The Ideal-Gas Equation

The Ideal Gas Equation

The three historically important gas laws derived relationships between two physical properties of a gas, while keeping other properties constant:

These different relationships can be combined into a single relationship to make a more general gas law:

If the proportionality constant is called "R", then we have:

Rearranging to a more familiar form:

This equation is known as the ideal-gas equation

Values for the gas constant R



L atm/mol K


cal/mol K


J/mol K


m3 Pa/mol K


L torr/mol K



If we had 1.0 mol of gas at 1.0 atm of pressure at 0C (273.15 K), what would be the volume?

PV = nRT

V = nRT/P

V = (1.0 mol)(0.0821 L atm/mol K)(273 K)/(1.0 atm)

V = 22.41 L

The molar volume of an ideal gas (any ideal gas) is 22.4 liters at STP

Example: Nitrate salts (NO3-) when heated can produce nitrites (NO2-) plus oxygen (O2). A sample of potassium nitrate is heated and the O2 gas produced is collected in a 750 ml flask. The pressure of the gas in the flask is 2.8 atmospheres and the temperature is recorded to be 53.6 C.

How many moles of O2 gas were produced?

PV = nRT

n = PV/RT

n = (2.8 atm * 0.75 L) / (0.0821 L atm/mol K * (53.6 + 273)K

n = (2.1 atm L) / (26.81 L atm/mol)

n = 0.078 mol O2 were produced

Relationship Between the Ideal-Gas Equation and the Gas Laws

Boyle's law, Charles's law and Avogadro's law represent special cases of the ideal gas law

PV = nRT

PV = constant

P = constant * (1/V)

P 1/V (Boyle's law)

PV = nRT

V = (nR/P) * T

V = constant * T

V T (Charles's law)

PV = nRT

V = n * (RT/P)

V = constant * n

V n (Avogadro's law)

PV = nRT

(PV)/T = nR = constant


A 1 liter sample of air at room temperature (25 C) and pressure (1 atm) is compressed to a volume of 3.3 mls at a pressure of 1000 atm. What is the temperature of the air sample?

1996 Michael Blaber