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Chapter 17: Problem 19

Describe how the following changes affect the positional probability of a substance. a. increase in volume of a gas at constant T b. increase in temperature of a gas at constant V c. increase in pressure of a gas at constant T

Short Answer

Expert verified
In summary: a. Increasing the volume of a gas at constant temperature results in a higher positional probability due to an increased number of positions for the particles to occupy. b. Increasing the temperature of a gas at constant volume leads to a higher positional probability as the particles move faster and have a higher probability of being found at different positions within the container. c. Increasing the pressure of a gas at constant temperature decreases the positional probability since the particles are forced into a smaller space, reducing the number of positions they can occupy.

Step by step solution

01

1. Increase in volume of a gas at constant T

To analyze this situation, we can use the ideal gas law. If the temperature (T) is held constant, then any change in volume (V) must be accompanied by a proportional change in pressure (P). When the volume of a gas increases, the particles of the gas get more space to occupy, thereby increasing the positional probability of the substance.
02

2. Increase in temperature of a gas at constant V

When the temperature of a gas is increased at a constant volume, the pressure of the gas (P) will also increase according to the ideal gas law. With a rise in temperature, the kinetic energy of the particles increases. This means that the particles will move faster and have a higher probability of being found at different positions within the container, hence increasing the positional probability of the substance.
03

3. Increase in pressure of a gas at constant T

If the pressure of a gas is increased while the temperature remains constant, the volume must change according to the ideal gas law. In this case, the volume (V) will decrease in response to the increased pressure (P). When the volume of a gas decreases, the particles are forced into a smaller space, decreasing the number of positions the particles can occupy, which in turn reduces the positional probability of the substance.

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Most popular questions from this chapter

At what temperatures will the following processes be spontaneous? a. \(\Delta H=-18 \mathrm{kJ}\) and \(\Delta S=-60 . \mathrm{J} / \mathrm{K}\) b. \(\Delta H=+18 \mathrm{kJ}\) and \(\Delta S=+60 . \mathrm{JK}\) c. \(\Delta H=+18 \mathrm{kJ}\) and \(\Delta S=-60 . \mathrm{J} / \mathrm{K}\) d. \(\Delta H=-18 \mathrm{kJ}\) and \(\Delta S=+60 . \mathrm{J} / \mathrm{K}\)

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