Ch.10 - Gases: Their Properties & Behavior

Problem 31

Chapter 10, Problem 31

Show the approximate level of the movable piston in drawings (a), (b), and (c) after the indicated changes have been made to the gas.

Verified step by step guidance

Identify the initial conditions: T_i = 200 K and P_i = 0.80 atm.

For drawing (a), note that the temperature increases to T_f = 250 K while the pressure remains constant at P_i = 0.80 atm. Use the ideal gas law (PV = nRT) to determine the change in volume.

For drawing (a), since the pressure is constant, the volume is directly proportional to the temperature (Charles's Law: V1/T1 = V2/T2). Calculate the new volume V2.

For drawing (b), note that the temperature remains constant at T_f = 200 K while the pressure increases to P_f = 1.20 atm. Use the ideal gas law to determine the change in volume.

For drawing (b), since the temperature is constant, the volume is inversely proportional to the pressure (Boyle's Law: P1V1 = P2V2). Calculate the new volume V2.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Ideal Gas Law

The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of a gas through the equation PV = nRT. This law is fundamental for understanding how changes in temperature and pressure affect the behavior of gases, particularly in closed systems like the piston-cylinder setup shown in the diagrams.

Charles's Law

Charles's Law states that the volume of a gas is directly proportional to its temperature when pressure is held constant. This concept is crucial for analyzing the changes in the piston level in the diagrams, especially in scenario (a) where the temperature increases while pressure remains constant.

Boyle's Law

Boyle's Law states that the pressure of a gas is inversely proportional to its volume when temperature is held constant. This principle is essential for understanding the changes in the piston level in scenario (b), where an increase in pressure at constant temperature will result in a decrease in volume, thus affecting the position of the piston.

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Boyle's Law

Related Practice

Textbook Question

Assume that you have a sample of gas in a cylinder with a movable piston, as shown in the following drawing:

Redraw the apparatus to show what the sample will look like after (a) the temperature is increased from 300 K to 450 K at constant pressure

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Textbook Question

Assume that you have a sample of gas in a cylinder with a movable piston, as shown in the following drawing:

Redraw the apparatus to show what the sample will look like after (b) the pressure is increased from 1 atm to 2 atm at constant temperature

358

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Textbook Question

Assume that you have a sample of gas in a cylinder with a movable piston, as shown in the following drawing:

Redraw the apparatus to show what the sample will look like after (c) the temperature is decreased from 300 K to 200 K and the pressure is decreased from 3 atm to 2 atm.

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Textbook Question

A 1:1 mixture of helium (red) and argon (blue) at 300 K isportrayed below on the left. Draw the same mixture whenthe temperature is lowered to 150 K.

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Textbook Question

Yet another common measure of pressure is the unit pounds per square inch (psi). How many pounds per square inch correspond to 1.00 atm? To 1.00 mm Hg?

If the density of water is 1.00 g/mL and the density of mercury is 13.6 g/mL, how high a column of water in meters can be supported by standard atmospheric pressure? By 1 bar?

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