A fixed quantity of gas at 23 ∘C
exhibits a pressure of 759 torr
and occupies a volume of 5.52 L
.Calculate the volume the gas will occupy if the temperature is increased to 170 ∘C
while the pressure is held constant.
Using the combined gas law formula, we can calculate the final volume of the gas:
\( \frac{P1 \times V1}{T1} = \frac{P2 \times V2}{T2} \)
Given:
\( P1 = 759 \, torr \)
\( V1 = 5.52 \, L \)
\( T1 = 23 \, ^\circ C + 273 = 296 \, K \)
\( T2 = 170 \, ^\circ C + 273 = 443 \, K \)
We are trying to find \( V2 \)
Substitute the given values into the formula:
\( \frac{759 \times 5.52}{296} = \frac{759 \times V2}{443} \)
\( \frac{4187.68}{296} = \frac{759 \times V2}{443} \)
\( 14.14 = \frac{759 \times V2}{443} \)
\( V2 = \frac{14.14 \times 443}{759} \)
\( V2 ≈ 8.24 \, L \)
Therefore, the gas will occupy approximately 8.24 L when the temperature is increased to 170 ∘C while the pressure is held constant.