# Worksheet: Particle Model of an Ideal Gas

In this worksheet, we will practice calculating the relationship between the number of particles or moles in an ideal gas and the values of its bulk properties.

**Q1: **

Find the number of moles of carbon atoms that is equal to atoms. Use a value of 12.0107 g/mol for the molar mass of carbon and use for the value of Avogadro’s number. Answer to three significant figures.

**Q2: **

A gas at a pressure of 125 kPa
and a temperature of 485 K consists
of particles with a molar mass of 30.5 g/mol. Find the density of the gas. Use
8.31 m^{2}⋅kg/s^{2}⋅K⋅mol for the value of the molar gas
constant. Answer in kilograms per cubic meter to three significant figures.

**Q3: **

Find the number of lithium atoms that is equal to 7.25 moles of lithium atoms. Use a value of 6.941 g/mol for the molar mass of lithium and for the value of Avogadro’s number. Answer to three significant figures.

- A atoms
- B atoms
- C atoms
- D atoms
- E atoms

**Q4: **

A cylinder with a movable lid contains a gas at a
temperature of 480 K and a pressure of
360 kPa. The gas contains
particles. Find the volume of the gas. Use m^{2}⋅kg/s^{2}⋅K
for the value of Boltzmann’s constant. Answer to three significant figures.

**Q5: **

A cloud of gas has a pressure of 220 kPa and a temperature
of 440 K. The gas contains
8.2 moles of a particle with a molar mass of
10.5 g/mol.
Find the volume of the cloud. Use 8.31 m^{2}⋅kg/s^{2}⋅K⋅mol for the value
of the molar gas constant. Answer to three significant figures.

**Q6: **

A gas consisting of 25.6 moles of carbon fills a volume of
0.128 m^{3} and has a pressure of 135 kPa.
Find the temperature of the
gas. Use a value of 12.0107 g/mol for the molar mass of carbon and
8.31 m^{2}⋅kg/s^{2}⋅K⋅mol
for the value of the molar gas constant. Answer to three significant figures.

**Q7: **

A gas at a pressure of 312 kPa consists of particles with a
molar mass of 10.2 g/mol.
The density of the gas is 1.16 kg/m^{3}. Find
the temperature of the gas. Use 8.31 m^{2}⋅kg/s^{2}⋅K⋅mol for
the value of the molar gas constant. Answer to three significant figures.

**Q8: **

A gas has a pressure of 125 kPa, a temperature of
355 K, and a
volume of 1.24 m^{3}. It consists of particles with a molar mass of
3.75 g/mol.

How many moles of these particles does the gas consist of?
Use m^{2}⋅kg/s^{2}⋅K for the
value of Boltzmann’s constant and for the value of
Avogadro’s number. Answer to three significant figures.

What is the mass of the gas? Answer in kilograms to three significant figures.

**Q9: **

A gas cylinder with a volume of 0.245 m^{3}
contains
a gas at a temperature of 350 K
and a pressure of 120 kPa.
Find the number of
moles of the gas particles in the cylinder. Use
8.31 m^{2}⋅kg/s^{2}⋅K⋅mol
for the value of the molar gas constant. Answer to three significant figures.

- A 10.1 mol
- B 5.68 mol
- C 85.5 mol
- D 45.9 mol
- E 63.7 mol

**Q10: **

A gas at a temperature of 305 K consists of particles with a
molar mass of 23.5 g/mol. The density of the gas is
1.07 kg/m^{3}. Find
the pressure of the gas. Use 8.31 m^{2}⋅kg/s^{2}⋅K⋅mol for the
value of the molar gas constant. Answer, in kilopascals, to three significant figures.