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

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.

[tex]V\propto T[/tex]

or,

[tex]\frac{V_1}{V_2}=\frac{T_1}{T_2}[/tex]

where,

[tex]V_1[/tex] = initial volume of gas = [tex]2.74\times 10^9L[/tex]

[tex]V_2[/tex] = final volume of gas = ?

[tex]T_1[/tex] = initial temperature of gas = [tex]20.0^oC=273+20.0=293K[/tex]

[tex]T_2[/tex] = final temperature of gas = [tex]-20.0^oC=273+(-20.0)=253K[/tex]

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

[tex]\frac{2.74\times 10^9L}{V_2}=\frac{293K}{253K}[/tex]

[tex]V_2=2.36\times 10^9L[/tex]

Therefore, the final volume of gas will be, [tex]2.36\times 10^9L[/tex]