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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

Draw a qualitative graph to show how the first property varies with the second in each of the following (assume 1 mole of an ideal gas and \(T\) in kelvins). a. \(P V\) versus \(V\) with constant \(T\) b. \(P\) versus \(T\) with constant \(\underline{V}\) c. \(T\) versus \(V\) with constant \(P\) d. \(P\) versus \(V\) with constant \(T\) e. \(P\) versus \(1 / V\) with constant \(T\) f. \(P V / T\) versus \(P\)

An ideal gas at \(7^{\circ} \mathrm{C}\) is in a spherical flexible container having a radius of \(1.00 \mathrm{~cm}\). The gas is heated at constant pressure to \(88^{\circ} \mathrm{C}\). Determine the radius of the spherical container after the gas is heated. [Volume of a sphere \(\left.=(4 / 3) \pi r^{3} .\right]\)

The rate of effusion of a particular gas was measured and found to be \(24.0 \mathrm{~mL} / \mathrm{min}\). Under the same conditions, the rate of effusion of pure methane \(\left(\mathrm{CH}_{4}\right)\) gas is \(47.8 \mathrm{~mL} / \mathrm{min}\). What is the molar mass of the unknown gas?

Which of the following statements is(are) true? For the false statements, correct them. a. At constant temperature, the lighter the gas molecules, the faster the average velocity of the gas molecules. b. At constant temperature, the heavier the gas molecules, the larger the average kinetic energy of the gas molecules. c. A real gas behaves most ideally when the container volume is relatively large and the gas molecules are moving relatively quickly. d. As temperature increases, the effect of interparticle interactions on gas behavior is increased. e. At constant \(V\) and \(T\), as gas molecules are added into a container, the number of collisions per unit area increases resulting in a higher pressure. f. The kinetic molecular theory predicts that pressure is inversely proportional to temperature at constant volume and moles of gas.

Sulfur trioxide, \(\mathrm{SO}_{3}\), is produced in enormous quantities each year for use in the synthesis of sulfuric acid. $$ \begin{aligned} \mathrm{S}(s)+\mathrm{O}_{2}(g) & \longrightarrow \mathrm{SO}_{2}(g) \\ 2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) & \longrightarrow 2 \mathrm{SO}_{3}(g) \end{aligned} $$ What volume of \(\mathrm{O}_{2}(g)\) at \(350 .{ }^{\circ} \mathrm{C}\) and a pressure of \(5.25 \mathrm{~atm}\) is needed to completely convert \(5.00 \mathrm{~g}\) sulfur to sulfur trioxide?
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