Guide Card, Part 8

Additional Topic! 

Gas Laws

The main distinguishing property of gases is their uncanny ability to be compressed into smaller and smaller spaces. Gases are also the least complex state of matter. Don't get it wrong, just because they are the simplest doesn't mean that they are not one of the most interesting and useful states of matter.

Boyle's Law

Boyle's Law states the volume of a definite quantity of dry gas is inversely proportional to the pressure, provided the temperature remains constant.

Mathematically Boyle's law can be expressed as P₁V₁ = P₂V₂

• V₁ is the original volume
• V₂ is the new volume
• P₁ is original pressure
• P₂ is the new pressure

Charles's Law

Charles's Law can be stated as the volume occupied by any sample of gas at a constant pressure is directly proportional to the absolute temperature.

V / T =constant

• V is the volume
• T is the absolute temperature (measured in Kelvin)

Charles's Law can be rearranged into two other useful equations.

V₁ / T₁ = V₂ / T₂

• V₁ is the initial volume
• T₁ is the initial temperature
• V₂ is the final volume
• T₂ is the final temperature

V₂ = V₁ (T₂ / T₁)

• V₂ is the final volume
• T₂ is the final temperature
• V₁ is the initial volume
• T₁ is the initial temperature

Important: Charles's Law only works when the pressure is constant.

Note: Charles's Law is fairly accurate but gases tend to deviate from it at very high and low pressures.

Combined Law

The combined gas law is a combination of Boyle's Law and Charles's Law; hence its name the combined gas law. In the combined gas law, the volume of gas is directly proportional to the absolute temperature and inversely proportional to the pressure.

This can be written as PV / T = constant. Since for a given amount of gas there is a constant then we can write P₁V₁ / T₁ = P₂V₂ / T₂.

• P₁ is the initial pressure
• V₁ is the initial volume
• T₁ is the initial temperature (in Kelvin)
• P₂ is the final pressure
• V₂ is the final volume
• T₂ is the final temperature (in Kelvin)

This equation is useful if you have the current volume, temperature, and pressure of a gas, and if you have two of the three final values of the gas.

Ideal Gas Law

The ideal gas law is a combination of all the gas laws. The ideal gas law can be expressed as PV = nRT.

• P is the pressure in atm
• V is the volume in liters
• n is the number of moles
• R is a constant
• T is the temperature in Kelvin

The constant R is calculated from a theroretical gas called the ideal gas. The most commonly used form of R is .0821 L * atm / (K * mol). This R will allow the units to cancel so the equation will work out.

Dalton's Law of Partial Pressure:  

The pressure of a mixture of gases is equal to the sum of the pressures of all of the constituent gases alone.

Mathematically, this can be represented as:

Pressure_Total = Pressure₁ + Pressure₂ ... Pressure_n