CHEMISTRY NOTES – Chapter 12

The Behavior of Gases

Goals : To gain an understanding of :

1. The kinetic theory of matter. 2. Avogadro's hypothesis. 3. The behavior of gases and the gas laws.

NOTES:

The kinetic theory of matter states that particles which make up all types of matter are in constant motion.

The kinetic theory of gases assumes three things :

• A gas is composed of tiny particles, usually atoms or molecules that have negligent volume and virtually no attractive or repulsive forces exist between particles. Virtually all of the volume of a gas is empty space through which these particles move.

• These particles move in a random and rapid constant motion until they collide with other particles or obstacles. • The collisions between particles is elastic, meaning the kinetic energy is conserved - the amount of motion

before and after the collision is equal. To understand the idea of elasticity think of dropping a "super ball." The amount of motion is pretty much conserved as the ball bounces and can therefore be described as elastic. Now think about dropping a ball of clay - inelastic.

The three factors which determine the physical behavior of gases are :

• Pressure - pressure will compress a gas, reducing its volume and giving it a greater density and concentration of particles.

• Temperature - The higher the temperature, the greater the kinetic energy of the particles and vice versa. • Volume - A change in the volume of a contained gas will change the gas' concentration and pressure.

Kinetic energy is the energy of motion of molecules.

When heat energy is added to a gas its particles will increase in kinetic energy (move faster) and the internal energy of the particles will increase.

Temperature is a measure of the average kinetic energy of the particles of a substance.

Heat energy is the sum of the kinetic energy of the particles of a substance, whereas temperature is the average kinetic energy of the particles of a substance. To illustrate this imagine the two blocks of brass below, one is 2.0 kg, the other is 0.5 kg, and both are at 300.0 K. They both have the same temperature (average kinetic energy), but the larger block, due to a greater number of particles, has a greater total kinetic energy (more heat energy).

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Absolute zero is the lowest theoretical has not been actually observed) temperature possible at which all motion of particles ceases (i.e. no kinetic energy - no temperature). On the Kelvin scale absolute zero is O K and on the Celsius scale it is -273 ºC.

There is no theoretical upper limit to the temperature scales.

The Kelvin scale is used in the gas laws because it is a direct measure of the average kinetic energy of the particles of a substance. That is whatever happens to temperature also happens to the average kinetic energy. For example, if we double the Kelvin temperature, we double the kinetic energy of the particles of the substance. If we cut the Kelvin temperature to a fourth, the average kinetic energy of the particles is cut to a fourth.

Gas pressure is the result of the simultaneous collisions of a very large number of gas particles striking an object.

A vacuum is the relatively empty space that results from the removal of gas particles from a closed container.

Atmospheric pressure is the result of the simultaneous collisions of atmospheric molecules striking objects. Three units used to measure atmospheric pressure are

• pascals (Pa) - SI unit of pressure • millimeter of mercury (mm Hg) - the pressure needed to support one mm Hg • atmospheres (atm) one standard atmosphere is equal to 760 mm Hg at 25 ºC

Two types of barometers are :

• mercury barometer - consists of an evacuated glass cylinder immersed in a pool of mercury. The pressure of the atmosphere then pushes the mercury into the glass cylinder and then can be measured (usually in mm).

• aneroid barometer - most common today - has a diaphragm which will be pushed in with greater pressure and be allowed to push out with less air pressure. These changes are then transferred to a dial or pointer which indicates air pressure.

Avogadro's hypothesis of gas volumes is that equal volumes of gases at the same temperature and pressure contain equal numbers of gas particles. This goes back to the assumption that the gas particles have negligent volume and therefore take up virtually no space. Although different gases (e.g. carbon dioxide and hydrogen) may have particles which actually do have different volumes, the volumes of the particles is so small that it can be ignored.

Another way to think about this is to focus on pressure. If two equal volumes of gases are at the same temperature (same average kinetic energy of particles) and have the same number of particles, then you would expect the number of collisions with the walls of the container (gas pressure) to be the same.

Adding a gas to a sealed container of fixed volume increases (keeping temperature constant) the pressure (more particles colliding with the walls of the container) and subtracting gases from a sealed container of fixed volume will decrease pressure (keeping temperature constant).

Increasing the size of a sealed container (keeping temperature constant and not adding any more gas particles) will reduce gas pressure and decreasing the size of a sealed contained will do the opposite.

Increasing the temperature on a sealed container of fixed volume will increase pressure, decreasing the temperature will decrease pressure.

The law of adiabatic expansion or compression states that any gas will cool that is allowed to expand freely from a higher pressure to a lower pressure without the transfer of external energy to the gas. Similarly, a gas will heat if compressed from a lower to a higher pressure in the absence of a transfer of energy from the gas.

Ideal gases are gases that follow the gas laws under all conditions of temperature and pressure. Ideal gases are theoretical, that is they do not really exist. In real gases the particles actually do have volumes and take up space and really do have attractive or repulsive forces between them. real gases will liquefy or solidify under certain conditions of temperature and pressure and then will not follow the gas laws.

Dalton's law of partial pressures states that at constant temperature and volume, the total pressure exerted by a mixture of gases is equal to the sum of the partial pressures. a partial pressure is the pressure exerted by one of the gases in the mixture. the equation is Ptotal = P1 + P2 + P3 .... Here is a sample problem :

Boyle's law states that for a given mass of gas at a constant temperature, the volume of a gas varies inversely with pressure. That is if we increase pressure the volume decreases and vice versa. If we increase volume the pressure decreases and vice versa. Quantitatively the equation is P1 x V1 = P2 x V2. Here is a sample problem.

Charles' law states that the volume of a fixed mass of gas is directly proportional to is Kelvin temperature if the pressure is kept constant. That is if we increase temperature volume increases and vice versa. Quantitatively the equation is V1/T1 = V2/T2. Here is a sample problem.

Gay-Lussac's law states that the pressure of a gas is directly proportional to the Kelvin temperature if the volume is kept constant. Quantitatively the equation is P1/T1 =P2/T2. Here is a sample problem :

The three major factors which affect determine the physical behavior of gases are temperature pressure and volume (T, P and V). If you notice in the above equations the factor which is held constant does not appear in the equations (use this to help remember the equations and laws). But what if all the factors change? Then the combined gas law is used. Its equation is P1 x V1 /T1 = P2 x V2 /T2. This law can also be used to derive the other laws. For example if T is constant it cancels out of the equation and we get the equation for Boyle's law where T is constant. Here is a sample problem using the combined gas law.

The ideal gas law is a mathematical expression that relates the moles of a gas (indicated in the equation by the variable "n") to T,V and P. It uses the ideal gas constant (R) which has been experimentally determined to be 0.0821 (L x atm)/(K x mol). These are some hefty units but observe how they cancel out in the sample problem below. The expression for the ideal gas law is PV = nRT. Here is a sample problem using the ideal gas law.