Question

a gas has an initial volume of 21.7 l at a pressure of 0.4 atm and a temperature of 252 k. the pressure of the gas increases to 2 atm as the temperature increases to 323 k. what is the final volume of the gas?
3.4 l
5.6 l
8.5 l
11.1 l

Explanation:

Step1: Identify the combined - gas law formula

The combined - gas law is $\frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2}$, where $P_1$ is the initial pressure, $V_1$ is the initial volume, $T_1$ is the initial temperature, $P_2$ is the final pressure, $V_2$ is the final volume, and $T_2$ is the final temperature.

Step2: Rearrange the formula to solve for $V_2$

$V_2=\frac{P_1V_1T_2}{T_1P_2}$

Step3: Substitute the given values

$P_1 = 0.4$ atm, $V_1=21.7$ L, $T_1 = 252$ K, $P_2 = 2$ atm, $T_2 = 323$ K.
$V_2=\frac{0.4\times21.7\times323}{252\times2}$
$V_2=\frac{0.4\times21.7\times323}{504}$
$V_2=\frac{0.4\times7009.1}{504}$
$V_2=\frac{2803.64}{504}\approx5.6$ L

Answer:

5.6 L