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Avogadro's Law & Gay Lussac's Law

4 g of an ide...

Question

4 g of an ideal gas was introduced into a bulb of volume of $0.821 {dm}^{3}$ at certain pressure, P and temperature T. The above bulb was placed in a thermostat maintained at temperature (T+125)K. 0.8 gm of the gas was leaked to keep the original pressure. Calculate the pressure in atm. [Molar mass of the gas is $40 {gmol}^{- 1}$ and R value is $0.0821 {lit-atm-k}^{- 1} {mol}^{- 1}$ ]

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Solution

Initial number of moles $= \frac{4}{40} = 0.1$
Final number of moles $= \frac{3.2}{40} = 0.08$
Since $P$ and $V$ are constant
$n_{1} T_{1} = n_{2} T_{2}$
$0.1 T_{1} = 0.08 (T_{1} + 125)$
$T_{1} = 500 K$
from $P V = n R T$
$P = \frac{0.1 \times 0.082 \times 500}{0.821} = 5 atm$

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