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The Gas Laws

Variables:

P is the Pressure of the system

V is Volume of the system

n is the Moles of molecular species in the system

T is the Temperature in Kelvin

Constants:

R is the Gas Constant where R = N_Ak_B

Standard Temperature and Pressure - STP

A gas is said to be at STP if the following conditions are met:

Temperature T is 0^oC = 273.15 K

Pressure P is 1 atm

The Ideal Gas Law

An Ideal Gas is assumed to be:

Monoatomic

Lacking in Intermolecular Interactions

Lacking any Molecular Volume

For Problems Involving One Set of Conditions:

Given three of four variables, it is relatively easy to rearrange the Ideal Gas Equation and thereby solve for the unknown variable.

P = nRT/V

V = nRT/P

n = PV/RT

T = PV/nR

The Molar Volume of a Gas at STP is derived thus:

For Problems Involving Two Sets of Conditions:

Since the Gas Constant (R) never changes, the value of R is the same under every set of equilibrium conditions. This allows us to relate a set of initial conditions to a final set of conditions. By solving for R under both intial and final conditions:

R = P₁V₁/n₁T₁

R = P₂V₂/n₂T₂

and then setting both equations equal to each other:

R =

At this point, we can find those variables that do not undergo any kind of change between the initial and final conditions and cancel them from both sides.

If we hold the number of moles n constant, we can derive the following Gas Laws:

Boyle's Law

Guy Lussac's Law

Charle's Law

The Combined Gas Law

Avogadro's Law