A container holds $50.0 m L$ of nitrogen at $25 ° C$ and a pressure of $736 m m H g$ . What will be its volume if the temperature increases by $35 ° C$ and pressure remains constant ?

55.9 m L N_{2}

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99.5 m L N_{2}

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0.55 m L N_{2}

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9.95 m L N_{2}

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Solution

The correct option is A $55.9 m L N_{2}$
$P_{1} = 736 m m H g$
$P_{2} = 736 m m H g$
$V_{1} = 50.0 m L$
$V_{2} = ?$
$T_{1} = 25 ° C + 273 = 298 K$
$T_{2} = 25 ° C + 35 ° C + 273 = 333 K$
Since the pressure is constant, by Charle's law,(The volume of the gas is directly proportional to temperature at constant pressure)
$\frac{V_{1}}{T_{1}}$ = $\frac{V_{2}}{T_{2}}$
or $V_{2} = V_{1} \times \frac{T_{2}}{T_{1}}$
Substituting the given values in the above equation, we get
$V_{2} = 50 \times \frac{333}{298} = 55.86 m L N_{2}$ .

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