# Gases Part 2 1 1 1 1.

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Gases Part 2 1 1 1 1

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 K. If a 1.00 mol sample of ANY gas is at STP, then the volume which this sample occupies is L. This means that at STP, we have another conversion factor: 1mol = L Problem: A 12.37L sample of gas is at STP. How many moles are in this sample?

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?

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.

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

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:

Dalton’s Law of Partial Pressures
We also use mol fractions, Xi: If the partial pressure of water vapor is torr at 25°C, what is the mol fraction of water if atmospheric pressure is 765 torr?

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:

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

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.

Graham’s Law of Effusion
More importantly, we can compare the rates of 2 gases:

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.

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

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

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!

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.

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):