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JEE CHEMISTRY MCQ: CHEMICAL KINETICS

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The half-life for the first-order decomposition of nitramide NH4NO2(aq)→N2O(g)+H2O(l)\mathrm{NH}_4 \mathrm{NO}_2(\mathrm{aq}) \rightarrow \mathrm{N}_2 \mathrm{O}(\mathrm{g})+\mathrm{H}_2 \mathrm{O}({l}) is 123 minutes at 27∘C27^{\circ} \mathrm{C}. If 200 ml200 \mathrm{~ml} of 0.02 M0.02 \mathrm{~M} NH4NO2\mathrm{NH}_4 \mathrm{NO}_2 solution is allowed to decompose, then how long must the reaction proceed to produce 49.26 ml49.26 \mathrm{~ml} of 'wet' N2O(g)\mathrm{N}_2 \mathrm{O}(\mathrm{g}) measured at 27∘C27^{\circ} \mathrm{C} and 785 mm Hg?785 \mathrm{~mm} \mathrm{~Hg}? The vapour pressure of water at 27∘C27^{\circ} \mathrm{C} is 25 mm Hg25 \mathrm{~mm} \mathrm{~Hg}.
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Correct option: A
123 min123 \mathrm{~min}
Option A (123 min) is correct because the reaction proceeds for one half-life to produce the given amount of N₂O.

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The reaction A2+B2→2AB\mathrm{A}_2+\mathrm{B}_2 \rightarrow 2 \mathrm{AB} follows the mechanism

A2⇌k−1k1A+A (fast) A+B2→k2AB+B (slow) A+B→AB (fast) \begin{aligned} & {{\text{A}}_2}\mathop \rightleftharpoons \limits_{{{\text{k}}_{ - 1}}}^{{{\text{k}}_1}} {\text{A}} + {\text{A (fast) }} \\ & \mathrm{A}+\mathrm{B}_2 \xrightarrow{\mathrm{k}_2} \mathrm{AB}+\mathrm{B} \text { (slow) } \\ & \mathrm{A}+\mathrm{B} \rightarrow \mathrm{AB} \text { (fast) } \end{aligned}

The overall order of the reaction is:
For the first order reaction with the rate constant kk, which expression gives the rate half-life period? (Initialconc.=a)(Initial\mathrm{ }conc.\mathrm{ } = a) Which of the following is a zero order reaction? For a certain reaction involving a single reactant, it is found that C0TC_0 \sqrt{T} is constant, where C0C_0 is the initial concentration of the reactant and TT is the half-life. What is the order of the reaction? Arrhenius equation is The energy of activation for an uncatalysed reaction is 100 kJ/mol.100 \mathrm{~kJ/mol}. Presence of a catalyst lowers the energy of activation by 75%75 \%. The log⁡10K2K1\log _{10} \frac{K_2}{K_1} of the ratio of rate constant of catalysed and uncatalysed reactions at 27∘C27^{\circ} \mathrm{C} is?

Assume the frequency factor is same for both reactions. (Given 2.303×8.314=19.1472.303 \times 8.314=19.147)
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