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Chapter 5: Problem 19

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?

Short Answer

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

Step by step solution

01

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 \(V_2\).
02

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 \(P_1V_1 = P_2V_2\).
03

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, \(V_2 = \frac{0.970 \mathrm{~atm} \times 725 \mathrm{~mL}}{0.541 \mathrm{~atm}}\).

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Most popular questions from this chapter

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