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Two vessels of volumes $16.4 \mathrm{~L}$ and $5 \mathrm{~L}$ contain two ideal gases of molecular existence at the respective temperature of $27^{\circ} \mathrm{C}$ and $227^{\circ} \mathrm{C}$ and exert 1.5 and 4.1 atmospheres respectively. The ratio of the number of molecules of the former to that of the later is
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Given conditions $\mathrm{V}_{1}=16.4 \mathrm{~L}, \mathrm{~V}_{2}=5 \mathrm{~L}$
$\mathrm{P}_{1}=1.5 \mathrm{~atm}, \mathrm{P}_{2}=4.1 \mathrm{~atm}$
$\mathrm{T}_{1}=273+27=300 \mathrm{~K}$
$\mathrm{T}_{2}=273+227=500 \mathrm{~K}$
Applying gas equation, $\frac{\mathrm{P}_{1} \mathrm{~V}_{1}}{\mathrm{P}_{2} \mathrm{~V}_{2}}=\frac{\mathrm{n}_{1} \mathrm{~T}_{1}}{\mathrm{n}_{2} \mathrm{~T}_{2}}$
$\frac{\mathrm{n}_{1}}{\mathrm{n}_{2}}=\frac{\mathrm{P}_{1} \mathrm{~V}_{1} \mathrm{~T}_{1}}{\mathrm{P}_{2} \mathrm{~V}_{2} \mathrm{~T}_{2}}$
$\therefore \frac{1.5 \times 16.4 \times 500}{4.1 \times 5 \times 300}=\frac{2}{1}$
$\mathrm{P}_{1}=1.5 \mathrm{~atm}, \mathrm{P}_{2}=4.1 \mathrm{~atm}$
$\mathrm{T}_{1}=273+27=300 \mathrm{~K}$
$\mathrm{T}_{2}=273+227=500 \mathrm{~K}$
Applying gas equation, $\frac{\mathrm{P}_{1} \mathrm{~V}_{1}}{\mathrm{P}_{2} \mathrm{~V}_{2}}=\frac{\mathrm{n}_{1} \mathrm{~T}_{1}}{\mathrm{n}_{2} \mathrm{~T}_{2}}$
$\frac{\mathrm{n}_{1}}{\mathrm{n}_{2}}=\frac{\mathrm{P}_{1} \mathrm{~V}_{1} \mathrm{~T}_{1}}{\mathrm{P}_{2} \mathrm{~V}_{2} \mathrm{~T}_{2}}$
$\therefore \frac{1.5 \times 16.4 \times 500}{4.1 \times 5 \times 300}=\frac{2}{1}$
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