Gases

Key Ideas

• Kinetic energy: the energy of all motion
• Elastic collision: the conservation of kinetic energy during collisions

Kinetic Molecular Theory

Gases are in continuous, chaotic motion and, except during elastic collisions, are widely separated from each other

• Gases are widely separated with no intermolecular bonding between molecules
• Rapid, chaotic, random movement in straight lines until they collide with another particle or the wall of the container
• When gases collide, kinetic energy can be transferred from one particle to another, but no energy is lost

Pressure

Pressure is the measure of the force exerted by the particles on the walls of the container during collisions.
Pressure $$=\frac{Force}{Area}$$ (The force per unit area of the container)

 Unit Symbol Conversion to kPa Kilopascal kPa 1 Pascal Pa 1000 Pa Atmosphere atm 0.987 atm Bar bar 1 bar Millimeters of Mercury mmHg 750 mmHg

The Universal Gas Equation

For all gas equations, units must be kept constant

• P: Pressure is in kPa
• V: Volume is in L
• n: mol is in mol
• T: Temperature is in Kelvin ($$0K\approx -273^oC$$)
• R: The gas constant is $$=8.31\,J\,K^{-1}\,mol^{-1}$$

Volume and Pressure

• Given an amount of gas at a constant temperature, the volume will be inversely proportional to the pressure
• $$P\propto \frac{1}{V}$$
• $$P_1V_1=P_2V_2$$

Volume and Temperature

• Given an amount of gas at a constant pressure, the volume of the gas will be directly proportional to the temperature
• $$V\propto T$$
• $$\frac{V_1}{T_1}=\frac{V_2}{T_2}$$

Combined Gas Law

• $$\frac{P_1\times V_1}{n_1\times T_1}=\frac{P_2\times V_2}{n_2\times T_2}$$

Universal Gas Equation

• $$P\times V=n\times R\times T$$

Molar Volume of Gas

• If an amount of gas has a constant pressure and a constant temperature, the volume of the gas will be the same. If the gas is at SLC - Standard Laboratory Conditions ($$100kPa,\,25^oC$$) then $$1\,\text{mol}$$ of gas occupies $$24.8L$$

Dalton's Law of Partial Pressure

The total pressure exerted by a mixture of gases is equal to the sun of all the partial pressures of the constituent gases

• $$P_{TOTAL}=P_1+P_2+P_3+P_{...}$$

Molar Volume

n=V/Vm

• Because gases theoretically all behave the same way, 1 mole of any gas (at a particular temperature and pressure) occupies a set volume called the molar volume.

• At standard laboratory conditions (SLC) of 25°C and 100kPa 1 mole of gas occupies 24.8L.

• Standard molar volume (Vm) = 24.8 L/mol

This constant can be used to determine the number of moles of gas present at SLC if a volume is provided.

3 main types of gas stoichiometry questions:

1) Mass-mass stoichiometry: asked to convert a mass of reactant into a mass of product or vice versa.

2) Mass-volume stoichiometry: asked to convert a mass of reactant into a volume of product or vice versa. • Note: the current study design states volume calculations are only required at SLC (Universal gas equation not included).

3) Volume-volume stoichiometry: asked to convert a volume of reactant into a volume of product and vice versa.

Mass-mass stoichiometry

Requires conversion to a number of moles first!!

• Question: calculate the mass of carbon dioxide produced if 2.3g of propane is reacted according to the equation: 6$$C_3H_8$$(g) + 5$$O_2$$(aq) --> 3$$CO_2$$(g) + 4$$H_2O$$(l)

1) Convert mass of propane into number of moles

2) Use mole ratios to work out the number of moles of carbon dioxide produced

3) Use m = nM to determine the mass of carbon dioxide formed.

Mass-volume stoichiometry

Must always convert to a number of moles first!!

• Question: Determine the volume of hydrogen gas evolved at SLC is 0.239g of solid zinc are reacted according to the equation: Zn(s) + $$H_2SO_4$$(aq) --> $$ZnSO_4$$(aq) + $$H_2$$(g)

1) Convert 0.239g of Zn into a molar amount.
2) Use mole ratios to determine the number of moles of hydrogen gas formed.
3) Calculate the volume of hydrogen gas evolved at SLC using n = V/Vm.

Volume-volume stoichiometry

Because 1 mole of any type of gas occupies the same volume under a set temperature and pressure, we can simply use mole ratios to work out the missing volume! No intermediate step requiring converting to a number of moles!!

• To use this rule: closed system at constant temperature and pressure