Ideal Gas Law

Calculator

Enter any 3 values — the 4th is computed automatically.

Green field = auto-calculated. R = 0.08206 L·atm/(mol·K).

What is the Ideal Gas Law?

The ideal gas law relates the pressure, volume, amount, and temperature
of a gas that behaves ideally. It combines Boyle’s Law, Charles’s Law,
and Avogadro’s Law into a single equation.

$P V = n R T$

This means: pressure times volume equals the number of moles times the ideal gas constant times the absolute temperature.

Parts of the Ideal Gas Law

$P V = n R T$

P : Pressure of the gas (atm, kPa, mmHg, bar)
V : Volume of the gas (L, mL, m³)
n : Amount of gas (moles)
R : Ideal gas constant
T : Absolute temperature (Kelvin)

R = 0.08206 L·atm / (mol·K) —
the value of R changes depending on which units are used for
pressure and volume. Temperature must always be converted to
Kelvin before using the equation.

Example 1: Solving for Volume

A sample of gas contains 2.00 mol at a temperature of 300 K and a
pressure of 1.50 atm. What is the volume?

$V = \frac{n R T}{P}$

Substitute the values:

V = (2.00 × 0.08206 × 300) ÷ 1.50

V ≈ 32.8 L

Example 2: Solving for Pressure

A 10.0 L container holds 0.500 mol of gas at 298 K. What is the
pressure?

$P = \frac{n R T}{V}$

Substitute the values:

P = (0.500 × 0.08206 × 298) ÷ 10.0

SOLVE THIS!

Example 3: Solving for Moles

A gas occupies 5.00 L at 2.00 atm and 350 K. How many moles are
present?

$n = \frac{P V}{R T}$

Substitute the values:

n = (2.00 × 5.00) ÷ (0.08206 × 350)

0.348 mol

Practice Problems

Problem 1

A gas sample occupies 22.4 L at 273 K and 1.00 atm. How many
moles of gas are present?

n = PV ÷ RT = 22.4 ÷ (0.08206 × 273) =
1.00 mol (these are standard conditions, STP)

Problem 2

3.00 mol of gas is at 2.50 atm and 310 K. Find the volume.

V = nRT ÷ P = (3.00 × 0.08206 × 310) ÷ 2.50
= 30.5 L

Problem 3

1.25 mol of gas occupies 15.0 L at 295 K. Find the pressure.

P = nRT ÷ V = (1.25 × 0.08206 × 295) ÷ 15.0
= 2.02 atm

Problem 4

0.750 mol of gas is held at 3.00 atm in an 8.00 L container.
Find the temperature.

T = PV ÷ nR = (3.00 × 8.00) ÷ (0.750 × 0.08206)
= 390 K

Problem 5

A 5.00 L container holds gas at 2.50 atm and 25°C. How many
moles of gas are inside? (Remember to convert to Kelvin first.)

T = 25 + 273.15 = 298.15 K
n = PV ÷ RT = (2.50 × 5.00) ÷ (0.08206 × 298.15)
= 0.511 mol

Combined Gas Law (comparing two states of the same gas sample):

$\frac{P_{1} V_{1}}{T_{1}} = \frac{P_{2} V_{2}}{T_{2}}$

Molar volume of an ideal gas at STP (0°C, 1 atm):

Calculator

What is the Ideal Gas Law?

P V = n R T

Parts of the Ideal Gas Law

P V = n R T

Example 1: Solving for Volume

V = nRT P

Example 2: Solving for Pressure

P = nRT V

Example 3: Solving for Moles

n = PV RT

Practice Problems

Problem 1

Answer+

Problem 2

Answer+

Problem 3

Answer+

Problem 4

Answer+

Problem 5

Answer+

Useful Formulas

P1V1 T1 = P2V2 T2

V = 22.4 L/mol

$P V = n R T$

$P V = n R T$

$V = \frac{n R T}{P}$

$P = \frac{n R T}{V}$

$n = \frac{P V}{R T}$

$\frac{P_{1} V_{1}}{T_{1}} = \frac{P_{2} V_{2}}{T_{2}}$

$V = 22.4 L/mol$