General Chemistry/Gas Laws

Gas Laws
As the result of many different science experiments, several gas laws have been discovered. These laws relate the various state variables of a gas.

These gas laws can be used to compare two different gases, or determine the properties of a gas after one of its state variables have changed.

Combined Gas Law
Combining Charles' Law, Boyle's Law, and Amontons's Law gives us the combined gas law.

Ideal Gas Law
When Avogadro's Law is considered, all four state variables can be combined into one equation. Furthermore, the "constant" that is used in the above gas laws becomes the Universal Gas Constant (R).

To better understand the Ideal Gas Law, you should first see how it is derived from the above gas laws. The ideal gas law is the most useful law, and it should be memorized. If you know the ideal gas law, you do not need to know any other gas laws, for it is a combination of all the other laws. If you know any three of the four state variables of a gas, the unknown can be found with this law. If you have two gases with different state variables, they can be compared.

There are three ways of writing the ideal gas law, but all of them are simply algebraic rearrangements of each other.

 Rules for Using the Ideal Gas Law 
 * Always convert the temperature to kelvins (K).
 * Always convert mass to moles (mol).
 * Always convert volume to liters (L).
 * It is preferable to convert pressure to kilopascals (kPa). R, the Universal Gas Constant, would be 8.314 (L·kPa)/(mol·K).

Kinetic Molecular Theory
The Kinetic Molecular Theory attempts to explain the gas laws. It describes the behavior of microscopic gas molecules to explain the macroscopic behavior of gases. According to this theory, an ideal gas is composed of continually moving molecules of negligible volume. The molecules move in straight lines unless they collide into each other or the walls of their container.

The gas laws are now explained by the microscopic behavior of gas molecules:
 * Boyle's Law: The pressure of a gas is inversely proportional to its volume. A container's volume and surface area are obviously proportional.  Based on the pressure equation, an increase in volume (and thus surface area) will decrease pressure.
 * Charles' Law: the volume of a gas is proportional to its temperature. As the volume (and surface area) increases, the pressure will decrease unless the force also increase.  When pressure is constant, the volume and temperature must be proportional.  The temperature equation above explains why:  the energy of the molecules (and their collision force) is proportional to temperature.
 * Gay-Lussac's Law: The temperature of a gas is directly proportional to its pressure. An increase in temperature will increase the kinetic energy of the molecules (shown by the temperature equation).  Greater kinetic energy causes the molecules to move faster.  Their collisions with the container will have more force, which increases pressure.
 * Avogadro's Law: Equal volumes of all ideal gases (at the same temperature and pressure) contain the same number of molecules. According to the Kinetic Molecular Theory, the size of individual molecules is negligible compared to distances between molecules. Even though different gases have different sized molecules, the size difference is negligible, and the volumes are the same.

Deviations from the Ideal Gas Law
In an ideal gas, there are no intermolecular attractions, and the volume of the gas particles is negligible. However, there is no real gas that can perfectly fits this behavior, so the Ideal Gas Law only approximates the behavior of gases. This approximation is very good at high temperatures and low pressures.

At high temperature the molecules have high kinetic energy, so intermolecular attractions are minimized. At low pressure the gas occupies more volume, making the size of the individual molecules negligible. These two factors make the gas behave ideally.

At low temperature or high pressure, the size of the individual molecules and intermolecular attractions becomes significant, and the ideal gas approximation becomes inaccurate.

Eudiometers and Water Vapor
A eudiometer is a device that measures the downward displacement of a gas. The apparatus for this procedure involves an inverted container or jar filled with water and submerged in a water basin. The lid of the jar has an opening for a tube through which the gas to be collected can pass. As the gas enters the inverted container, it forces water to leave the jar (displacing it downward). To fill the entire container with gas, there must enough gas pumped into the container to expel all of the water.



As seen in this diagram, the downward displacement involves water. Therefore, in the container where the gas is collected, there is unwanted water vapor. To account for the water vapor, subtract the pressure of water vapor from the pressure of the gases in the container to find the pressure of the collected gas. This is simply a restatement of Dalton's Law of Partial Pressure: $$P_\text{total} = P_\text{water vapor} + P_\text{gas}$$

The pressure of water vapour can be found on this webpage.

Gas Laws Practice Questions

 * 1) Between the Combined Gas Law and the Ideal Gas Law, which one accounts for chemical change? Explain.
 * 2) Calculate the density of hydrogen at a temperature of 298 K and pressure of 100.0 kPa.
 * 3) What volume does 5.3 moles of oxygen take up at 313 K and 96.0 kPa?
 * 4) Hydrogen and sulfur chemically combine to form the gas hydrogen sulfide, according to the reaction: . How many liters of hydrogen are required to form 7.4 L of hydrogen sulfide (at STP: 273 K, 101.3 kPa)?

Answers to Gas Laws Practice Questions