Chemical Kinetics

For a reversible reaction $\mathbf R\rightleftharpoons\mathbf P$, at constant temperature, both the forward and the backward reactions are first order elementary reactions with rate constants $k_f$ and $k_b$, respectively. At time zero, the concentration of $\mathbf R$ is $[\mathbf R]_0$ and the concentration of $\mathbf P$ is zero. At any given time, $[\mathbf R]$ and $[\mathbf P]$ are the concentrations of $\mathbf R$ and $\mathbf P$, respectively. If $k_b=4k_f$, the correct graphical representation of the reaction is

For a first-order reaction $\mathbf R\longrightarrow\mathbf P$ at a given temperature, $k$ is the rate constant. For this reaction, at the given temperature, the concentrations of $\mathbf R$ and $\mathbf P$ at a time $t$ are $[\mathbf R]$ and $[\mathbf P]$, respectively. The correct graphical representation(s) for this reaction is(are)

$t_{100\%}$ is the time required for the 100% completion of the reaction while $t_{1/2}$ is the time required for 50% of the reaction to be completed. Which of the following option correctly represents the relation between $t_{100\%}$ and $t_{1/2}$ for zero and first order reactions respectively ?

For reaction $\ce{A -> P}$, rate constant $k=1.5\times10^3$ s$^{-1}$ at 27 °C.
If activation energy for the above reaction is 60 kJ mol$^{-1}$, then the temperature (in °C) at which rate constant, $k=4.5\times10^3$ s$^{-1}$ is ________. (Nearest integer)
Given : $\log2=0.30$, $\log3=0.48$, $R=8.3$ J K$^{-1}$ mol$^{-1}$, $\ln10=2.3$

Consider the reaction $\ce{aX -> bY}$, for which the rate constant at 30 °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 $\ce{N2O5}$ is an example of the above reaction.

E. The graph of $\ln\dfrac{[R_0]}{[R]}$ against time shown 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 °C.
$$\ce{2A(g) -> 4B(g) + C(g)}$$

time (min)	total pressure of the system (mm Hg)
30	300
∞	600

The pressure of C(g) at 30 minutes time interval would be ________ mm Hg. (nearest integer)

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

Consider the given graph showing variation of reactant concentration with time.

Three different reactions were started with identical initial concentration of reactants. Which of the following statement is correct?

For a first order reaction $\ce{A -> B}$

t/min	[A]/M
0	0.6500
$x$	0.0650
20	0.00065

$x$ = ________ min. (Nearest integer)

First order gas phase reaction
$$\ce{A -> B + C}$$
$p_i$ = 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 : $\log 2 = 0.3010$)

For a reaction $\ce{A -> P}$ at T K, the half life ($t_{1/2}$) is plotted as a function of initial concentration $[\mathrm A]_o$ of A as given below.

The value of $x$ in the given figure is ________ s (Nearest integer)

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)

Decomposition of a hydrocarbon follows the equation $k=\left(5.5\times10^{11}\text{ s}^{-1}\right)e^{-28000\,\mathrm K/T}$. The activation energy of reaction is ________ kJ mol$^{-1}$. (Nearest Integer)

Given : R = 8.3 J K$^{-1}$ mol$^{-1}$

Given below are two statements :

R = 8.314 J K$^{-1}$ mol$^{-1}$ and 1 cal = 4.2 J

Statement I : When Ea = 12.6 kcal/mol, the room temperature rate constant is doubled by a 10 °C increase in temperature (298 K to 308 K)

Statement II : For a first order reactions A → B, the plot of $t_{1/2}$ against $[\mathrm A]_o$ is as shown. Here $[\mathrm A]_o$ is the initial concentration of A and $t_{1/2}$ is half life of reaction.

In the light of the above statements, choose the correct answer from the options given below :

Consider a reaction $A + R \longrightarrow \textit{Product}$. The rate of this reaction is measured to be $k[A][R]$. At the start of the reaction, the concentration of $R$, $[R]_0$, is 10-times the concentration of $A$, $[A]_0$. The reaction can be considered to be a pseudo first order reaction with assumption that $k[R] = k'$ is constant. Due to this assumption, the relative error (in %) in the rate when this reaction is 40 % complete, is _____.

[$k$ and $k'$ represent corresponding rate constants]

Consider the following reaction,

$$\ce{2H2(g) + 2NO(g) -> N2(g) + 2H2O(g)}$$

which follows the mechanism given below:

$$\ce{2NO(g)} \underset{k_{-1}}{\overset{k_1}{\rightleftharpoons}} \ce{N2O2(g)} \qquad \text{(fast equlibrium)}$$
$$\ce{N2O2(g) + H2(g)} \xrightarrow{k_2} \ce{N2O(g) + H2O(g)} \qquad \text{(slow reaction)}$$
$$\ce{N2O(g) + H2(g)} \xrightarrow{k_3} \ce{N2(g) + H2O(g)} \qquad \text{(fast reaction)}$$

The order of the reaction is _____.

A sample initially contains only U-238 isotope of uranium. With time, some of the U-238 radioactively decays into Pb-206 while the rest of it remains undisintegrated.

When the age of the sample is $\mathbf{P}\times10^8$ years, the ratio of mass of Pb-206 to that of U-238 in the sample is found to be 7. The value of P is _____.

[Given: Half-life of U-238 is $4.5\times10^9$ years; $\log_e 2 = 0.693$]

The plot of $\log k_f$ versus $1/T$ for a reversible reaction $\ce{A(g) <=> P(g)}$ is shown.

Pre-exponential factors for the forward and backward reactions are $10^{15}\,\mathrm{s^{-1}}$ and $10^{11}\,\mathrm{s^{-1}}$, respectively. If the value of $\log K$ for the reaction at 500 K is 6, the value of $|\log k_b|$ at 250 K is _____.

[$K$ = equilibrium constant of the reaction; $k_f$ = rate constant of forward reaction; $k_b$ = rate constant of backward reaction]

Match the rate expressions in LIST-I for the decomposition of X with the corresponding profiles provided in LIST-II. $\mathrm X_s$ and k are constants having appropriate units.