Graham’s Law of Diffusion

Graham’s Law KE = ½mv 2 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 Courtesy Christy Johannesson

Derivation of Graham’s Law The average kinetic energy of gas molecules depends on the temperature: where m is the mass and v is the speed Consider two gases:

Graham’s Law Consider two gases at same temp. Gas 1: KE 1 = ½ m 1 v 1 2 Gas 2: KE 2 = ½ m 2 v 2 2 Since temp. is same, then… KE 1 = KE 2 ½ m 1 v 1 2 = ½ m 2 v 2 2 m 1 v 1 2 = m 2 v 2 2 Divide both sides by m 1 v 2 2 … Take square root of both sides to get Graham’s Law:

On average, carbon dioxide travels at 410 m/s at 25 o C. Find the average speed of chlorine at 25 o C. **Hint: Put whatever you’re looking for in the numerator.

At a certain temperature fluorine gas travels at 582 m/s and a noble gas travels at 394 m/s. noble gas What is the noble gas?

CH 4 moves 1.58 times faster than which noble gas? Governing relation:

So HCl dist. = m/s (0.487 s) = m HClNH m DISTANCE = RATE x TIME HCl and NH 3 are released at same time from opposite ends of 1.20 m horizontal tube. Where do gases meet? Velocities are relative; pick easy #s:

Graham’s Law Consider two gases at same temp. Gas 1: KE 1 = ½ m 1 v 1 2 Gas 2: KE 2 = ½ m 2 v 2 2 Since temp. is same, then… KE 1 = KE 2 ½ m 1 v 1 2 = ½ m 2 v 2 2 m 1 v 1 2 = m 2 v 2 2 Divide both sides by m 1 v 2 2 … Take square root of both sides to get Graham’s Law: “mouse in the house”

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

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. Courtesy Christy Johannesson

Graham’s Law The rate of diffusion/effusion is proportional to the mass of the molecules –The rate is inversely proportional to the square root of the molar mass of the gas 250 g 80 g Large molecules move slower than small molecules

Step 1) Write given information GAS 1 = helium M 1 = 4.0 g v 1 = x GAS 2 = chlorine M 2 = 71.0 g v 2 = x HeCl 2 Step 2) Equation Step 3) Substitute into equation and solve v1v1 v2v2 = 71.0 g 4.0 g Find the relative rate of diffusion of helium and chlorine gas He diffuses 4.21 times faster than Cl 2 Cl He

If fluorine gas diffuses at a rate of 363 m/s at a certain temperature, what is the rate of diffusion of neon gas at the same temperature? Step 1) Write given information GAS 1 = fluorine M 1 = 38.0 g v 1 = 363 m/s GAS 2 = Neon M 2 = g v 2 = x F2F2 Ne Step 2) Equation Step 3) Substitute into equation and solve 363 m/s v2v2 = g 38.0 g 498 m/s Rate of diffusion of Ne = 498 m/s Ne F

Find the molar mass of a gas that diffuses about 4.45 times faster than argon gas. What gas is this? Hydrogen gas: H 2 Step 1) Write given information GAS 1 = unknown M 1 = x g v 1 = 4.45 GAS 2 = Argon M 2 = g v 2 = 1 ?Ar Step 2) Equation Step 3) Substitute into equation and solve = g x g 2.02 g/mol H Ar

Where should the NH 3 and the HCl meet in the tube if it is approximately 70 cm long? 41.6 cm from NH cm from HCl Ammonium hydroxide (NH 4 OH) is ammonia (NH 3 ) dissolved in water (H 2 O) NH 3 (g) + H 2 O (l) NH 4 OH (aq) Stopper 1 cm diameter Cotton plug Stopper Clamps 70-cm glass tube

Graham’s Law of Diffusion HCl NH cm Choice 1: Both gases move at the same speed and meet in the middle. NH 4 Cl(s)

Diffusion HCl NH cm cm NH 4 Cl(s) Choice 2: Lighter gas moves faster; meet closer to heavier gas.

Calculation of Diffusion Rate NH 3 V 1 = X M 1 = 17 amu HCl V 2 = X M 2 = 36.5 amu Substitute values into equation V 1 moves 1.465x for each 1x move of V 2 NH 3 HCl x + 1x = cm / = 81.1 cm for x

Calculation of Diffusion Rate V 1 m 2 V 2 m 1 = NH 3 V 1 = X M 1 = 17 amu HCl V 2 = X M 2 = 36.5 amu Substitute values into equation V V 2 17 = V1V1 V2V2 = V 1 moves 1.465x for each 1x move of v 2 NH 3 HCl x + 1x = cm / = 81.1 cm for x

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Determine the relative rate of diffusion for krypton and bromine. Kr diffuses times faster than Br 2. Graham’s Law The first gas is “Gas A” and the second gas is “Gas B”. Relative rate mean find the ratio “v A /v B ”. Courtesy Christy Johannesson Kr Br

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? Graham’s Law Put the gas with the unknown speed as “Gas A”. Courtesy Christy Johannesson O H

An unknown gas diffuses 4.0 times faster than O 2. Find its molar mass. Graham’s Law The first gas is “Gas A” and the second gas is “Gas B”. The ratio “v A /v B ” is 4.0. Square both sides to get rid of the square root sign. Courtesy Christy Johannesson O H H 2 = 2 g/mol

Graham's Law Keys Graham's Law