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Standard XII

Chemistry

Vant Hoff's Equation and Effect of Temperature on Equilibrium Constant

The decomposi...

Question

The decomposition of an equal mole of two reactants P and Q obey 1st order kinetics with half-life 54 and 18 minutes respectively. If both are allowed to run for 54 minutes. The ratio of mole of Q and P left after decomposition will be:

3

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\frac{1}{4}

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4

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16

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Solution

The correct option is B $\frac{1}{4}$
Let initially $X$ moles of P and $X$ moles of Q are present.

For P, $18$ minutes corresponds to $1$ half-life and for Q, $54$ minutes corresponds to $3$ half-life periods.

After $1$ half life period, the number of moles of P left $= \frac{X}{2}$

After $3$ half life periods, number of moles of Q left $= \frac{X}{2^{3}} = \frac{X}{8}$

The ratio of mole of Q and P left after decomposition will be $= \frac{\frac{X}{8}}{\frac{X}{2}} = \frac{1}{4}$

Hence, option B is correct.

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