Answer
The final volume of the gas is 0.70 L
Work Step by Step
The Charle's gas law defines the relationship between temperature and volume. According to this, the volume of gas is directly proportional to its temperature at a constant pressure.
$\frac{V}{T}$ = constant
Therefore as the temperature of a gas increases the volume of the gas increases and as the temperature of a gas decreases the volume of the gas decreases.
For a gas, we can create two equations with $V_{1}$ as the initial volume of the gas and $V_{2}$ as the final volume of the gas.
$V_{1}$= 2.7 L,
$T_{1}$= 298 K
$T_{2}$= 77 K.
$\frac{V_{1}}{T_{1}} = \frac{V_{2}}{T_{2}}$
rearrange the equation for $V_{2}$
$V_{2} = \frac{T_{2}V_{1}}{T_{1}}$
Plug in the values for the variables
$V_{2} = \frac{77 K \times 2.7 L}{298 K}$
Solve using a calculator
$V_{2} = 0.70 L$
