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* 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,

`(V_1)/(V_2)=(T_1)/(T_2)`

where,

`V_1` = initial volume of gas =
`2.74* 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.

`(2.74* 10^9L)/(V_2)=(293K)/(253K)`

`V_2=2.36* 10^9L`

Therefore, the final volume of gas will be,
`2.36* 10^9L`