Graham’s Law of Diffusion

Graham’s Law of Diffusion HCl NH3 NH4Cl(s) 100 cm 100 cm Choice 1: Both gases move at the same speed and meet in the middle.

Diffusion NH4Cl(s) HCl NH3 81.1 cm 118.9 cm Choice 2: Lighter gas moves faster; meet closer to heavier gas.

Graham’s Law Consider two gases at same temp. Gas 1: KE1 = ½ m1 v12 Since temp. is same, then… KE1 = KE2 ½ m1 v12 = ½ m2 v22 m1 v12 = m2 v22 Divide both sides by m1 v22… Take square root of both sides to get Graham’s Law:

Graham’s Law Diffusion Effusion Spreading of gas molecules throughout a container until evenly distributed. Effusion Passing of gas molecules through a tiny opening in a container

KE = ½mv2 Graham’s Law Speed of diffusion/effusion Kinetic energy is determined by the temperature of the gas. At the same temp & KE, heavier molecules move more slowly. Larger m  smaller v KE = ½mv2

Graham’s Law Graham’s Law Rate of diffusion of a gas is inversely related to the square root of its molar mass. The equation shows the ratio of Gas A’s speed to Gas B’s speed.

Br 79.904 35 Kr 83.80 36 Graham’s Law Determine the relative rate of diffusion for krypton and bromine. The first gas is “Gas A” and the second gas is “Gas B”. Relative rate mean find the ratio “vA/vB”. Kr diffuses 1.381 times faster than Br2.

Put the gas with the unknown speed as “Gas A”. 15.9994 8 H 1.00794 1 Graham’s Law A molecule of oxygen gas has an average speed of 12.3 m/s at a given temp and pressure. What is the average speed of hydrogen molecules at the same conditions? Put the gas with the unknown speed as “Gas A”.

1 O 15.9994 8 Graham’s Law H 2.0 An unknown gas diffuses 4.0 times faster than O2. Find its molar mass. The first gas is “Gas A” and the second gas is “Gas B”. The ratio “vA/vB” is 4.0. Square both sides to get rid of the square root sign.

Graham's Law         Graham's Law         Graham's Law

Diffusion

Gas Diffusion and Effusion Graham's law governs effusion and diffusion of gas molecules. Rate of effusion is inversely proportional to its molar mass. Thomas Graham (1805 - 1869)

To use Graham’s Law, both gases must be at same temperature. diffusion: particle movement from high to low concentration NET MOVEMENT effusion: diffusion of gas particles through an opening For gases, rates of diffusion & effusion obey Graham’s law: more massive = slow; less massive = fast

Effusion Particles in regions of high concentration spread out into regions of low concentration, filling the space available to them.

Weather and Diffusion LOW Air Pressure HIGH Air Pressure Map showing tornado risk in the U.S. Highest High

Calculation of Diffusion Rate V1 = y M1 = 17 amu V2 = x M2 = 36.5 amu NH3 HCl Substitute values into equation V1 moves 1.465x for each 1x move of V2 NH3 (y= 1.465x) HCl x 1.465 x + 1x = 2.465 x Thus in the example at the beginning of the ppt: 200 cm / 2.465 = 81.1 cm for x In the 200 cm tube, HCl covers 81.1 cm and NH3 covers (200-81.1) 118.9cm of the distance within the tube