AP Chemistry“The Behavior of Gases”

Effusion and Diffusion Root Mean Speed

Average Kinetic Energy

Diffusion is:

Effusion: Gas escaping through a tiny hole in a container.

Both of these depend on the molar mass of the particle, which determines the speed.

Molecules moving from areas of high concentration to low concentration.Example: perfume molecules spreading across the room.

•Diffusion: describes the mixing of gases. The rate of diffusion is the rate of gas mixing.

•Molecules move from areas of high concentration to low concentration.

Effusion: a gas escapes through a tiny hole in its container

-Think of a nail in your car tire…

Diffusion and effusion are explained by the next gas law: Graham’s

Graham’s Law

The rate of effusion and diffusion is inversely proportional to the square root of the molar mass of the molecules.

Derived from: Kinetic energy = 1/2 mv2

m = the molar mass, and v = the velocity.

RateA MassB

RateB MassA

=

Comparing distance Comparing distance traveledtraveled

You can compare the distanced traveled by 2 gases in the same amount of time using this equation also.

Distance traveled by A = MassB

Distance traveled by B MassA

Sample: compare rates of effusion of Helium with Nitrogen –

With effusion and diffusion, the type of particle is important: Gases of lower molar mass diffuse and

effuse faster than gases of higher molar mass.

Helium effuses and diffuses faster than nitrogen – thus, helium escapes from a balloon quicker than many other gases!

Graham’s Law

How much faster does methane How much faster does methane (CH(CH44) effuse than propane (C) effuse than propane (C33HH88)?)?

Determine molar masses of each gasDetermine molar masses of each gas CHCH44 = 16.04 g/mol = 16.04 g/mol

CC33HH88 = 44.09 g/mol = 44.09 g/mol Plug into formula Plug into formula Rate Rate CH4CH4 M M C3H8C3H8

Rate Rate C3H8 C3H8 MMCH4CH4

= = 44.09 = 1.65 44.09 = 1.65

16.0416.04 This means that methane diffuses This means that methane diffuses

1.65 times faster than propane gas1.65 times faster than propane gas

Graham’s Law of Effusion Graham’s Law of Effusion ExamplesExamples

1) 1) A compound effuses through a A compound effuses through a porous cylinder 1.41 times faster porous cylinder 1.41 times faster than helium. What is it’s molar mass? than helium. What is it’s molar mass?

Rate Gas x = √He

Rate He √X

1.41 = √4

√x

1.41 (√x ) = 2

√x = 2/1.41

X = (1.41)2 = 2.01 g/mole =

Hydrogen (H2)

If 0.00251 mol of NHIf 0.00251 mol of NH33 effuse through effuse through a hole in 2.47 min, how much HCl a hole in 2.47 min, how much HCl would effuse in the same time?would effuse in the same time?

Assuming the time is the same, we can use the following relationship with Graham’s Law

Moles NH3 = √MHCl

Moles HCL √MNH30.00251 = √36.45Moles HCl √17

0.00251 = 1.46428Moles HCl

Moles HCl = 0.0017 Moles

A sample of NA sample of N22 effuses through a effuses through a hole in 38 seconds. what must be hole in 38 seconds. what must be the molecular weight of gas that the molecular weight of gas that effuses in 55 seconds under effuses in 55 seconds under identical conditions?identical conditions?

Moles / 55sec = √ MN2

Moles / 38sec √Mgas

38 = √28 55 √Mgas

Mgas = 58.5 g/mol

Molecular Speeds andMolecular Speeds andAverage Kinetic EnergyAverage Kinetic Energy

The Kelvin temperature scale is a The Kelvin temperature scale is a measurement of the measurement of the average kinetic average kinetic energyenergy of gas particles. of gas particles.

KE = ½ mvKE = ½ mv22

As kinetic energy increases, then the As kinetic energy increases, then the temperature increases, and molecules temperature increases, and molecules move faster.move faster.

KEKEavgavg = 3 RT = 3 RT 22Where = 8.3145 J/Kelvin MoleWhere = 8.3145 J/Kelvin Mole This formula represents the average This formula represents the average

energy of the particles at a given energy of the particles at a given temperature.temperature.

Maxwell Speed Distribution Curve •Peaks represent

the average speeds

•Remember, some are moving faster and some slower at the same temperature!

•Peak moves to greater speed with higher temps.

•Curve flattens due to more molecules moving at greater speeds.

Root Mean Square Speed (or Root Mean Square Speed (or Velocity)Velocity) rms or rms or μμrms rms (Units are meters/sec)(Units are meters/sec)

Estimates the average molecular speed based on molecular mass and temperature.

ΜΜrms = rms = √3RT√3RT √ √MM

M = Molar Mass in kg/moleM = Molar Mass in kg/mole R = 8.3145 J/K Mol T = Temperature in Kelvin

This Formula relates the difference in This Formula relates the difference in speed (speed (not kinetic energy!) not kinetic energy!) to the to the molar massmolar mass of the gas. of the gas.

Maxwell Speed Distribution CurveMaxwell Speed Distribution CurveOxygen (O2)

Helium

Hydrogen (H2)

•These are speed distribution curves for 3 different gases a the same temperature

•Shows that lighter molecules (like hydrogen) move faster on average than heavier ones (like oxygen)

Big Points to RememberBig Points to Remember:: All gases at the same temperature have All gases at the same temperature have

the same average kinetic energy.the same average kinetic energy. But, they do not have the same average But, they do not have the same average

velocity (or speed!)velocity (or speed!) Speed depends on Molar Mass (root Speed depends on Molar Mass (root

mean square speed!)mean square speed!) The heavier the gas, the slower it moves!The heavier the gas, the slower it moves! The lighter the gas, the faster it moves!The lighter the gas, the faster it moves!