Mole Concept

Since it is not possible to calculate the weight of particles individually, a collection of such particles called mole is taken for all practical purposes. Avogadro discovered that under standard conditions of temperature and pressure, (1atm and 273K) a sample of gas occupies a volume of 22.4 L.

It was discovered that the number of atoms present in 12g of carbon is 6.023 x 10²³ atoms. This is referred to as Avogadro number.

A mole of a gas is the amount of a substance containing 6.023 x 10²³ particles.

Avogadro number is the number of atoms present in C¹² isotope = 12g of C.

One mole of any gas at STP will have a volume of 22.4 L.

Volumes of gases change with changes of temperature and pressure. Therefore standard temperature and pressure (abbreviated STP) have been chosen of comparing volumes of gases. Standard temperature is 0^oC and standard pressure is 1 atm or 760mm. Volumes of gases are corrected to STP prior to most stoichiometric calculations by performing a combined Boyle's law-Charles law calculation.

The number of moles of gas is required to perform stoichiometric calculation using the mole concept. It has been found experimentally that one mole of any ideal gas at STP occupies 22.4 liters. Thus 1.00 mole H₂ (2.02 grams) at STP occupies 22.4 liters; 0.500 mole H₂ (1.01 gram) at STP occupies 11.2 liters.

Example Problem

1. A sample of hydrogen gas has a volume of 1.10 liters at -40^oC and 0.520atm. What will be its volume at STP.Solution

Convert the required temperature to K.
K = C + 273 = -40 + 273 = 273K (T₁)
K = C + 273 = 0 + 273 = 273K (T₂)
P₁ = 0.520atm, V₁ = 1.10 liters
P₂ = 1.00atm, V₂ = ?

Using the combined gas equation

P₁V₁ / T₁ = P₂V₂ / T₂

Then V₂ (Volume of H₂ at STP) = (1.10 liters) {(0.520atm / 1.00atm) (273K / 273K)}

Ans: V₂ = 0.670 liters

2. Calculate the number of moles of hydrogen collected in the above example problem.Solution

The volume of H₂ at STP is 0.670 liters. Determine the number of moles of H₂ by dividing the volume by the molar volume of an ideal gas.

Number of moles of H₂ = {0.670 liters / (22.4 liter / mole)}

Ans: Number of moles of H₂ = 0.0299 moles of H₂

The relationship between the mass of gas present and its volume is described by Avogadro law, which states that equal volumes of gases at the same temperature and pressure contain equal numbers of molecules. Thus if the temperature, pressure and volume of two gases are the same then the two gases contain the same number of molecules regardless of their identity.

The actual temperature and pressure at which we compare two or more gases do not matter. It is convenient however to select one temperature and one pressure as standard and chemists have chosen 1atm as the standard pressure and 0^oC as the standard temperature. These conditions are called Standard temperature and pressure (STP).

Avogadro law: Equal volumes of gases measured at the same temperature and pressure contain equal number of molecules.
Avogadro law allows us to write a gas that is valid not only for any pressure,volume and temperature but also for any quantity of gas. This law called the ideal gas law expressed as

T = Temperature of gas in kelvin (K)
R = Ideal gas constant

1. In the equation 2C₂H₆ + 7O₂ → 4CO₂ + 6H₂O, how many molecules of C₂H₆ are needed to produce 27.0 grams of H₂O?Solution:

The solution map for this problem is given below.
The problem is solved by factor label method (FLV)



2. In the equation 4NH₃(g) + 5O_2(g) → 4NO_(g) + 6H₂O(l) how many liters of NH₃(g) at STP are needed to react with 200 liters of O₂(g) at STP?Solution:

To solve this problem we need to convert between volume and numbers of moles. Our solution map is

The solution is given below


Volume-volume problems are particularly easy to solve because the factor22.4 always cancels in the calculations.

3. How many grams of O₂ are required to burn completely 114g of octane.Solution:

The combustion reaction is written as follows



Molecular weight of octane = 114g
Number of moles of octane = 114 / 114 = 1 mole.
According to the equation one mole of octane reacts with 25 / 2 moles of O₂.
Therefore,
Weight of O₂ = Number of moles x Molecular weight
= (25 / 2) x 32
= 400g

Gram molar volume

The volume occupied by one mole of a gas at STP is known as its gram molar volume.
1 mole of gas = 6.023 x 10²³ molecules = 22.4 L in STP
Moles of a gas = Volume of the gas at STP in L / 22.4 L

4. Calculate the volume of O₂ at STP produced by heating 12,25g of KClO₃Solution:

Molecular weight of KClO₃ = 122.5g

2KClO₃ → 2KCl + 3O₂

Number of moles of KClO₃ taken = 12.25 / 122.5 = 1/10 = 0.1mole
According to the equation
2 moles of KClO₃ = 3 moles of O₂ = 3 x 22.4 L of O₂ at STP
0.1 mole of KClO₃ = {(3 x 0.1) / 2} moles of O₂
= {(3 x 0.1) x 22.4 / 2} L of O₂ at STP
= 3.36 L of O₂ at STP

5. Calculate the amount of water formed when a mixture of 1g H₂ and 2g O₂ is sparked.Solution:

1 gm H₂ = 1 / 2 mole H₂; 2gm O₂ = 2 / 32 mole O₂ or 1 / 16 mole O₂

Now the equation for the formation of water is