$C H_{2} = C H_{2} (g) + H_{2} (g) N i (s) \to C H_{3} - C H_{3}$
For this reaction calculate the ratio of $t_{75}$ and $t_{50}$ (half life).

1.5

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2

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2.5

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1.25

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Solution

The correct option is B $2$
$C H_{2} = C H + H_{2} N i - \to C H_{3} - C H_{3}$
It is a first order reaction.
$t_{1} = \frac{2.303}{K} l o g [\frac{A_{o}}{A_{t}}]$
Let $A_{o} = 100; A_{75} = 100 - 75 = 25; A_{50} = 100 - 50 = 50$
$\frac{t_{75}}{t_{50}} = \frac{\frac{2.303}{K} l o g [\frac{A_{o}}{A_{75}}]}{\frac{2.303}{K} l o g [\frac{A_{o}}{A_{50}}]}$
$\Rightarrow \frac{t_{75}}{t_{50}} = \frac{l o g [\frac{100}{25}]}{l o g [\frac{100}{50}]}$
$\frac{t_{75}}{t_{50}} = \frac{l o g (4)}{l o g (2)} = 2$

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