Gas Density: Summary

The molar concentrations and densities of gases increase as they are compressed (less volume, right?), but decrease as they are heated (volume increases, right?). The density of a gas depends on its molar mass.

The Stoichiometry of Reacting Gases

• Many reactions occur in the gas phase and we can use the ideal gas law to determine the volume of gas produced or consumed in a chemical reaction– How much oxygen will it take to saturate

the hemoglobin molecules in a red blood cell?

Steps to working with stoichiometry in the gas phase:

1. Balance the chemical equation

2. Calculate the number of moles of reactant consumed

3. Use the stoichiometric coefficients from the chemical reaction to relate the # moles of product made to the # of moles of reactant consumed.

Mixtures of Gases

• Most gases we encounter and use every day are actually mixtures– The atmosphere of the earth– The breath we exhale

• If the gases in a mixture do not react with each other, we may consider the mixture to be a single, pure gas for the sake of computation

Mixtures and Partial Pressures

• Dalton came up with the law that allows us to calculate the pressure of a mixture and the contribution of the individual gases that comprise it

• How did he arrive at this conclusion?• He determined that if he combined the gases,

the pressure of the mixture would be the sum of the Partial Pressures of the individual gases. And it is.

Dalton’s Law of Partial Pressures

• The total pressure of a mixture of gases is the sum of the partial pressures of its components

Mole Fractions

• The best way to explain/understand the relationship between total pressure and partial pressures is to look at the mole fractions of each gas in a mixture

• For a mixture of gases with components A, B and C, the mole fraction (xA) is:

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xA =nA

nA + nB + nC

Mole Fractions

• We know that xA + xB + xC = 1

• Each gas exerts a pressure that is the mole fraction of the gas times the total pressure in the vessel

PA = xAP

Molecular Motion

• We have derived the gas laws and worked with an equation of state: The Ideal Gas Law

• Now, we need to look at the motion of the gas molecules themselves

Diffusion and Effusion

Diffusion

Effusion

Graham’s Law of Effusion• Scottish chemist Thomas Graham

studied the effusion of gases

• He found that at constant temperature, the rate of effusion of a gas is inversely proportional to the square root of its Molar Mass.

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Rate of effusion ∝ 1

M or Average Speed ∝

1

M

•Does this make sense to you?

Graham’s Law of Effusion

• The average speed of the molecules will be inversely proportional to the molar mass– Bigger molecules move slower at constant

temperature than smaller ones.– Think of it in terms of energy and getting

the molecules to move

Graham’s Law of Effusion• We can use this relationship to identify

compounds/molecules with unknown molar mass by comparing the Rate of Effusion of an unknown gas to that of another with known Molar Mass

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Rate of Effusion of Gas A

Rate of Effusion of Gas B=

MB

MA

or Time for Gas A to effuse

Time for Gas B to effuse=

MA

MB

Remember: rate is in units of m/s and time is just seconds, so we flip the relationship

Effusion Rate and Temperature• If you raise the temperature, what

happens to the Effusion rate?

…

• This shows us that the average speed of the gas molecules is directly dependent on temperature

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Rate of Effusion of a gas at T2

Rate of Effusion of a gas at T1

=T2

T1

This tells us that The average speed of the molecules in a gas is proportional to the square root of the temperature

This is BIG!!!

Average Speed and Temperature

• We can combine the observations on the relationship between the average speed of a gas to the temperature and its molar mass

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Average Speed ∝ T

M

The average speed of the molecules in a gas is directly proportional to the square root of the temperature and inversely proportional to the square root of the molar mass

Kinetic Molecular Theory

• All of this leads to the theory describing the behaviour of gas molecules: KMT

1. A gas consists of a collection of molecules in continuous, random motion

2. Gas molecules are infinitesimally small points3. The molecules move in a straight line until

they collide4. The molecules do not influence each other

until they collide (No attractive forces b/w molecules)

Kinetic Molecular Theory

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vrms =3RT

MRoot mean square

Why use vrms?

Ek=1/2(mvrms2)