Chemical Kinetics

Consider the reaction $a\mathrm{X}\rightarrow b\mathrm{Y}$, for which the rate constant at 30$^\circ$C is $1\times10^{-3}$ mol$^{-1}$ L s$^{-1}$. Which of the following statements are true ? A. When concentration of 'X' is increased to four times, the rate of reaction becomes 16 times. B. The reaction is a second order reaction. C. The half-life period is independent of the concentration of X. D. Decomposition of $\mathrm{N_2O_5}$ is an example of the above reaction. E. A plot of $\ln\frac{[R_0]}{[R]}$ versus time (a straight line through the origin) is valid for the above reaction. Choose the correct answer from the options given below :

Consider the following gas phase reaction being carried out in a closed vessel at 25$^\circ$C. $2\mathrm{A(g)}\rightarrow4\mathrm{B(g)}+\mathrm{C(g)}$. Time (min) and total pressure of the system (mm Hg): at 30 min, 300; at $\infty$, 600. The pressure of C(g) at 30 minutes time interval would be ______ mm Hg. (nearest integer)

Consider the first order reaction $\mathrm{R\to P}$. The fraction of molecules decomposed in the given first order reaction can be expressed as

For a first order reaction $\mathrm{A\to B}$: at $t=0$ min, [A] = 0.6500 M; at $t=x$ min, [A] = 0.0650 M; at $t=20$ min, [A] = 0.00065 M. $x=$ ______ min. (Nearest integer)

First order gas phase reaction $\mathrm{A \rightarrow B + C}$; $p_i$ = initial pressure of gas A, $p_t$ = total pressure of the reaction mixture at time $t$. Expression of rate constant (k) is

If the half life of a first order reaction is 6.93 minutes then the time required for completion of 99% of the reaction will be ________ minutes . (Given : log 2 = 0.3010)

Sucrose hydrolyses in acidic medium into glucose and fructose by first order rate law with $t_{1/2}=3$ hour. The percentage of sucrose remaining after 6 hours is _____. (Nearest integer) (Given : log 2 = 0.3010 and log 3 = 0.4771)

Which of the following statement is not true for radioactive decay?

$\mathrm{A\to B}$. The molecule A changes into its isomeric form B by following a first order kinetics at a temperature of 1000 K. If the energy barrier with respect to reactant energy for such isomeric transformation is 191.48 kJ mol$^{-1}$ and the frequency factor is $10^{20}$, the time required for 50% molecules of A to become B is ______ picoseconds (nearest integer). [R = 8.314 J K$^{-1}$ mol$^{-1}$]