Gases

Ideal State

When dealing with gases, we consider them to be in a hypothetical 'ideal' state We assume that they have nonexistant intermolecular forces and occupy no volume

Gases Properties

1. Volumes of gases change extensively with changes in pressure and tempertaure. 2. Gases expand to fill their containers (gas volume - volume of container) 3. Gases are quite compressable under high pressure (pressure = force/area) 4. Form homogenous mixtures with other gases, regardless of their identities, with liquids this is not alway the case

Gases Standard Temperature and Pressure

Temp = 0.0⁰C, 273.15K Pressure = 1 atm Volumer of 1 mole of any gas at STP = 22.4 litres

Gases Kinetic Molecular Theory of Gases

1. Attractive and reulsive forces between gas molecules are negligable 2. The volume of all molecules of the gas are negligable compared to the volume in which the gas is contained 3. Collisions between gas molecules are elastic - there is no gain or loss of energy 4. Gas molecules collide with each other and the walls of the container in a random, continous manner 5. The average kinetic energy of gas particles is proportional to their absolute temperature and is the same for all gases at a given temperature

Gases Graham's Law of Effusion

Rates of effusion are inversely proportional to the square root of the densities of the gases: Rate of effusion of gas A/Rate of effusion of gas B = Square root(Density of A/Density of B) = Square root (Molecular Mass A/Molecular Mass B) Lightweight gases effuse and diffuse more rapidly than gases of large molecular weight

Gases Effusion

The flow of gas from one compartment to another via a small opening Rates of effusion can be compared by keeping temperature and pressure constant.

Gases Dalton's Law

Dalton's Law of partial pressures states that the total pressure of a mixture of gases is equal to the sum of the individual pressures exerted by all the gases Ptotal = P1 + P2 + P3 +... Ptotal = RT/V (n1 + n2 + n3 +...) where: R = 0.0821 L-atm/K-mol T = Kelvin temperature n = number of moles

Gases Boyle's Law

Pressure and volume are inversely proportional to one another and remperature is constant P1V1 = P2V2

Gases Charles's Law

Volume and absolute temperature are directly proportional and pressure is constant V1/T1 = V2/T2

Gases Ideal Gas Law

Assumes that each gas occupies the entire volume of the vessel with its own partial pressure. \this relationship can be used to find the density and molar mass of the gas PV = nRT

Gases Ideal Gas Law Density

1. Obtain the number of grams from n(grams/molecular weight) 2. Obtain the number of litres by solving the ideal gas equation for V 3. Density = grams per litre

Gases Ideal Gas Law Molar Mass

1. Divide the weight by the volume 2. Multiply this number (g/l) by 22.4 litres per mole

Under isothermal conditions what would be the volume of 1L sample of helium after its pressure is changed from 12atm to 4atm?

Boyle's Law: PV1 = PV2

(12 x 1) = (4x)

x = 3L

If the absolute temperature of 2L gas at constant pressure is changed from 283.15K to 566.30K, what would be the final volume?

Charles' Law: V1/T1 = V2/T2

2/283.15 = x/566.30

x = 4L

Volume of 1 mole gas under standard conditions

22.4L

What volume would 12g helium occupy at 20^{O}C and 380mm Hg?

PV = nRT

n = 12/4 = 3 mol

P = 1/760 x 380 = 0.5atm

T = 20 + 273 = 293K

V = (3 x 0.0821 x 293) / 0.5 = 144.4 L

Gas Constant, R

0.0821 L** ·** atm/(mol **·** K)

Conversion mm Hg to atm

760 mm Hg = 1 atm

Conversion degrees to Kelvin

Add 273.15

What is the density of HCl gas at 2atm and 45^{o}C?

PV = nRT

P = 2atm, n = 1, R = 0.0821, T = (273.15 + 45) = 318.15K

V = (1 x 0.0821 x 318.15) / 2 = 13L

Density = mass/V = (1+35)/13 = 2.77g/L

What is the molar mass of a 2L sample of gas that weighs 8g at 15^{o}C and 1.5atm

PV = nRT

P = 1.5atm, V = 2L, R = 0.0821, T = (273.15 + 15) = 288.15K

n = (1.5 x 2) / (0.0821 x 288.15) = 0.13

Molar mass = 1/0.13 x 8 = 63.1 g/mol

Real Gases

1. Deviations due to pressure

2. Deviations due to temperature

1. As the pressure of a gas increases, particles are pushed closer together. Intermolecular forces of attraction become more significant at the gas condenses into a liquid state

2. As the temperature of a gas is decreased the average velocity of gas particles decreases and attractive intermolecular forces become significant. As condensation temperature is approached for a given pressure, these forces cause the gas to condense into a liquid state

A vessel contains 0.75 mol N, 0.20 mol H and 0.05 mol F at a total pressure of 2.5 atm. What is the partial pressure of each gas?

Nitrogen: 0.75/(0.75+0.20+0.05) = 0.75 x 2.5 = 1.875 atm

Hydrogen: 0.20/(0.75+0.20+0.05) = 0.20 x 2.5 = 0.5 atm

Fluorine = 0.05/(0.75+0.20+0.05) = 0.05 x 2.5 = 0.125 atm