Question

The natural gas in a storage reservoir, under a pressure of 1.00 atmosphere, has a volume of 2.74 × 109 L at 20.0°C. The temperature at a later date falls to –20.0°C, but the pressure remains constant. Calculate the volume that the gas now occupies

Answer 1

Answer : The final volume of gas will be, $2.36\times 10^9L$

Explanation :

Charles' Law : It is defined as the volume of gas is directly proportional to the temperature of the gas at constant pressure and number of moles.

$V\propto T$

or,

$\frac{V_1}{V_2}=\frac{T_1}{T_2}$

where,

$V_1$ = initial volume of gas = $2.74\times 10^9L$

$V_2$ = final volume of gas = ?

$T_1$ = initial temperature of gas = $20.0^oC=273+20.0=293K$

$T_2$ = final temperature of gas = $-20.0^oC=273+(-20.0)=253K$

Now put all the given values in the above formula, we get the final volume of the gas.

$\frac{2.74\times 10^9L}{V_2}=\frac{293K}{253K}$

$V_2=2.36\times 10^9L$

Therefore, the final volume of gas will be, $2.36\times 10^9L$