The half-life of ⁹²U₂₃₈ against \(\alpha\)-decay is 4.5 × 10⁹ year.  The time taken in a year for the decay of the 15/16 part of this isotope will be:

1. $9.0\times {10}^9$

2. $1.8\times {10}^{10}$

3. $4.5\times {10}^9$

4. $2.7\times {10}^{10}$

For a chemical reaction $\mathrm{A}\to$ product, the postulated mechanism of the reaction is as follows.

$\mathrm{A}\underset{{\mathrm{k}}_2}{\overset{{\mathrm{k}}_1}{\rightleftharpoons }}3\mathrm{B}\underset{\mathrm{R}.\mathrm{D}.\mathrm{S}}{\overset{{\mathrm{k}}_3}{\to }}{\mathrm{C}}_{}$
If the rate constants for individual reactions are  k₁, k₂ and k₃, and activation energies are 
\(E_{a_{1}} = 180 \ kJ \ mol^{-1}, \)
\( E_{a_{2}} = 90 \ kJ \ mol^{-1}, \)
\( E_{a_{3}} = 40 \ kJ \ mol^{-1}\)
then overall activation energy for the reaction given above is

1. 70 kJ mol^-1

2. -10 kJ mol^-1

3. 310 kJ mol^-1

4. 130 kJ mol^-1

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

1. $1.0\times {10}^6$ $s^{-1}$ $and$ $9.2$ $kJ$ $mo{l}^{-1}$

2. $6.0$ $s^{-1}$ $and$ $16.6$ $kJ$ $mo{l}^{-1}$

3. $1.0\times {10}^6$ $s^{-1}$ $and$ $16.6$ $kJ$ $mo{l}^{-1}$

4. $1.0\times {10}^6$ $s^{-1}$ $and$ $38.3$ $kJ$ $mo{l}^{-1}$

An increase in the concentration of the reactants of a reaction leads to a change in:

The rate constant for a first-order reaction is $4.606\times {10}^{-3}$ $s^{-1}$. The time required to reduce 2.0 g of the reactant to 0.2 g will be:

${}_{}$

1. Pseudo-first-order reaction

2. First-order reaction

3. Second order reaction

4. Third-order reaction

For a general reaction A $\to$ B, the plot of the concentration of A vs. time is given in the figure.
 

The slope of the curve will be:

The half-life of the two samples is 0.1 and 0.4 seconds, respectively. Their concentrations are 200 and 50, respectively. The order of the reactions will be:

1. 0

2. 2

3. 1

4. 4

For a reaction A → B, the Arrhenius equation is given as  \(log_{e}k \ = \ 4 \ - \ \frac{1000}{T}\) the activation energy in J/mol for the given reaction will be:

1. 8314

2. 2000

3. 2814

4. 3412

A first-order reaction takes 40 min for 30 % decomposition. The half life of the reaction will be: