Question

The pressure exerted by 12 g of an ideal gas at temperature $t^o$C in a vessel of volume $V$ is one atm. When the temperature is increased by 10 degrees at the same volume, the pressure increases by 10%. Calculate the temperature $t$ and volume $V$.

[Molecular weight of gas = 120]

Answer 1

$pv=nRT$

$P\alpha T$

$\frac{P_1}{T_1}=\frac{P_2}{T_2}$

$\to \frac{1}{t}=\frac{1+10\%of1}{t+10}$

$\Rightarrow t+10=(1+0.1)t$

$\Rightarrow 0.1t=10$

$\Rightarrow t=100K$

Now,

no. of moles $=\frac{12}{120}=0.1$

$\therefore V=\frac{nRT}{P}$

$=\frac{0.1}{10}\times \frac{1}{12}\times \frac{100}{1}=\frac{5}{6}lt$