Chemical Kinetics and Nuclear Chemistry

For a first-order reaction $\mathbf{R} \rightarrow \mathbf{P}$ 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}...

For a reversible reaction $R \rightleftharpoons P$, 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 conce...

Consider a reaction $A+R \rightarrow$ 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 t...

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

When the age of the sample is $\mathbf{P} \times 10^8$ years,...

Consider the following reaction,

\(2 \mathrm{H}_2(\mathrm{~g})+2 \mathrm{NO}(\mathrm{g}) \rightarrow \mathrm{N}_2(\mathrm{~g})+2 \mathrm{H}_2 \mathrm{O}(\mathrm{g})\)

which follows the mechanism given below :

$$ \begin{array}{ll} 2 \ma...

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

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For the following reaction,
\(2X + Y\buildrel k \over \longrightarrow P\) the rate of reaction is \({{d[P]} \over {dt}} = k[X]\). Two moles of X are mixed with one mole of Y to make 1.0 L of solution. At 50 s, 0.5 mole of Y is left in the ...

Which of the following plots is(are) correct for the given reaction?([P]0 is the initial concentration of P)

\(_{92}^{238}U\) is known to undergo radioactive decay to form \(_{82}^{206}Pb\) by emitting alpha and beta particles. A rock initially contained 68 \(\times\) 10\(-\)6 g of \(_{92}^{238}U\). If the number of alpha particles that it would...

The decomposition reaction\(2{N_2}{O_5}(g)\buildrel \Delta \over \longrightarrow 2{N_2}{O_4}(g) + {O_2}(g)\) is started in a closed cylinder under isothermal isochoric condition at an initial pressure of 1 atm. After Y \(\times\) 103 s,...

Consider the kinetic data given in the following table for the reaction A + B + C \(\to\) 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 \(\times\) 10-5 mol dm-3s-...

In the decay sequence. x1, x2, x3 and x4 are particles/radiation emitted by the respective isotopes. The correct option(s) is(are)

Consider the following reversible reaction, \(A\left( g \right) + B\left( g \right) \to AB\left( g \right).\)
The activation energy of the backward reaction exceeds that of the forward reaction by \(2RT\) (in \(J\,mo{l^{ - 1}}\)). If the ...

For a first order reaction \(A\left( g \right) \to 2B\left( g \right) + C\left( g \right)\) at constant volume and \(300K,\) the total pressure at the beginning \((t=0)\) and at time \(t\) are \({P_0}\) and \({P_1},\) respectively. Initiall...

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

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 ...

In dilute aqueous H2SO4, the complex diaquodioxalatoferrate(II) is oxidized by \(MnO_4^-\). For this reaction,
the ratio of the rate of change of [H+] to the rate of change of \([MnO_4^-]\) is

A closed vessel with rigid walls contains 1 mol of \({}_{92}^{238}U\) and 1 mol of air at 298 K. Considering complete decay of \({}_{92}^{238}U\) to \({}_{82}^{206}Pb\), the ratio of the final pressure to the initial pressure of the system ...

The % yield of ammonia as a function of time in the reaction
N2(g) + 3H2(g) \(\rightleftharpoons\) 2NH3(g), \(\Delta\)H < 0 at (P, T1) is given below:

If this reactions is conducted at (P, T2), with T2 > T1, the % yield of ammonia as a fun...

For the elementary reaction M \(\to\) N, the rate of disappearance of M increases by a factor of 8 upon
doubling the concentration of M. The order of the reaction with respect to M is

The experimental value of d is found to be smaller than the estimate obtained using Graham's law. This is due to

The value of d in cm (shown in the figure), as estimated from Graham's law, is

In the nuclear transmutation
9Be4 + X \(\to\) 8Be4 + Y
(X, Y) is (are) :

In the reaction, P + Q \(\to\) R + S, the time taken for 75% reaction of P is twice the time taken for 50% reaction of P. The concentration of Q varies with reaction time as shown in the figure. The overall order of the reaction is

An organic compound undergoes first-order decomposition. The time taken for its decomposition to 1/8 and 1/10 of its initial concentration are t1/8 and t1/10 respectively. What is the value of $$\left[ {{{{t_{1/8}}} \over {{t_{1/10}}}}} \ri...

The periodic table consists of 18 groups. An isotope of copper, on bombardment with protons undergoes a nuclear reaction yielding element X as shown below. To which group, element X belongs in the periodic table?
\({}_{29}^{63}Cu\) + $${}_1...

For the first order reaction
2N2O5 (g) \(\to\) 4NO2 (g) + O2 (g)

Bombardment of aluminium by \(\alpha\)-particle leads to its artificial disintegration in two ways : (i) and (ii) as shown. Products X, Y and Z, respectively, are

The number of neutrons emitted when \({}_{92}^{235}U\) undergoes controlled nuclear fission to \({}_{54}^{142}Xe\) and \({}_{38}^{90}Sr\) is

The concentration of R in the reaction R \(\to\) P was measured as a function of time and the following data is obtained


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Plots showing the variation of the rate constant (\(k\)) with temperature (\(T\)) are given below. The point that follows Arrhenius equation is

The total number of \(\alpha\) and \(\beta\) particles emitted in the nuclear reaction \(_{92}^{238}U \to _{82}^{214}Pb\) is _________.

For a first-order reaction A \(\to\) P, the temperature (T) dependent rate constant (k) was found to follow the equation \(\log k = - (2000){1 \over T} + 6.0\). The pre-exponential factor A and activation energy \(E_a\), respectively, are

Under the same reaction conditions, initial concentration of 1.386 mol dm\(^{-3}\) of a substance becomes half in 40 seconds and 20 seconds through first order and zero order kinetics, respectively. Ratio $$\left( {{{{k_1}} \over {{k_0}}}} ...

Consider a reaction aG + bH \(\to\) Products. When concentration of both the reactants G and H is doubled, the rate
increases by eight times. However, when concentration of G is doubled keeping the concentration of H fixed, the rate is
doub...

\(\text { Match Column I with Column II : }\)
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A nuclear explosion has taken place leading to increase in concentration of ${ }^{14} \mathrm{C}$ in nearby areas. ${ }^{14} \mathrm{C}$ concentration is $\mathrm{C}_1$ in nearby areas and $C_2$ in areas far away. If the age of the fossil i...

What should be the age of fossil for meaningful determination of its age?

Which of the following option is correct?

For the following reaction
2X(g) \(\to\) 3Y(g) + 2Z(g)
assuming ideal gas conditions, the data for change of partial pressure with time is as follows:
$$
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\hline \text { Time (in min) } & 0 & 100 & 200 \\
\hline \begin{ar...

Fill in the blanks:
(A) \(_{92}^{235}\)U + \(_{0}^{1}\)n \(\to\) \(_{52}^{137}\)A + \(_{40}^{97}\)B + ____________.
(B) \(_{34}^{82}\)Se \(\to\) 2 \({}_{ - 1}{e^0}\) + __________.

At constant temperature and volume, X decomposes as 2X(g) \(\to\) 3Y(g) + 2Z(g); Px is the partial pressure of X.


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For the given reactions, A + B \(\to\) Products, following data were obtained


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The vapour pressure of the two miscible liquids (A) and (B) are 300 and 500 mm of Hg respectively. In a flask 10 moles of (A) is mixed with 12 moles of (B). However, as soon as (B) is added, (A) starts polymerizing into a completely insolub...

The rate of a first order reaction is 0.04 mol litre-1 s-1 at 10 minutes and 0.03 mol litre-1 s-1 at 20 minutes after initiation. Find the half-life of the reaction.

A hydrogenation reaction is carried out at 500 K. If the same reaction is carried out in the presence of a catalyst at the same rate, the temperature required is 400 K. Calculate the activation energy of the reaction if the catalyst lowers ...

The rate constant for an isomerisation reaction, A \(\to\) B is 4.5 \(\times\) 10-3 min-1. If the initial concentration of A is 1 M, calculate the rate of the reaction after 1 h.

The rate constant of a reaction is 1.5 \(\times\) 107 s-1 at 50oC and 4.5 \(\times\) 107 s-1 at 100oC. Evaluate the Arrhenius parameters A and Ea.

The ionisation constant of \(NH_4^+\) in water is 5.6 \(\times\) 10-10 at 25oC. The rate constant for the reaction of \(NH_4^+\) and \(OH^-\) to form NH3 and H2O at 25oC is 3.4 \(\times\) 1010 L mol-1s-1. Calculate the rate constant for pro...