Mole in Chemistry

23rd Jul 2019 @ 18 min read

The mole is a unit of measurement. It is one of the seven fundamental SI base units, others are the kilogram, the second, the metre, the ampere, the kelvin, the candela. The mole is the SI unit of amount of substance. The approximate value of one mole of any substance is 6.022 × 10²³. The symbol mol is used to denote it.

The unit is typically used to represent the measurement of atomic-scale particles like atoms, molecules, ions and radicals, subatomic particles like electrons and protons.

Consider an example, when we say one mole of sodium chloride in the beaker (NaCl), it means there are approximately 6.022 × 10²³ molecules of NaCl in the beaker.

Etymology

The word “mole” has multiple meanings in the English language. Some common meanings are a small dark-furred mammal, a spy, a small raised blotch on the skin etc. None of them relates to the mole in chemistry. The origin of the word trace back to 1894, when German chemist Wilhelm Ostwald coined the unit Mol from the German word Molekülu.

Definition of Mole

The definition of the mole has been subjected to multiple revisions from time to time.

2019 Redefinition

In November 2018, the General Conference on Weights and Measures (CGPM) approved the revision of all the SI units including the mole. The new definitions came into effect on 20^th May 2019. The 2019 redefinition of the mole fixes the value of one mole to an exact number, and the number is 6.022 140 76 × 10²³.

According to the 2019 redefinition, one mole of a substance is exactly 6.022 140 76 × 10²³ elementary entities.

The new definition is also criticised by some authors as it unlinks the traditional relationship between the kilogram and the mole. This is discussed below.

Prior to 2019 Redefinition

Prior to the 2019 redefinition, the definition of the mole was based on the atomic mass of carbon-12. One mole was defined as the number of atoms present in 12 g of carbon-12. Thus, 12 g of carbon-12 contains exactly one mole of ¹²C atoms. The relation between the mole and the atomic mass of carbon-12 (m_(¹²C)) is as follows:

$1\,\text{g}\, \text{mol}^{-1} =m_{(^{12}\text{C})} \times N_\text{A}$

where N_A is the Avogadro constant, which is explained later in this article.

Note: The above relation is no longer valid because of 2019 redefinition, but it is true approximately (see the table below). For practical purposes, we can use for the above relation if high precision is not needed. The atomic mass of carbon-12 is expressed in the unified mass unit (u). The unified mass unit is the standard unit of the atomic mass and can be expressed in the kilogram. Invalidating equation the above equation, not only breaks the relationship between the mole and the unified mass unit but also between the mole and the kilogram.

All the above points are summarised in the table below.

Table 1: Consequence of 2019 Redefinition
2019 Redefinition	Prior to 2019 Redefinition
One mole is 6.022 140 76 × 10²³ elementary units.	The number of ¹²C atoms in 12 g of carbon-12 equals one mole
1 mol = 6.022 140 76 × 10²³ elementary units	1 mol = 6.022 140 78(18) × 10²³ elementary units
1 g mol⁻¹ ≈ m_(¹²C) × N_A	1 g mol⁻¹ = m_(¹²C) × N_A

As we see from the above table the difference between the values of 1 mol in both definitions is very small and can be ignored for practical purposes.

Necessity of Mole

The mole was adopted as the unit of amount of substance. The question is why do we need a unit to measure the amount of substance. We already have the kilogram to measure the mass of a substance. The answer to the question is chemical reactions. Chemical reactions are governed by the number of species (atoms and molecules), not the mass. Consider an example of a neutralisation reaction.

$\text{NaOH} + \text{HCl} \longrightarrow \text{NaCl} + \text{H}_2\text{O}$

In the above reaction, one molecule of sodium hydroxide (NaOH) reacts with one molecule of hydrochloric acid (HCl) to form one molecule of sodium chloride (NaCl) and one molecule of water (H₂O). Thus, the number of molecules participating controls the reaction, not the mass of species. This is true for all reactions.

Generally, chemists do not deal with a single atom or molecule, and it is not practically feasible to monitor reactions involving a single atom or molecule. This is where the mole concept comes into play. One mole represents approximately (6.022 × 10²³) entities. It is a very large number and practically useful for atomic-scale entities. So, we can monitor one mole of sodium hydroxide (≈ 40 g) reacting with one mole of hydrochloric acid (≈ 36.5 g) to form one mole of sodium chloride (≈ 58.5 g) and one water (≈ 18 g). Thus, we can say the mole bridges the gap between the atomic world and the macroscopic world.

Figure 3: 1 mole of NaCl is equivalent to 58.5 g. Also, we can see from the figure that 1 mole of NaCl is a measurable quantity.
[Image Source: Wikimedia]

Note: This is possible because we can establish the relationship between the mole and the gram, which we also called the molar mass. The molar mass is explained later in this article.

Avogadro’s Constant and Mole

The number 6.022 140 76 × 10²³ is also called the Avogadro number. The number is christened in honour after Amedeo Avogadro, an Italian Chemist, who is known by Avogadro’s law. When the unit mol⁻¹ is assigned to the number, it becomes the Avogadro constant. The Avogadro constant is denoted by N_A.

$N_\text{A} = 6.022\,140\,76 \times 10^{23} \,\text{mol}^{-1}$

The difference between the mole and the Avogadro constant is that the mole is a unit while the Avogadro constant is a quantity with the unit of the reciprocal of the mole. The equation below describes the relationship between both.

$1\,\text{mol} =\frac{6.022\,140\,76 \times 10^{23}}{N_\text{A}}$

Molar Mass

The molar mass is the mass of a substance per unit mole. It is a bulk property, not molecular. The molar mass is a useful quantity, we can calculate the mass of any element or compound for a given mole from the molar mass.

Different elements and molecules have different masses, so, one mole of a chemical substance weighs differently from others. The figure below depicts the same.

1 mole of common chemicals — Figure 4: 1 Mole of Common Chemicals (From the Left to the Right: Mercury Oxide, 216 g mol⁻¹; Sucrose, 342 g mol⁻¹; Sulphur, 32 g mol⁻¹; Copper Sulphate Pentahydrate, 250 g mol⁻¹; Sodium Chloride, 58.5 g mol⁻¹; Copper, 63.5 g mol⁻¹
[Image Source: 2012books.lardbucket.org]

The molar mass and the atomic weight approximately have the same value, but they have different units. For example, the atomic weight of water is 18, and the molar mass is 18 g mol⁻¹.

We can calculate the number of moles (n) for a given mass (m) of a substance using the molar mass (M) of the substance.

$n =\frac{m}{M}$

Molar Density

The molar density is the density calculated using the number of moles instead of the mass. It is defined as the number of moles per unit volume.

$\rho_\text{m} =\frac{\text{moles}}{\text{volume}} =\frac{n}{V}$

The reciprocal of the molar density is the molar volume (V_m).

$V_\text{m} =\frac{1}{\rho_\text{m}} =\frac{V}{n}$

For an ideal gas, the molar volume is estimated by the following expression.

$V_\text{m}=\frac{1}{\rho_\text{m}} =\frac{RT}{P}$

Concentration

The number of moles is essential to calculate concentrations like molarity, mole fraction. The molarity is the number of moles of solute per unit volume and expressed in mol dm⁻³. While the mole fraction is the ratio of the moles of solute to the total number of moles and it is a dimensionless quantity.

Examples and Calculations

Below are some examples which will help to comprehend the mole concept.

Example 1: To Determine Moles of Iron from Its Molar Mass

Statement: Find the number of moles of 9.5 g of Iron.

Solution: Iron is a metal with the chemical symbol Fe. The molar mass of iron is 55.8 g mol⁻¹. Thus, one mole of Fe weighs 55.8 g.

For 9.5 g of Fe, the number of moles (n) is

$n =\frac{m}{M} &=\frac{9.5}{55.8}\\ &=0.17 \,\text{mol}$

Thus, there are 0.17 mol of Fe atoms in 9.5 g.

We can also determine the number of Fe atoms (N) if multiple by the Avogadro constant (N_A).

$N =n \times N_\text{A} =0.17 \times 6.022 \times 10^{23} =1.0\,\times 10^{23}$

Therefore, in 9.5 g of Fe, there are 1.0 × 10²³ atoms.

Example 2: To Estimate Mass of Iodine Atom.

Statement: Find the mass of iodine atoms from its molar mass.

Solution: The molar mass of iodine is 126.9 g mol⁻¹ i.e., one mole of iodine weighs 126.9 g mol⁻¹.

In one mole of iodine, there are around 6.022 × 10²³ atoms.

So, the mass of one atom of iodine is the molar mass divided by the Avogadro constant.

$m_\text{I} =\frac{M}{N_\text{A}} &=\frac{126.9}{6.022 \times 10^{23}}\\ &=21.07 \times 10^{-23}\\ &=2.107 \times 10^{-22} \,\text{g}$

Thus, the mass of one atom of iodine is 2.107 × 10⁻²² g.

Note: This is the average mass of an iodine atom. The actual mass of an iodine atom can vary depending on its isotopes.

Example 3: To Determine Moles of Isopropyl Alcohol

Statement: A beaker contains equal moles of isopropyl alcohol and water. The mass of isopropyl alcohol in the beaker is 40.5 g. Find the mass of water.

Solution: The molar mass of isopropyl alcohol is 60 gmol⁻¹ and of water, 18 g mol⁻¹.

We know the mass of isopropyl alcohol (C₃H₈O) is 40.5 g; so, the number of moles can be calculated as:

$n_{\text{C}_3\text{H}_8\text{O}} &=\frac{m_{\text{C}_3\text{H}_8\text{O}}}{M_{\text{C}_3\text{H}_8\text{O}}}\\ &=\frac{40.5}{60}\\ &=0.675\,\text{mol}$

There are equal moles of isopropyl alcohol and water in the beaker. Thus, the moles of water 0.675 mol. From the mole of water, we calculate the mass of water in the beaker.

$m_{\text{H}_2\text{O}} &=n_{\text{H}_2\text{O}} \times M_{\text{H}_2\text{O}} \\ &=0.675\times 18 \\ & \approx 12 \,\text{g}$

Therefore, the mass of water in the beaker is 12 g.

Example 4: To Determine Iron Atoms in Haemoglobin

Statement: Haemoglobin is a very important biomolecule in mammals. It is responsible for the transport of oxygen from the lungs to the cells of the body. Calculate the number of iron atoms in the human body.

Data: The concentration of haemoglobin in healthy human blood is approximately 0.18 g ml⁻¹. The molar mass of haemoglobin is 65 000g mol⁻¹. One molecule of haemoglobin contains four atoms of iron. The average amount of blood in the body is 500 0 mL.

structure of haemoglobin — Figure 5: Structure of Haemoglobin
[Image Source: Wikimedia]

Solution: The blood in the human body is 500 0 mL, and the concentration of haemoglobin in blood is 0.18 g ml⁻¹. So, the multiplying both numbers, we can get the mass of haemoglobin m_h in the body.

$m_\text{h} =500\,0 \times 0.18 =900 \,\text{g}$

Using the molar mass of 65 000 g mol⁻¹, we can determine the moles of haemoglobin in the body.

$n_\text{h} =\frac{m_\text{h}}{M_\text{h}} =\frac{900}{65\,000} =0.013\,8 \,\text{mol}$

Thus, the human body contains 0.0138 mol moles of haemoglobin. But each molecule of haemoglobin contains four atoms of iron. So, the number of moles of iron in the human body is 0.013 8 × 4 = 0.055 2 mol.

Multiplying the number of moles of iron by the Avogadro constant, we get the total number of iron atoms in the body.

$N_\text{Fe} =n_\text{Fe} \times N_\text{A} =0.055\,2 \times 6.022 \times 10^{23} =3.3 \times 10^{22}$

Therefore, there are 3.3 × 10²² atoms of iron in the human body.

Example 5: To Determine Moles of Ammonia

Statement: Consider the reaction of the formation of ammonia below.

$\text{N}_2 + 3\text{H}_2 \longrightarrow 2\text{NH}_3$

The initial amount of nitrogen is 23 g. Calculate the moles of ammonia formed if the nitrogen is the limiting reactant.

Solution: The initial moles of nitrogen is the initial mass of nitrogen divided by the molar of nitrogen. The molar of nitrogen is 28 g mol⁻¹.

$n_{\text{N}_2} =\frac{m_{\text{N}_2}}{M_{\text{N}_2}} =\frac{23}{28} =0.821 \,\text{mol}$

From the reaction, each mole of nitrogen consumed two moles of ammonia is formed. So, for 0.821 mol of nitrogen consumed, moles of ammonia is 0.821 × 2 ≈ 1.6 mol.

Example 6: To Determine Moles of Carbon, Hydrogen, Nitrogen, and Oxygen in Folic Acid

Statement: Folic acid is an important vitamin. It is commonly known as folate, folacin, or vitamin B₉. Folate is vital for DNA and RNA synthesis. The deficiency of the acid can result in anaemia. Daily adult intake recommended is 400 µg.

The molecular formula of folic acid is C₁₉H₁₉N₇O₆ and the molar mass is 441.4 g mol⁻¹. Calculate the moles of carbon, hydrogen, nitrogen, oxygen in 500 g of the acid.

Solution: The mole of 500 g of folic acid is calculated as:

$n_\text{FA} =\frac{500}{441.4} =1.133 \,\text{mol}$

Each mole of folic acid contains nineteen moles of carbon, nineteen moles of hydrogen, seven moles of nitrogen, and six moles of oxygen. The calculations are shown in the table below.

Table 2: Moles of Carbon, Hydrogen, Nitrogen, and Oxygen in 1.133 mol of Folic Acid
Elements	For Each Mole of Folic Acid	For 1.133 Moles of Folic Acid
Carbon	19	21.53
Hydrogen	19	21.53
Nitrogen	7	7.93
Oxygen	6	6.80

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