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Gases Part 2

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Standard Temp and Pressure, STP• For gases, chemists have defined a standard set of

conditions: standard temperature and pressure or STP.• STP is defined as 1.00 atm pressure and 0°C or

273.15K.• If a 1.00 mol sample of ANY gas is at STP, then the

volume which this sample occupies is 22.414L.• This means that at STP, we have another conversion

factor: 1mol = 22.414L• Problem: A 12.37L sample of gas is at STP. How many

moles are in this sample?

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Using PV=nRT to find density• Density of gases is given as mass/volume or g/L.• But in PV = nRT, this is very close to n/V or

mol/volume.• Then we have:•

• But we really want g/L, not mol/L.• How can we get from n in mol to g?

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Using PV=nRT to find density• We know that:

n = g/MW where MW is the molar mass (really mol. mass)

• Now we substitute in n = g/MW in the above to get:

• Problem: Find the density of helium at STP and at

30°C and 1.00atm.

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Using PV=nRT to find MW• This is similar to the above:

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Dalton’s Law of Partial Pressures• When we have a mixture of 2 or more gases,

they act essentially independently of each other.• This means that they each exert their own

pressure, or partial pressure.• Therefore, the total pressure of the gas mixture

is equal to the sum of the partial pressures of the individual gases in the mixture.

• This is stated thus:

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Dalton’s Law of Partial Pressures• We also use mol fractions, Xi:

• If the partial pressure of water vapor is 23.756 torr at 25°C, what is the mol fraction of water if atmospheric pressure is 765 torr?

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RMS Speed of Gas Particles• For gas particles, we talk about the root-

mean square speed (RMS speed) of particles instead of the average speed:

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RMS Speed of Gas Particles• What does this mean?• That heavy gases move slower than light

ones!

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Graham’s Law of Effusion• Effusion is when gas particles escape through

pinholes.• Diffusion is when gas particles mix throughout

a container.• The speed or rate of effusion is related to the

molar mass or molecular weight as seen above.

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Graham’s Law of Effusion• More importantly, we can compare the rates of

2 gases:

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Graham’s Law of Effusion• Again, this tells us what we already knew (or

would have guessed intuitively): lighter gases effuse faster.

• However, this difference in the rate of effusion is actually used to separate gases with different molecular weights.

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Gas Stoichiometry• We can use PV = nRT or the fact that at STP 1 mol =

22.414 L to solve gas stoichiometry problems.• Let’s look at the rxn of hydrogen gas with oxygen gas to

produce liquid water:

• How many g of water can be produced from 5.72 L of hydrogen gas at STP?

• If 17.9 g of water is produced at 25°C and 1.00 atm, how many liters of oxygen were consumed?

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Deviations from the Ideal Gas Law• The Ideal Gas Law, PV = nRT is based on some

assumptions.

1) Gases have negligible volume!– Wrong! Particularly for high pressures, the

volume of gas particles may take up as much as 10% of the total volume of the container.

– This means that gas particles exert a greater pressure, or Preal > Pideal

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Deviations from the Ideal Gas Law• Next wrong assumption:

2) Gas particles have no interactions!– Wrong! They do interact to some extent.– When they do interact, the pressure

decreases, or Preal < Pideal

• So these 2 factors tend to cancel each other out, and for pressures below around 4 atm, they pretty much do!

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Deviations from the Ideal Gas Law• So if the pressure is below 4 atm, we ignore

deviations from ideal gas behavior.• For intermediate pressures the gas particle

interactions are more important, so Preal < Pideal.

• For high pressures the particles are closer and closer together, so the volume effect is much greater, or Preal > Pideal.

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Deviations from the Ideal Gas Law• These 2 deviation may be seen in the Van der

Waals equation (don’t need to memorize or use):