# Kinetic Molecular Theory of Gases, cont.

### Consequences/predictions:

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. (Overhead 42, Zumdahl figure 5.20, p 205)

public domain image via Wikipedia Creative Commons‡

Note that for kinetic energy, KE = 1/2 mV2, so V 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 (88 ft/s) is much worse that one at 30 mph - four times as much energy is involved!)

# Energy

### Law of Conservation of Energy

Energy can be transformed, but is neither created nor destroyed in chemical processes. Thus radiant energy can be transformed into heat which may to used to expand the volume of a gas and vice versa, bond energy can be converted into heat and/or light, etc.

Some common forms of energy important to our study include:

• Kinetic Energy (KE) - energy due to motion. KE = 1/2 mv2.
• Potential Energy (PE) - energy due to position. In chemical systems we also say it is due to composition, though ultimately this reduces to positions of atoms and electrons relative to each other.

#### State Functions

Kinetic energy, potential energy, pressure, and volume are all examples of State Functions. They are all properties that depend only on the current state - they are all independent of the path used to reach this state.

# The First Law of Thermodynamics

The First Law of Thermodynamics says that the energy of the Universe is constant. Thus it is another name for the law of conservation of energy. Symbolically it is written:

E = q + w

where E is energy, q is heat, and w is work.

Note that according to this law we can still do things with energy, its just that they are always compensated. (Thus as the Universe expands, work is done against gravity and the heat in the Universe decreases as manifested by a decreasing average temperature.)

Generally in thermodynamics we refer to systems. A system is simply a portion of the universe we wish to work with. For the expression

E = q + w

where E is the internal energy (the total KE and PE) of the system.

q = the quantity of heat exchanged by the system:

• if the system gains heat, q = positive, and we say the process is endothermic.
• if the system loses heat, q = negative, and we say the process is exothermic.

Notice in each case endo- and exo- are in respect to the system, not the surroundings. For example, a fire is exothermic, because heat comes out of the fire - the fuel loses heat, even though you (part of the surroundings) may gain some of it.

Keep in mind that heat always flows naturally from hotter to cooler systems. Energy must be used up to move heat in the opposite direction, as in a refrigerator.

w (in chemistry) = the work done by or on the system:

• w = positive when work is done on the system (e.g. as gas is compressed)
• w = negative when the system does work on its surroundings (e.g. a gas moves a piston by expansion - notice that an ideal gas expanding in space does no work!).

Note that if no heat is transferred to or from a system (it is isolated in a "thermos"), then all energy must appear as work. On the other hand, if no work is done, then all energy must appear as heat (this is utilized in calorimetry which is discussed below).

Example: A quantity of air in a cylinder expands against a piston doing 4.5 kJ of work while 10.0 kJ of heat is added. How much has the energy of the air changed?

E = q + w

• Heat is added, therefore q is (+)
• Work is done by the system (the air expands), therefore w is (-)

So E = 10.0 kJ + (- 4.5 kJ) = 5.5 kJ

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