Boyle's Law
Key Points:
  • Temperature and moles of gas are constant
  • Graph is hyperbolic (see right) and asymptotic to both axes
  • Pressure and volume are inversely proportional to each other

animation
Charles's Law
Key Points:
  • Pressure and moles of gas are constant
  • Graph is linear (see right)
  • Volume and temperature are directly proportional to each other

animation
Gay-Lussac's Law
Key Points:
  • Volume and moles of gas are constant
  • Graph is linear (see right)
  • Pressure and temperature are directly proportional to each other

animation
Combined Gas Law
The combined gas law integrates Boyle, Charles, and Gay-Lussac's laws.  Here, the only constant is the number of moles of gas. Notice that if you cover on set of variables, either Charles, Boyle, or Gay-Lussac's Law remains. For example, if you cover T1 and T2, the remaining equation is the same as Boyle's Law. Removing P1 and P2 leaves Charles's Law and eliminating V1 and V2 leaves Gay-Lussac's Law.
Ideal Gas Law
The ideal gas law is used to approximate the behavior of a gas at conditions given by the pressure, temperature, and volume variables. Typically, the approximation is reasonable for situations close to STP (1 atm pressure/273.15 K), but deviates greatly at extreme pressures and temperatures.
Dalton's Law of Partial Pressures
Like the ideal gas law, Dalton's law makes some key assumptions. Namely, the gases must be unreactive and follow ideal gas behavior.
Density of Gases
In the derivation to the left, M represents the molar mass for the particular gas and m represents the mass of the gas sample.  Note that unlike Boyle's, Charles's, or Gay-Lussac's Law, the identity of the gas makes a difference when determining density, but ultimately the mass of the sample does not. The initial substitution of n (moles) for m/M reflects how the number of moles of a substance is calculated - from dividing mass by molar mass.
Carbon Dioxide
Carbon dioxide can be produced in several ways. The video below shows the decomposition of a carbonate.
Copper(II) carbonate is heated in a beaker so an environment of carbon dioxide is created as it decomposes. A lit piece of magnesium is placed inside and reacts strongly with the carbon dioxide. In the combustion of hydrocarbons, the presence of carbon dioxide (a product of the combustion) will extinguish a flame. Here, the carbon dioxide increases the vigor of magnesium's oxidation.
In addition to water vapor, the complete combustion of a hydrocarbon will produce carbon dioxide. A third method of generating carbon dioxide is to add an acid to a solid carbonate. The volcanoes students make for science fairs utilize this reaction. Baking soda (sodium bicarbonate) reacts vigorously with vinegar (acetic acid) to produce sodium acetate, water, and carbon dioxide gas. The rapid evolution of the gas is what forces the aqueous sodium acetate and water out of the volcano.
Hydrogen
Hydrogen gas can be produced from the action of an acid on a metal.
Zinc reacts with sulfuric acid vigorously to yield aqueous zinc sulfate and hydrogen gas.
Nitrogen Dioxide
A copper penny is added to concentrated nitric acid. The visible products are nitrogen dioxide and copper (II) nitrate.
Oxygen
After heating potassium chlorate, a hot oxygen environment is produced. This allows for the spontaneous combustion of a Peep, which is made of sucrose. The decomposition of a metal chlorate will always yield a metal chloride and oxygen gas. Potassium chlorate and sodium chlorate are commonly used for this purpose.