Problem 19 - Chemistry

Question

A gas occupying a volume of \(725 \mathrm{~mL}\) at a pressure of 0.970 atm is allowed to expand at constant temperature until its pressure reaches 0.541 atm. What is its final volume?

Step-by-Step Solution

Answer

After performing the calculation, the final volume \(V_2\) comes out to be approximately \(1378 \mathrm{~mL}\).

Step 1: Understand and write down the given information

Initially, the gas has a volume of \(725 \mathrm{~mL}\) or \(V_1 = 725 \mathrm{~mL}\) and pressure of \(0.970 \mathrm{~atm}\) or \(P_1 = 0.970 \mathrm{~atm}\). Finally, the pressure of the gas is \(0.541 \mathrm{~atm}\) or \(P_2 = 0.541 \mathrm{~atm}\). The goal is to find the final volume \(V_2\).

Step 2: Apply Boyle's Law

Boyle's Law states that the product of initial pressure \(P_1\) and initial volume \(V_1\) equals the product of final pressure \(P_2\) and final volume \(V_2\) given that temperature remains constant. This can be written as \(P_1V_1 = P_2V_2\).

Step 3: Calculate the final volume

Rearrange the equation to solve for the final volume \(V_2\): \(V_2 = \frac{P_1V_1}{P_2}\). Substituting the given values, \(V_2 = \frac{0.970 \mathrm{~atm} \times 725 \mathrm{~mL}}{0.541 \mathrm{~atm}}\).