than that of uncatalysed reaction? (Given ${\mathrm{e}}^{3.33}=28$)

For the reaction $\mathrm{A}\to \mathrm{B}$, the rate law expression is $-\frac{\mathrm{d}\left[\mathrm{A}\right]}{\mathrm{dt}}=\mathrm{K}{\left[\mathrm{A}\right]}^{1/2}.$ If initial concentration of $\mathrm{A}$is ${\mathrm{A}}_0.$

Calculate:

(a) Integrated form of the rate law expression

(b) Nature of plot of $\left[\mathrm{A}\right]{}^{1/2}$ vs time.

(c) Half life period.