Gas Laws

Jamie Z 2024-06-08

Learning Goals

• Use kinetic theory of gases to describe and explain behaviour of a gas
• Use appropriate mathematical representations to solve problems and make predictions using Boyle’s and Charles’s Law

Boyles Law

• The relationship between the pressure and volume of a gas
• When volume decreases, pressure increases, when volume increases, the pressure decreases

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• A plot of V versus P is a straight line and gradient is K

Equation

\[ P_1V_1=P_2V_2 \]

Charles Law

• Increased temperature means that particles have higher kinetic energy
• There is higher pressure due to collisions and the volume increases
• The volume is directly proportional to the temperature as long as the pressure and amount of gas are constant
• The relationship between volume and temperature is linear

Equation

\[ \frac{V_1}{T_1}=\frac{V_2}{T_2} \]

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Avogadro’s Law

• Temperature and pressure is constant
• Amount of reactant (moles) or volume changes
• The volume of a gas is directly proportionate to the amount of gas (moles). As the number of particles increase, the volume increases

Equation

\[ \frac{V_1}{n_1}=\frac{V_2}{n_2} \]

Gay-Lussac’s Law

• The pressure of a gas is proportionate to its temperature when volume and amount of gas is constant

Equation

\[ \frac{T_1}{P_1}=\frac{T_2}{P_2} \]

Ideal Gas Law

• There is no such thing as an ideal gas. Real gases exhibit non-ideal behaviour under ordinary conditions
• Assumptions can be made for non-ideal gases

Equation

\[ \frac{PV}{Tn}=R \]

\[ R=8.314JK^{-1}mol^{-1} \]

Universal Gas Constant

• Universal gas constant is 8.314 joules per kelvin per mol
• Always convert temperature to Kelvin and pressure to kPa

Unit Conversions

\[ 0\degree C = 273\degree K \]

\[ 1;kPa = 1000;Pa\ 1;atm = 101.3 ;kPa = 101300 ;Pa \]