5.3 L.
Explanation
By Charles's Law,
- the volume of an ideal gas is proportional to its absolute temperature when its pressure is held constant.
In other words,
[tex]\dfrac{V_2}{V_1} = \dfrac{T_2}{T_1}[/tex],
where
- [tex]V[/tex] is the volume of the gas, and
- [tex]T[/tex] is the absolute temperature of the gas in degrees Kelvins.
As a noble gas, helium is quite "ideal" with rather weak attractions between its particles unless in direct contact.
Convert the temperatures:
- [tex]T_1 = -45 \textdegree\text{C} = (-45 + {\bf 273.15} ) \; {\textbf{K}} = 228.15 \; \text{K}[/tex];
- [tex]T_2 = 45 \textdegree\text{C} = (45 + {\bf 273.15} ) \; {\textbf{K}} = 318.15 \; \text{K}[/tex].
Apply Charles's Law,
[tex]V_2 = V_1 \cdot \dfrac{T_2}{T_1} = 3.8 \times \dfrac{228.15}{318.15} = 5.3 \; \text{L}[/tex].
