In a reaction $A \to p r o d u c t s$ , the concentrations of reactant A are $C_{0}, a C_{0}, a^{2} C_{0}, a^{3} C_{0}$ after time interval 0, t, 2t, 3t, where a is constant. Given 0 < a < 1. The relation in k, a and t is :

k = \frac{2.303}{t} l o g \frac{1}{a}

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k = \frac{2.303}{t} l o g \frac{1}{a^{2}}

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k = \frac{2.303}{t} l o g \frac{1}{a^{3}}

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k = \frac{2.303}{t} l o g \frac{1}{a^{4}}

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Solution

The correct option is A $k = \frac{2.303}{t} l o g \frac{1}{a}$
The integrated rate law for the first order reaction is $k = \frac{2.303}{t} l o g \frac{[A]_{0}}{[A]_{t}}$
At $t = t$ , $k = \frac{2.303}{t} l o g \frac{C_{0}}{(a C_{0})} = \frac{2.303}{t} l o g \frac{1}{a}$
At $t = 2 t$ , $k = \frac{2.303}{(2 t)} l o g (C_{0} / (a^{2} C_{0})) = \frac{2.303}{(2 t)} l o g (1 / a^{2}) = \frac{2 \times 2.303}{2 t} l o g \frac{1}{a} = \frac{2.303}{t} l o g \frac{1}{a}$

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In a reaction A→products, the concentrations of reactant A are C0, aC0, a2C0, a3C0 after time interval 0, t, 2t, 3t, where a is constant. Given 0 < a < 1. The relation in k, a and t is :

The correct option is A k=2.303tlog1aThe integrated rate law for the first order reaction is k=2.303tlog[A]0[A]tAt t=t, k=2.303tlogC0(aC0)=2.303tlog1aAt t=2t, k=2.303(2t)log(C0/(a2C0))=2.303(2t)log(1/a2)=2×2.3032tlog1a=2.303tlog1a

In a reaction $A \to p r o d u c t s$ , the concentrations of reactant A are $C_{0}, a C_{0}, a^{2} C_{0}, a^{3} C_{0}$ after time interval 0, t, 2t, 3t, where a is constant. Given 0 < a < 1. The relation in k, a and t is :