Chemical Kinetics

For the given first order reaction

A → B

the half life of the reaction is 0.3010 min. The ratio of the initial concentration of reactant to the concentration of reactant at time 2.0 min will be equal to ______. (Nearest integer)

For a reaction, given below is the graph of ln k vs $\dfrac1T$. The activation energy for the reaction is equal to ______ cal mol$^{-1}$. (nearest integer)

(Given : R = 2 cal K$^{-1}$ mol$^{-1}$)

The reaction between X and Y is first order with respect to X and zero order with respect to Y.

Experiment	[X] / mol L$^{-1}$	[Y] / mol L$^{-1}$	Initial rate / mol L$^{-1}$ min$^{-1}$
I	0.1	0.1	$2\times10^{-3}$
II	L	0.2	$4\times10^{-3}$
III	0.4	0.4	$M\times10^{-3}$
IV	0.1	0.2	$2\times10^{-3}$

Examine the data of table and calculate ratio of numerical values of M and L. (Nearest Integer)

Assuming 1 μg of trace radioactive element X with a half life of 30 years is absorbed by a growing tree. The amount of X remaining in the tree after 100 years is _______ $\times10^{-1}$ μg.

[Given: ln 10 = 2.303; log 2 = 0.30]

X → Y + Z

X decomposes at 700 K to give Y and Z. The results of two measurements are :

Initial concentration of X / (mol/L)	6.0	12.0
Half life / s	1.0	2.0

The rate constant for the reaction is _______ (in appropriate unit)

For the following reaction
$$2\mathbf X + \mathbf Y \xrightarrow{k} \mathbf P$$
the rate of reaction is $\dfrac{d[\mathbf P]}{dt} = k[\mathbf X]$. Two moles of $\mathbf X$ are mixed with one mole of $\mathbf Y$ to make 1.0 L of solution. At 50 s, 0.5 mole of $\mathbf Y$ is left in the reaction mixture. The correct statement(s) about the reaction is(are)

(Use: $\ln 2 = 0.693$)

Gaseous cyclobutene isomerizes to butadiene in a first order process which has a 'k' value of $3.3\times10^{-4}$ s$^{-1}$ at 153°C. The time in minutes it takes for the isomerization to proceed 40% to completion at this temperature is _______. (Rounded off to the nearest integer)

$\ce{^{238}_{92}U}$ is known to undergo radioactive decay to form $\ce{^{206}_{82}Pb}$ by emitting alpha and beta particles. A rock initially contained $68\times10^{-6}$ g of $\ce{^{238}_{92}U}$. If the number of alpha particles that it would emit during its radioactive decay of $\ce{^{238}_{92}U}$ to $\ce{^{206}_{82}Pb}$ in three half-lives is $Z\times10^{18}$, then what is the value of $Z$?

Which of the following plots is(are) correct for the given reaction?

($[\mathbf P]_0$ is the initial concentration of P)

In the decay sequence,

$$\ce{^{238}_{92}U ->[-x_1] ^{234}_{90}Th ->[-x_2] ^{234}_{91}Pa ->[-x_3] ^{234}\mathbf{Z} ->[-x_4] ^{230}_{90}Th}$$

$x_1$, $x_2$, $x_3$ and $x_4$ are particles/radiation emitted by the respective isotopes. The correct option(s) is(are)

Consider the kinetic data given in the following table for the reaction $\ce{A + B + C -> Product}$.

The rate of the reaction for [A] = 0.15 mol dm⁻³, [B] = 0.25 mol dm⁻³ and [C] = 0.15 mol dm⁻³ is found to be $Y\times10^{-5}$ mol dm⁻³ s⁻¹. The value of $Y$ is ______

The decomposition reaction $\ce{2N2O5(g) ->[\Delta] 2N2O4(g) + O2(g)}$ is started in a closed cylinder under isothermal isochoric condition at an initial pressure of 1 atm. After $Y\times10^3$ s, the pressure inside the cylinder is found to be 1.45 atm. If the rate constant of the reaction is $5\times10^{-4}\ \mathrm{s^{-1}}$, assuming ideal gas behavior, the value of $Y$ is ______

For a first order reaction $\mathrm{A(g)} \to \mathrm{2B(g)} + \mathrm{C(g)}$ at constant volume and 300 K, the total pressure at the beginning ($t = 0$) and at time $t$ are $P_0$ and $P_t$, respectively. Initially, only A is present with concentration $[\mathrm{A}]_0$, and $t_{1/3}$ is the time required for the partial pressure of A to reach 1/3$^{\text{rd}}$ of its initial value. The correct option(s) is (are)

(Assume that all these gases behave as ideal gases)

Consider the following reversible reaction,

$$\mathrm{A(g) + B(g) \rightleftharpoons AB(g)}.$$

The activation energy of the backward reaction exceeds that of the forward reaction by $2RT$ (in J mol$^{-1}$). If the pre-exponential factor of the forward reaction is 4 times that of the reverse reaction, the absolute value of $\Delta G^\ominus$ (in J mol$^{-1}$) for the reaction at 300 K is ____.

(Given; ln(2) = 0.7, $RT$ = 2500 J mol$^{-1}$ at 300 K and $G$ is the Gibbs energy)

In a bimolecular reaction, the steric factor P was experimentally determined to be 4.5. The correct option(s) among the following is(are)

Two reactions $R_1$ and $R_2$ have identical pre-exponential factors. Activation energy of $R_1$ exceeds that of $R_2$ by 10 kJ mol$^{-1}$. If $k_1$ and $k_2$ are rate constants for reactions $R_1$ and $R_2$ respectively at 300 K, then $\ln(k_2/k_1)$ is equal to :

(R = 8.314 J mol$^{-1}$K$^{-1}$)

The rate of a reaction A doubles on increasing the temperature from 300 to 310 K. By how much, the temperature of reaction B should be increased from 300 K so that rate doubles if activation energy of the reaction B is twice to that of reaction A.

The rate of a reaction quadruples when the temperature changes from 300 to 310 K. The activation energy of this reaction is :

(Assume activation energy and pre-exponential factor are independent of temperature; ln 2 = 0.693; R = 8.314 J mol$^{-1}$ K$^{-1}$)

According to the Arrhenius equation,

A plot of the number of neutrons $(N)$ against the number of protons $(P)$ of stable nuclei exhibits upward deviation from linearity for atomic number, $Z>20$. For an unstable nucleus having $N/P$ ratio less than 1, the possible mode(s) of decay is(are)