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First Order Reaction

Consider a fi...

Question

Consider a first order gas phase decomposition reaction given below

$A (g) \to B (g) + C (g)$ The initial prssure of the system before decomposition of A was $p_{i}$ . After lapse of time 't' total pressure of the system increased by x units and became ' $p_{t}$ '. The rate constant k for the reaction is given as ...... .

$(a) k = \frac{2.303}{t} l o g \frac{p_{i}}{p_{i} - x} (b) k = \frac{2.303}{t} l o g \frac{p_{i}}{2 p_{i} - p_{t}} (c) k = \frac{2.303}{t} l o g \frac{p_{i}}{2 p_{i} + p_{t}} (d) k = \frac{2.303}{t} l o g \frac{p_{i}}{p_{i} - x}$

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Solution

Answer: (b).

Initially At time t $A (g) p_{i} p_{i} - x \to B (g) 0 x + C (g) 0 x$

$p_{t} = p_{i} - x + x + x = p_{i} + x$

For first order reaction $x = p_{t} - p_{i}$

$k = \frac{2.303}{t} l o g \frac{p_{i}}{p_{i} - x} = \frac{2.303}{t} l o g \frac{p_{i}}{p_{i} - (p_{t} - p_{i})} = \frac{2.303}{t} l o g \frac{p_{i}}{2 p_{i} - p_{t}}$

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