.
The mole as a unit of measurement
\[\require{mhchem}\]
In everyday language we use \(1\) dozen \(=12\) objects, \(1\) decade \(=10\) years, \(1\) ream\(=500\) sheets paper. Likewise, in chemistry, chemists consider: \[ 1\textrm{mole}=6.022\times10^{23}\textrm{objects} \]
The objects can be anything such as houses, sand, eggs, or oranges. However, in chemistry, objects are mainly atoms, ions or molecules.
One mole of anything contains \(6.022\times10^{23}\) objects. For instance, one mole of eggs contains \(6.022\times10^{23}\) eggs, one mole of carbon contains \(6.022\times10^{23}\) carbon atoms, one mole of carbon dioxide contains \(6.022\times10^{23}\) carbon dioxide molecules.
The symbol of moles is “mol”.
- Thus, three moles of particles is three times \(6.022\times10^{23}\)particles \(\left(3\times6.022\times10^{23}\right)\), and ten moles of particles is ten times \(6.022\times10^{23}\)particles \(\left(10\times6.022\times10^{23}\right)\).
- If we had \(3.011\times10^{24}\) atoms of gold \(\left(\ce{Au}\right)\), the number of mole, of gold would be:
Moles of \(\ce{Au}=\frac{3.011\times10^{24}\textrm{atoms}}{6.022\times10^{23}\textrm{atoms mole}^{-1}}=5.000\textrm{mol}\)
Avogadro’s Number (N)
Avogadro’s number is the term used for \(6.022\times10^{23}\) objects. \[ N_{A}=6.022\times10^{23}\textrm{mol}^{-1} \]
Avogadro’s number is the link between the number of atoms (or molecule or ions) of a material and the number of moles of material.
Molar Mass (\(M\))
Atomic mass is the average mass of an atom of an element measured in atomic mass units (amu).
One atomic mass unit is equal to \(1.66054\times10^{-24}\textrm{g}\), which is equal to \(\frac{1}{12}\) of the mass of a \(^{12}\ce{C}\) atom. \[ 1\textrm{amu}=1.66054\times10^{-24}\textrm{g}=\frac{1}{12}\times\textrm{mass of }^{12}\ce{C}\textrm{ atom} \]
Thus, the mass of one \(^{12}\ce{C}\) atom is \[ 1.66054\times10^{-24}\textrm{g}\times12=1.99265\times10^{-23}\textrm{g} \]
Then the mass of a mole of \(^{12}\ce{C}\) atoms will be \[ 1.99265\times10^{-23}\textrm{g}\times6.02214\times10^{23}\textrm{mol}^{-1}=12.0000\textrm{gmol}^{-1} \]
Molar mass is the mass of one mole of the substance. For instance, the molar mass of \(^{12}\ce{C}\) is \(12.0000\textrm{g}\). However, the mass of one mole of apples can be expected to be higher than the molar mass of \(^{12}\ce{C}\). Therefore, depending on the mass of individual objects, molar mass can vary, although the number of objects in a mole is fixed.
SI units of molar mass are kg mol. However, in practice, g mol is frequently used as the unit.
The molar mass of an atom and the atomic mass of an atom have the same numerical values, but units are different. For instance, the atomic mass of \(\ce{Mg}\) is \(24.31\textrm{amu}\): therefore, one mole of \(\ce{Mg}\) weighs \(24.31\textrm{g}\).
To calculate the molar mass of a compound or molecule, get the atomic mass of each atom from the periodic table, multiply it by the number of each type of atom and then total the answers obtained for each type of atom.
For example: Molar mass of \(\ce{Na}_{2}\ce{CO}_{3}\). Atomic mass of \(\ce{O}\), \(\ce{C}\) and \(\ce{Na}\) can be obtained from the periodic table in units of gram. \(\ce{O}=16.0\textrm{g}/\textrm{mol}\), \(\ce{C}=12.0\textrm{g}/\textrm{mol}\), \(\ce{Na}=23.0\textrm{g}/\textrm{mol}\). Sodium carbonate contains two \(\ce{Na}\) atoms, one \(\ce{C}\) atom and three \(\ce{O}\) atoms. \[\begin{align*} \textrm{The molar mass} & =\textrm{Sum of masses of atoms in a mole of the chemical species}\\ = & \left(2\times23.0\textrm{g}/\textrm{mol}\right)+12.0\textrm{g}/\textrm{mol}+\left(3\times16.0\textrm{g}/\textrm{mol}\right)\\ = & 106\textrm{g}/\textrm{mol} \end{align*}\]
Definition of molar mass creates an important relationship between the amount of substance (moles) and the mass of the substance (m): \[ M=\frac{m}{n} \]
Where, \(M=\) Molar mass \(\left(\textrm{g}/\textrm{mol}\right)\)
\(m=\)mass of the substance \(\left(\textrm{g}\right)\)
\(n=\)Number of Moles \(\left(\textrm{mol}\right)\)
Example: Calculate the amount of silver present in \(50.00\textrm{g}\) of silver. Molar mass of \(\ce{Ag}\) is \(107.87\textrm{g}/\textrm{mol}\).
Question states to calculate the amount of silver, which means the number of moles of silver. The molar mass of silver and the mass of silver are given in the question. Therefore, you can use \(M=\frac{m}{n}\) equation to find the number of moles \(\left(n\right)\). First, rearrange the equation to make \(n\) the subject and then substitute given values for \(M\) and \(m\). Make sure you write the units as well. \[\begin{align*} M & =\frac{m}{n}\\ n & =\frac{m}{M}\\ n & =\frac{50.00\textrm{g}}{107.87\textrm{g}/\textrm{mol}}\\ n & =0.4635\textrm{mol} \end{align*}\]
The Mole and chemical formulas
As we know, chemical formulas indicate the number of atoms of each element present in the compound. For instance, \(\ce{Na}_{2}\ce{CO}_{3}\): one molecule of sodium carbonate contains two atoms of sodium, one atom of carbon and three atoms of oxygen. Similarly, chemical formulas can also indicate the number of moles of atoms of each type of element present in one mole of the compound. Let’s take the same example \(\ce{Na}_{2}\ce{CO}_{3}\) again; this time the chemical formula of sodium carbonate indicates that 2 moles of sodium, one mole of carbon and three moles of oxygen are present in one mole of sodium carbonate.