Question

a cylinder with a moveable piston contains 1.0 l of gas. when the initial pressure of 1.25 atm decreases to 0.94 atm and the temperature decreases from 315 k to 305 k, what is the final volume of the system?

Explanation:

Step1: Recall combined gas law

$\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}$

Step2: Rearrange for $V_2$

$V_2 = V_1 \times \frac{P_1}{P_2} \times \frac{T_2}{T_1}$

Step3: Substitute values

$V_2 = 1.0\ \text{L} \times \frac{1.25\ \text{atm}}{0.94\ \text{atm}} \times \frac{305\ \text{K}}{315\ \text{K}}$

Step4: Calculate result

$V_2 \approx 1.0 \times 1.3298 \times 0.9683 \approx 1.288\ \text{L}$

Answer:

1.3 L (rounded to two significant figures) or 1.29 L (more precise)