Question

a gas has an initial volume of 2.4 l at a pressure of 1.5 atm and a temperature of 273 k. the pressure of the gas increases to 4.5 atm, and the temperature of the gas increases to 313 k. what is the final volume of the gas? 0.70 l 0.92 l 6.3 l 8.3 l

Explanation:

Step1: Recall 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: Identify the given values

$P_1 = 1.5$ atm, $V_1=2.4$ L, $T_1 = 273$ K, $P_2 = 4.5$ atm, $T_2=313$ K.

Step3: Rearrange the formula to solve for $V_2$

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

Step4: Substitute the values into the formula

$V_2=\frac{1.5\times2.4\times313}{4.5\times273}$.
First, calculate the numerator: $1.5\times2.4\times313 = 1.5\times751.2=1126.8$.
Then, calculate the denominator: $4.5\times273 = 1228.5$.
$V_2=\frac{1126.8}{1228.5}\approx0.92$ L.

Answer:

0.92 L