Question

a gas has an initial volume of 168 cm³ at a temperature of 255 k and a pressure of 1.6 atm. the pressure of the gas decreases to 1.3 atm, and the temperature of the gas increases to 285 k. what is the final volume of the gas? 122 cm³ 153 cm³ 185 cm³ 231 cm³

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

$P_1 = 1.6$ atm, $V_1=168$ cm³, $T_1 = 255$ K, $P_2 = 1.3$ atm, $T_2 = 285$ K. We need to find $V_2$.

Step3: Rearrange the combined - gas law formula to solve for $V_2$

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

Step4: Substitute the values into the formula

$V_2=\frac{1.6\times168\times285}{255\times1.3}$
First, calculate the numerator: $1.6\times168\times285 = 1.6\times47880=76608$.
Then, calculate the denominator: $255\times1.3 = 331.5$.
$V_2=\frac{76608}{331.5}=231$ cm³

Answer:

$231$ cm³