Question

At $0^{0}C$ and $760mm$ Hg pressure, a gas occupies a volume of $100^{0}C{m}^3$. The kelvin temperature of the gas is inc hakeased by one-fifth while the pressure is increased one and half-times. Calculate the final volume of the gas.

• A. 80 cc
• B. 60 cc
• C. 100 cc
• D. 90 cc

Answer 1

Answer: (A)

80 cc

Solution:- (A) $80cc$

Given that at $100℃$ and $760\text{mm Hg}$ pressure, a gas occupies a volume of $100{cm}^3$.

$P_1=760\text{mm Hg}$

$T_1=0℃=273K$

$V_1=100{cm}^3$

The kelvin temperature of the gas is increased by one-fifth while the pressure is increased one and half-times.

$P_2=760+\frac{1}{2}\times 760=1140\text{mm Hg}$

$T_2=273+\frac{1}{5}\times 273=327.6K$

$V_2=?$

Using combined gas law, we have

$\frac{P_1{V}_1}{T_1}=\frac{P_2{V}_2}{T_2}$

$\Rightarrow \frac{760\times 100}{273}=\frac{1140\times V_2}{327.6}$

$\Rightarrow V_2=80{cm}^3$

Hence the final volume of the gas will be $80cc$.