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Chapter 5: Problem 19

For each of the quantities listed below, explain which of the following properties (mass of the molecule, density of the gas sample, temperature of the gas sample, size of the molecule, and number of moles of gas) must be known to calculate the quantity. a. average kinetic energy b. average number of collisions per second with other gas molecules c. average force of each impact with the wall of the container d. root mean square velocity e. average number of collisions with a given area of the container f. distance between collisions

Short Answer

Expert verified
To calculate the given quantities, the required properties are: a. Average Kinetic Energy: mass of the molecule and temperature of the gas sample. b. Average number of collisions per second: size of the molecule, density of the gas sample, and root mean square velocity. c. Average force of each impact: mass of the molecule, density of the gas sample, and temperature of the gas sample. d. Root mean square velocity: mass of the molecule and temperature of the gas sample. e. Average number of collisions with a given area: size of the molecule, density of the gas sample, and root mean square velocity. f. Distance between collisions: size of the molecule and root mean square velocity.

Step by step solution

01

a. Average Kinetic Energy

To calculate the average kinetic energy of a gas sample, we need to know the mass of the molecule and the temperature of the gas sample. The formula for average kinetic energy is given by: \(KE_{avg} = \frac{3}{2} kT \), where \(k\) is Boltzmann's constant and \(T\) is the temperature of the gas sample.
02

b. Average number of collisions per second with other gas molecules

To calculate the average number of collisions per second with other gas molecules, we need to know the size of the molecule, the density of the gas sample, and the root mean square velocity. The collision frequency is given by the formula: \(\nu = \frac{n v_{rms}}{2}\), where \(n\) is the number density of the gas and \(v_{rms}\) is the root mean square velocity.
03

c. Average force of each impact with the wall of the container

To calculate the average force of each impact with the wall of the container, we need to know the mass of the molecule, the density of the gas sample, and the temperature of the gas sample. Using the momentum and pressure of the gas molecules, we can determine the average force exerted by each molecule on the container walls.
04

d. Root mean square velocity

To calculate the root mean square velocity of the gas molecules, we need to know the mass of the molecule, and the temperature of the gas sample. The formula for root mean square velocity is given by: \(v_{rms} = \sqrt{\frac{3kT}{m}}\), where \(m\) is the mass of the molecule, \(k\) is Boltzmann's constant, and \(T\) is the temperature of the gas sample.
05

e. Average number of collisions with a given area of the container

To calculate the average number of collisions with a given area of the container, we need to know the size of the molecule, the density of the gas sample, and the root mean square velocity. Using the collision frequency and the area, we can determine the average number of collisions with a given area of the container.
06

f. Distance between collisions

To calculate the distance between collisions, we need to know the size of the molecule and the root mean square velocity. Since the root mean square velocity determines the average speed of molecules and the size of the molecule affects the probability of collisions, we can calculate the distance between collisions using these two properties.

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