Physics Chapter on Gas Laws

Graham's Law of Diffusion

• The rate of diffusion of a gas is inversely proportional to the square root of its density.
• This means that lighter gases diffuse faster than heavier gases.
• The equation for Graham's law is: $\frac{R_1}{R_2} = \sqrt{\frac{d_2}{d_1}}$

Gas Pressure and Kinetic Energy

• The pressure of a gas is proportional to its kinetic energy per unit volume.
• The equation for pressure is: $P = \frac{1}{3} \frac{M}{V} c^2$
• The pressure is equal to two-thirds of the kinetic energy per unit volume: $P = \frac{2}{3}\frac{KE}{V}$

Force acting on molecules due to wall

• The force exerted by a gas molecule on a wall is a result of the molecule's momentum change during a collision.
• The pressure of the gas is related to the average kinetic energy of the molecules.

Gay-Lussac's Law of Pressure

• The pressure of a gas is directly proportional to its absolute temperature when the volume is constant.
• The equation for Gay-Lussac's law is: $\frac{P_2}{T_2} = \frac{P_1}{T_1}$

Pressure Coefficient

• The pressure coefficient of a gas at constant volume is the change in pressure per unit degree centigrade rise in temperature.

Dalton's Law of Partial Pressures

• The total pressure of a mixture of gases is equal to the sum of the partial pressures of the individual gases.
• The equation for Dalton's law is: $P = P_1 + P_2 +...$

Gas Pressure Calculation

• The pressure exerted by a gas is related to the frequency of collisions of gas molecules with the container walls and their momentum change during collisions.

Avogadro's Law

• Equal volumes of all gases under the same conditions of temperature and pressure contain the same number of molecules.
• This is represented mathematically as: $PV = \frac{m}{M}RT$
• Avogadro's number is $6.023 \times 10^{23}$.

Gas Laws

• Boyle's Law: PV = constant, where pressure is inversely proportional to volume.
• Charles' Law: V/T = constant, where volume is directly proportional to temperature.
• Volume coefficient: The change in volume per degree rise in temperature at constant pressure.

Ideal Gas vs. Real Gas

• Ideal gas equation: $PV = nRT$
• Specific gas constant (r): $r = \frac{R}{M}$
• Real gases deviate from ideal behavior at high pressure and low temperatures.
• Vander Waals equation: $P + \frac{a}{V^2}(V-b) = RT$

Chapter 9: Behaviour of Perfect Gas and Kinetic Theory

• Ideal Gas: An ideal gas has zero molecular size and zero intermolecular forces. This state is attainable at low pressure and high temperature.
• Ideal Gas Equation: $\frac{V_1}{T_1} = \frac{V_2}{T_2}$
• Universal Gas Constant (R): It is constant for all gases and its value can be determined as $R = \frac{P_o V_o}{T_o}$
• Note: Normal Pressure = $P_o = 0.76 \times 13600 \times 9.8$ N/m⁻² and $V_o = 22.4 \ L = 0.0224 \ m^3$