Partial Pressure Calculator

Dalton's law — each gas exerts the pressure it would if the others were not there.

Partial pressure of N279.0335 kPa0.78 × 101.325 — Dalton's law. Each gas exerts the pressure it would if the others were not there

Partial pressure of O221.2783 kPa

Remaining fraction0.01at 1.0133 kPa — argon, carbon dioxide and the rest, in air

Molar masses28.014 and 31.998 g/mol

Graham's law effusion ratio1.06874N2 effuses 1.0687× as fast as O2 — the INVERSE SQUARE ROOT of the masses, because both gases have the same kinetic energy and the lighter one must therefore move faster

Why the square root½mv² is the same for bothequal temperature means equal average kinetic energy, so v goes as one over the square root of m. Everything about effusion follows from that

Hydrogen against oxygen3.984×the classic demonstration — hydrogen effuses almost four times as fast as oxygen despite being sixteen times lighter, because it is the square root that counts

Uranium enrichment1.004303×the separation factor for UF₆ of the two isotopes. Four parts in a thousand per stage, which is why gaseous diffusion plants needed thousands of stages and consumed the output of dedicated power stations

The formula

p_i = x_i·P; rate₁/rate₂ = √(M₂/M₁)

Each gas ignores the others

Dalton's law says the pressure a gas exerts in a mixture is what it would exert alone in the same volume.

Air at sea level is 78% nitrogen, so nitrogen contributes 79 kPa of the 101. Oxygen contributes 21. The molecules are far enough apart that they genuinely do not notice each other, which is what makes the ideal gas approximation work.

Lighter gases are faster by the square root

At the same temperature every gas has the same average kinetic energy, and energy is ½mv².

So velocity goes as one over the square root of mass. Hydrogen is sixteen times lighter than oxygen and only four times faster, and every result about effusion and diffusion follows from that single square root.

Four parts in a thousand, ten thousand times

Uranium hexafluoride made from U-235 and U-238 differs in molar mass by less than one percent.

Graham's law gives a separation factor of 1.0043 per stage, so enrichment by gaseous diffusion needs thousands of stages in cascade. The Oak Ridge plant consumed roughly one percent of American electricity, and that square root is the reason.

Ideal behaviour is an approximation

The colligative and gas relations here assume dilute solutions and ideal gases, which real systems approach and do not reach.

At high concentration or high pressure the deviations become large, and the corrections are substance-specific. These figures are right where the assumptions hold and approximate where they do not.