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Chapter 11: Problem 109

(a) If the temperature of a gas is doubled while the pressure is kept constant, the volume of the gas (b) If the pressure of a gas is halved while the temperature is kept constant, the volume of the gas

Short Answer

Expert verified
(a) When the temperature of a gas is doubled while the pressure is kept constant, the volume of the gas is doubled (\(V2 = 2 * V1\)). (b) When the pressure of a gas is halved while the temperature is kept constant, the volume of the gas is doubled (\(V2 = 2 * V1\)).

Step by step solution

01

Write down the ideal gas law equation

The ideal gas law states that (P * V) / T = constant.
02

Find the initial and final states

In this case, the initial state has temperature T1, pressure P1, and volume V1. The final state has temperature 2 * T1 (since the temperature is doubled), pressure P1 (since the pressure is constant), and volume V2.
03

Apply the ideal gas law for the initial and final states

For the initial state: (P1 * V1) / T1 = C For the final state: (P1 * V2) / (2 * T1) = C
04

Compare the initial and final states

Since the constant C is the same for both equations, we can set them equal to each other: (P1 * V1) / T1 = (P1 * V2) / (2 * T1)
05

Solve for the final volume V2

By cross-multiplying and simplifying, we get: V2 = 2 * V1 So, the volume of the gas when the temperature is doubled and the pressure is kept constant is double the initial volume. #Scenario 2: Pressure halved while the temperature is kept constant#
06

Write down the ideal gas law equation

The ideal gas law states that (P * V) / T = constant.
07

Find the initial and final states

In this case, the initial state has temperature T1, pressure P1, and volume V1. The final state has temperature T1 (since the temperature is constant), pressure P1/2 (since the pressure is halved), and volume V2.
08

Apply the ideal gas law for the initial and final states

For the initial state: (P1 * V1) / T1 = C For the final state: ((P1/2) * V2) / T1 = C
09

Compare the initial and final states

Since the constant C is the same for both equations, we can set them equal to each other: (P1 * V1) / T1 = ((P1/2) * V2) / T1
10

Solve for the final volume V2

By cross-multiplying and simplifying, we get: V2 = 2 * V1 So, the volume of the gas when the pressure is halved and the temperature is kept constant is double the initial volume.

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Most popular questions from this chapter

Explain why gases always occupy the entire container they are in, but solids and liquids do not.

Describe how a mercury barometer works.

Carbon dioxide and carbon monoxide are very different gases. For example, you exhale CO_2. but \(C O\) is extremely toxic. Suppose you have two balloons, one filled with \(1.00\) mole of CO and the other filled with 1 mole of \(\mathrm{CO}_{2}\). Both gases are at \(1.00 \mathrm{~atm}\) and \(25.0^{\circ} \mathrm{C}\). (a) What is the volume in liters of each balloon? (b) What did you learn about gases from doing this problem?

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