Answer
The final volume, V₂ the gas occupies = 8.81 L
Explanation
Given data:
Initial temperature, T₁ = 31 °C = 31 +273 K = 304 K
Initial volume, V₁ = 7.74 L
Final temperature, T₂ = 73 °C = 73 + 273 K = 346 K
Note: The pressure is kept constant.
What to find:
The final volume, V₂ the gas occupies.
Step-by-step solution
Using Charle's law:
[tex]\frac{V_1}{T_1}=\frac{V_2}{T_2}[/tex]
To get V₂, substitute the given parameters into the equation above:
[tex]\begin{gathered} \frac{7.74\text{ L}}{304\text{ K}}=\frac{V_2}{346\text{ K}} \\ \text{Cross multiply} \\ V_2\times304\text{ K }=7.74\text{ L }\times346\text{ K} \\ \text{Divide both sides by 304 K} \\ \frac{V_2\times304\text{ K }}{304\text{ K }}=\frac{7.74\text{ L }\times346\text{ K}}{304\text{ K }} \\ V_2=8.81\text{ L} \end{gathered}[/tex]
The final volume, V₂ the gas occupies is 8.81 L
