Question

for each of the quantities listed below, explain which of the following properties (mass of the molecule, number 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 directly.
(a) average kinetic energy for a mole of gas particles
(select all that apply.)
o mass of the molecule
o number density of the gas sample
o temperature of the gas sample
o size of the molecule
o number of moles of gas
(b) average number of collisions per second with other gas molecules
(select all that apply.)
o mass of the molecule
o number density of the gas sample
o temperature of the gas sample
o size of the molecule
o number of moles of gas
(c) average force of each impact with the wall of the container
(select all that apply.)
o mass of the molecule
o number density of the gas sample
o temperature of the gas sample
o size of the molecule
o number of moles of gas
(d) average number of collisions with a given area of the container
(select all that apply.)
o mass of the molecule
o number density of the gas sample
o temperature of the gas sample
o size of the molecule
o number of moles of gas

Explanation:

• For part (a): The formula for average kinetic energy per molecule is \(E_{k}=\frac{3}{2}kT\), where \(k\) is Boltzmann's constant and \(T\) is temperature. So temperature of the gas sample is needed.
• For part (b): The formula for average number of collisions per second with other gas molecules involves number density of the gas sample (related to concentration of molecules), size of the molecule (affects collision cross - section), and average speed (related to temperature).
• For part (c): The formula for average force of each impact with the wall of the container involves mass of the molecule (for momentum change), average speed (related to temperature), and number density (to know how many molecules hit the wall per unit time).
• For part (d): The formula for average number of collisions with a given area of the container involves number density (to know molecule concentration near the area), average speed (related to temperature), and size of the molecule (affects collision cross - section).

Answer:

(a) temperature of the gas sample
(b) number density of the gas sample, size of the molecule, temperature of the gas sample
(c) mass of the molecule, number density of the gas sample, temperature of the gas sample
(d) number density of the gas sample, size of the molecule, temperature of the gas sample