### Richard A. Paselk

Chem 107

Fundamentals of Chemistry

Fall 2009

Lecture Notes: 29 October

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# Gases & Gas Laws, cont.

### Continuing our exploration of gas laws, let's try some more examples:

Example: A student ignores the warning labels and throws an empty (no liquid left, no spray) can of hair spray into his campfire. Assuming an ambient temperature of 25 °C and atmospheric pressure of 7.20 x 102mmHg, and a temperature in the coals of 600 °C, find the pressure in the can in the fire, assuming it doesn't burst or expand.

Example: One of the student's colleagues on this ill fated trip tossed an "empty" 0.500 L propane cylinder into the fire. Unfortunately, 3.50 g of propane remained in the cylinder. What pressure would be reached in the cylinder assuming no deformation and no bursting at 550 °C (assume 3 sig figs for the temp.).

Now we can expand our view of gas behavior with two additional observations, both consistant with our picture of gas behavior.

Equal volumes of different gases at the same temperature (T) and pressure (P) have the same number of particles (same number of moles).

Example: 2.40 L of ethene gas (C2H4) is combined with 7.35 L of oxygen and ignited. If all volumes of reactants and products are measured at the same temperature and pressure (above 100 °C - so water is a vapor), calculate the volume of each substance after the reaction is complete.

• ### Dalton's Law of Partial Pressures:

The pressure of a gas is independent of the presence of other gases.

• .

One of the most common applications of Dalton's Law of Partial Pressures is the determination of gas pressures above water. We will see in lab that the vapor pressure (gas pressure) of water is fixed by the temperature, and that there will always be a contribution to the total pressure by water when it is present.

Example: 50.0mL of oxygen is collected over water from a specimen of Anacris water weed illuminated by controlled lighting. If the temperature is 20.0°C and the pressure of the collected gas is 760.5 mmHg how many moles of oxygen were collected? (the vapor pressure of water = 17.5 mmHg at 20.0°C).

# Kinetic Molecular Theory of Gases

We have been looking at the various properties of gases, now we want to look at a theory to explain those behaviors. A simple model is the kinetic-molecular theory. There are four basic postulates:

1. A gas is composed of a large number of tiny particles (molecules, or atoms for the inert gases). These particles are so small that the sum of the particles volumes is negligible compared to the volume of their container - most of the container volume is empty space.
2. The particles of a gas are in rapid, linear motion. They make frequent collisions with each other and the walls of any vessel containing them. All collisions between gas particles and between gas particles and container walls are elastic. (There is no net loss of kinetic energy in collision - energy can be exchanged between particles, but the total stays the same.)
3. Except when they are colliding, the particles are completely independent of each other. That is, there are no forces of attraction or of repulsion between them.
4. The particle in a gas have a wide range of velocities: some may be nearly still, while others move at great speed. Thus there is a wide range of kinetic energies in any gas. However, the average kinetic energy for any gas is the same at a given temperature. The average kinetic energy for the particles in a gas is proportional to the absolute temperature of the gas. (KE = 3/2 RT, R is still the Gas constant, but different units.)

#### Consequences/predictions for each postulate:

1. Gases are easy to compress - expected if there is lots of empty space between them.
2. This explains why gases rapidly fill their containers. We also note that they don't condense out as a liquid or solid if they are left in an insulated container (they don't lose energy as they collide with walls.) Brownian motion is also a consequence of their rapid movement.
3. Three is a bit more subtle, and we won't worry about it.
4. From this postulate we expect a distribution of velocities, as seen in the diagram below.

Note that for kinetic energy, KE = 1/2 mv2, so v (velocity) varies as the square root of the mass (m1/2). Notice also that the energy increases with the square of the velocity. (This is why an accident at 60 mph is much worse that one at 30 mph - four times as much energy is involved!).

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