GEN CHEM `1 | Kinetic Molecular Theory, Gas Laws, and Manometer

Macroscopic Properties

properties that can be visualized or measured by the naked eye, such as pressure, temperature, and volume

Volume (V)

the space occupied by a gas, equal to the size of the container; expressed in liters

Temperature (T)

the determining factor of the kinetic energy and rate of motion of gas particles; expressed in Kelvin

Pressure (P)

force exerted by a gas against the walls of the container; also the amount of collisions against the walls; expressed in atmospheres

1 atm into mmHg

760

1 atm into torr

760

1 atm into Pascal

101 325

Amount (n)

number of gas particles inside the container

Assumptions of the Kinetic Molecular Theory

1. The volume occupied by the individual particles of a gas is negligible compared to the volume of gas.

2. The particles of an ideal gas exert no attractive forces on each other or on their surroundings.

3. Gas particles are in a constant state of random motion and move in straight lines until they collide with another body.

4. The collisions exhibited by gas particles are completely elastic, meaning the kinetic energy is conserved.

5. The average kinetic energy of gas molecules is directly proportional to absolute temperature, meaning molecular motion stops at absolute zero.

Diffusion of Gas Particles

Diffusion, which is the movement of particles from an area of high concentration to low concentration, occurs due to its kinetic energy. It is faster at higher temperatures due to higher kinetic energy.

Effusion

movement of gas molecules through a tiny hole

Graham’s Law

effusion rate is inversely proportional to the square root of the pass of its particles

Boyle’s Law | Definition

At a constant temperature and amount of gas, pressure and volume are inversely proportional. This is because increasing the volume entails that collisions will be more likely.

Boyle’s Law | Formula

V₁P₁ = V₂P₂

Charles’ Law | Definition

At a constant pressure and amount of gas, temperature and volume are directly proportional. When the temperature increases, the higher kinetic energy leads to more collisions and therefore higher pressure. To maintain constant pressure, the volume will increase to lower the pressure.

Charles’ Law | Formula

V₁/T₁ = V₂/T₂

Gay-Lussac’s Law | Definition

At a constant volume and amount of gas, temperature and pressure are directly proportional. When the temperature increases, the higher kinetic energy leads to more collisions and therefore higher pressure.

Gay-Lussac’s Law | Formula

P₁/T₁ = P₂/T₂

Avogadro’s Law | Definition

At a constant pressure and temperature, amount of gas and volume are directly proportional.

Avagadro’s Law | Formula

V₁/n₁ = V₂/n₂

Barometer

It is used to measure atmospheric pressure. Atmospheric Pressure pushes down on the mercury in the basin, which makes the mercury in the column rise.

Manometer

It is a u-shaped device that measures to pressure difference. It has a liquid, which is usually mercury. When both sides are open to the air, the level of the liquid will be the same by default on both sides. By adding a gas with a different pressure on one side, you can solve the pressure from the difference of the heights on the two sides.

Close-end Manometer

It is not open to the air. It is read by taking the difference between the heights of the two columns.

Open-end Manometer

It has one side open to the atmospheric pressure. The difference in height is due to the difference of the unknown pressure of the gas added to the close end and the air pressure.

Atm of Atmosphere

760 mmHg

Reading an Open-end Manometer if the Column of Mercury is Higher in the Open End

Because the gas pressure is higher than the atmospheric pressure in this scenario, the pressure of the gas is obtained by adding the height difference to the air pressure.

Reading an Open-end Manometer if the Column of Mercury is Higher in the Closed End

Because the gas pressure is lower than the atmospheric pressure in this scenario, the pressure of the gas is obtained by subtracting the height difference from the air pressure.

Gas Mixture and Pressure

each gas exerts its partial pressure. which is equal to the pressure they would exert if they were the only gas in the container

Dalton’s Law | Definition

the total pressure of a gas mixture is the sum of the partial pressures of the gas in the mixture

Dalton’s Law Formula For Total Pressure

P_total = P₁ + P₂ + P₃ + …; P = pressure

Dalton’s Law Formula for Partial Pressure

P_A = X_iP_T; X is the mole fraction; P is the pressure

Diffusion

movement of gases from high concentration to low concentration; affected my temperature and molecular mass

Effusion

movement of gas molecules through a small hole; affected by temperature and molecular mass

Graham’s Law Definition

the rate of diffusion/effusion of gas is inversely proportional to the square root of its molecular mass

Graham’s law Formula if Rate is Given

rate₁/rate₂ = sqrt(M₂)/sqrt(M₁)

Graham’s Law Formula if Time is Given

t₂/t₁ = sqrt(M₂)/sqrt(M₁)

Gas Stochiometry

Use the stochiometric calculations to solve for the quantity of the substance.

Use the Ideal Gas Equation to solve for the moles of the needed gases.