Answer:
[tex]\boxed{\text{2.47 L}}[/tex]
Explanation:
The pressure is constant, so, to calculate the volume, we can use Charles' Law.
[tex]\dfrac{V_{1}}{T_{1}} = \dfrac{V_{2}}{T_{2}}[/tex]
Data:
V₁ = 2.98 L; T₁ = 32.8 °C
V₂ = ?; T₂ = -19.9 °C
Calculations:
(a) Convert temperatures to kelvins
T₁ = ( 32.8 + 273.15) K = 305.95 K
T₂ = (-19.9 + 273.15) K = 253.25 K
(b) Calculate the new volume
[tex]\begin{array}{rcl}\dfrac{V_{1}}{T_{1}} &= &\dfrac{V_{2}}{T_{2}}\\\\\dfrac{2.98}{305.95} &= &\dfrac{V_{2}}{253.25}\\\\9.740 \times 10^{-3} &= &\dfrac{V_{2}}{253.25}\\\\{ V_{2}} &=& 9.740 \times 10^{-3} \times 253.25\\&=& \textbf{2.47 L}\\\end{array}\\\text{The gas will occupy $\large \boxed{\textbf{2.47 L}}$}[/tex]
