Question

a cylinder with a moveable piston contains 4.78 l of a gas at 417 mm hg and 497 k. the pressure increases to 576 mm hg and temperature decreases to 386 k. what is the new volume of the cylinder?

Explanation:

Step1: Recall combined gas law

The combined gas law is $\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}$, where $P_1=417$ mmHg, $V_1=4.78$ L, $T_1=497$ K, $P_2=576$ mmHg, $T_2=386$ K, and $V_2$ is unknown.

Step2: Rearrange for $V_2$

$V_2 = \frac{P_1V_1T_2}{P_2T_1}$

Step3: Plug in values

$V_2 = \frac{417 \times 4.78 \times 386}{576 \times 497}$

Step4: Calculate the result

First compute numerator: $417×4.78≈2003.26$; $2003.26×386≈773258.36$
Denominator: $576×497≈286272$
$V_2≈\frac{773258.36}{286272}≈2.70$

Answer:

2.70 L