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Chapter 12: Problem 82

Explain, in terms of the kinetic molecular theory, how an increase in the temperature of a gas confined to a rigid container causes an increase in the pressure of the gas.

Short Answer

Expert verified
In terms of the kinetic molecular theory, an increase in the temperature of a gas confined in a rigid container leads to an increase in the average kinetic energy and, consequently, the average velocity of the gas molecules. This results in more frequent and forceful collisions with the container walls, which ultimately increases the pressure exerted by the gas.

Step by step solution

01

Understanding the Kinetic Molecular Theory

The kinetic molecular theory is a model used to explain the behavior of gases. According to this theory, a gas is made up of numerous tiny molecules that are in constant motion. These motions include both translation (moving through space) and random collisions with each other and with the walls of the container. The pressure that a confined gas exerts on the walls of its container is due to these collisions.
02

Connecting Temperature with Molecular Velocity

The temperature of a gas is related to the average kinetic energy of its molecules. Higher temperatures result in higher average kinetic energy. Since the kinetic energy of a molecule (KE) is given by KE = \(0.5 脳 m 脳 v^2\), where m is the mass and v is the velocity of the molecule, an increase in the average kinetic energy means an increase in the average velocity of the gas molecules.
03

Effect of Increased Molecular Velocity on Pressure

When the average velocity of the gas molecules increases (due to an increase in temperature), the molecules will collide with the walls of the container more often and with greater force. As a result, the gas molecules transfer more momentum to the walls of the container, thereby increasing the pressure exerted by the gas.
04

Conclusion

In conclusion, according to the kinetic molecular theory, an increase in the temperature of a gas confined in a rigid container leads to an increase in the average velocity of the gas molecules. This, in turn, causes the molecules to collide with the walls of the container more frequently and with greater force. The increased momentum transfer to the walls results in a higher gas pressure.

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Most popular questions from this chapter

What do we mean by an ideal gas?

Many transition metal salts are hydrates: they contain a fixed number of water molecules bound per formula unit of the salt. For example, copper(II) sulfate most commonly exists as the pentahydrate, \(\mathrm{CuSO}_{4} \cdot 5 \mathrm{H}_{2} \mathrm{O} .\) If \(5.00 \mathrm{g}\) of \(\mathrm{CuSO}_{4} \cdot 5 \mathrm{H}_{2} \mathrm{O}\) is heated strongly so as to drive off all of the waters of hydration as water vapor, what volume will this water vapor occupy at \(350 .^{\circ}\) C and a pressure of 1.04 atm?

What will the volume of the sample become if 459 mL of an ideal gas at \(27^{\circ} \mathrm{C}\) and 1.05 atm is cooled to \(15^{\circ} \mathrm{C}\) and 0.997 atm?

What mass of helium gas is needed to pressurize a 100.0-L tank to 255 atm at \(25^{\circ} \mathrm{C}\) ? What mass of oxygen gas would be needed to pressurize a similar tank to the same specifications?

What is the pressure inside a 10.0 -L flask containing \(14.2 \mathrm{g}\) of \(\mathrm{N}_{2}\) at \(26^{\circ} \mathrm{C} ?\)
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