Question

a cylinder with a moveable piston initially contains 4.10 l of a gas at 1.53 atm and 280 k. the final volume and temperature of the cylinder are 3.50 l and 270 k. what is the final pressure of the cylinder?

Explanation:

Step1: Recall combined gas law

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

Step2: Rearrange for final pressure $P_2$

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

Step3: Substitute given values

$$P_2 = 1.53\ \text{atm} \times \frac{4.10\ \text{L}}{3.50\ \text{L}} \times \frac{270\ \text{K}}{280\ \text{K}}$$

Step4: Calculate step by step

First: $\frac{4.10}{3.50} \approx 1.1714$; Second: $\frac{270}{280} \approx 0.9643$; Third: $1.53 \times 1.1714 \times 0.9643 \approx 1.72$

Answer:

1.72 atm