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Chapter 5: Problem 17

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 respective quantities for a gas sample, the following properties are needed: a. Average Kinetic Energy: 1. Temperature of the gas sample, 2. Mass of the molecule. b. Average Number of Collisions per Second with Other Gas Molecules: 1. Density of gas sample, 2. Temperature of gas sample, 3. Mass of the molecule, 4. Size of the molecule. c. Average Force of Each Impact with the Wall of the Container: 1. Mass of the molecule, 2. Root mean square velocity. d. Root Mean Square Velocity: 1. Temperature of the gas sample, 2. Mass of the molecule. e. Average Number of Collisions with a Given Area of the Container: 1. Density of the gas sample, 2. Size of the molecule, 3. Root mean square velocity. f. Distance Between Collisions: 1. Density of the gas sample, 2. Size of the molecule.

Step by step solution

01

a. Average Kinetic Energy

To calculate the average kinetic energy, we need to know the following properties: 1. Temperature of the gas sample 2. Mass of the molecule Using the formula for average kinetic energy, \(KE_{avg} = \dfrac{3}{2}k_BT\), where \(k_B\) is the Boltzmann constant and \(T\) is the temperature in Kelvin. Note: The mass of the molecules can be obtained by the molar mass of the substance.
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 following properties: 1. Density of gas sample 2. Temperature of gas sample 3. Mass of the molecule 4. Size of the molecule This calculation will require the use of the collision frequency formula.
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 following properties: 1. Mass of the molecule 2. Root mean square velocity The average force can be calculated using the impulse-momentum theorem.
04

d. Root Mean Square Velocity

To calculate the root mean square velocity, we need to know the following properties: 1. Temperature of the gas sample 2. Mass of the molecule The root mean square velocity can be calculated using the formula \(v_{rms} = \sqrt{\dfrac{3k_BT}{m}}\), where m is the mass of the molecule.
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 following properties: 1. Density of the gas sample 2. Size of the molecule 3. Root mean square velocity This calculation requires the use of the average collision rate formula.
06

f. Distance Between Collisions

To calculate the distance between collisions, we need to know the following properties: 1. Density of the gas sample 2. Size of the molecule The mean free path formula can be used to calculate the distance between collisions.

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Most popular questions from this chapter

A steel cylinder contains \(5.00 \mathrm{~mol}\) graphite (pure carbon) and \(5.00 \mathrm{~mol} \mathrm{O}_{2} .\) The mixture is ignited and all the graphite reacts. Combustion produces a mixture of \(\mathrm{CO}\) gas and \(\mathrm{CO}_{2}\) gas. After the cylinder has cooled to its original temperature, it is found that the pressure of the cylinder has increased by \(17.0 \% .\) Calculate the mole fractions of \(\mathrm{CO}, \mathrm{CO}_{2}\), and \(\mathrm{O}_{2}\) in the final gaseous mixture.

Consider separate \(1.0-\mathrm{L}\) gaseous samples of \(\mathrm{H}_{2}, \mathrm{Xe}, \mathrm{Cl}_{2}\), and \(\mathrm{O}_{2}\) all at STP. a. Rank the gases in order of increasing average kinetic energy. b. Rank the gases in order of increasing average velocity. c. How can separate \(1.0-\mathrm{L}\) samples of \(\mathrm{O}_{2}\) and \(\mathrm{H}_{2}\) each have the same average velocity?

Methanol \(\left(\mathrm{CH}_{3} \mathrm{OH}\right)\) can be produced by the following reaction: $$ \mathrm{CO}(g)+2 \mathrm{H}_{2}(g) \longrightarrow \mathrm{CH}_{3} \mathrm{OH}(g) $$ Hydrogen at STP flows into a reactor at a rate of \(16.0 \mathrm{~L} / \mathrm{min}\) Carbon monoxide at STP flows into the reactor at a rate of \(25.0\) L/min. If \(5.30 \mathrm{~g}\) methanol is produced per minute, what is the percent yield of the reaction?

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