Chapter U4.76, Problem 2E

Interpretation Introduction

Interpretation: The term molar mass needs to be defined.

Concept Introduction: The molar mass of a substance is an important concept in chemistry and is used in almost all stoichiometric calculations.

Answer to Problem 2E

The molar mass of a substance is defined as the mass of one mole of the substance. As per Avogadro, a mole of a substance is defined the weight of the substance which contains $6.02\times {10}^{23}$ units (atoms, molecules or ions) of the substance. Thus, the molar mass of the substance is the mass of $6.02\times {10}^{23}$ units of the substance. The molar mass of the substance is often taken to be equal to the molecular mass or the molecular weight of the substance expressed in the units of g.mol-1.

Thus, the unit of molar mass is g.mol-1.

Explanation of Solution

The molar mass of a substance is the sum total of the atomic masses of the elements forming the substance multiplied by the number of times each element occurs in the chemical formula of the substance. For example, let us consider the molar mass of carbon dioxide, ${\text{CO}}_2$ . The atomic masses (expressed in g.mol-1) are

C: $12.011\text{ g}{\text{.mol}}^{-1}$

O: $15.999\text{ g}{\text{.mol}}^{-1}$

Since carbon occurs once and oxygen occurs twice in the chemical formula of carbon dioxide, hence, the molar mass of ${\text{CO}}_2$ is given as

$\begin{array}{c}\text{Molar mass =}\left(1\times 12.011+2\times 15.999\right)\text{ g}{\text{.mol}}^{-1}\\ =44.009\text{ g}{\text{.mol}}^{-1}\end{array}$

Thus, the molar mass of ${\text{CO}}_2$ , which is equal to $44.009\text{ g}{\text{.mol}}^{-1}$ , is the mass of $6.02\times {10}^{23}$ molecules of ${\text{CO}}_2$ .

Conclusion

The molar mass of a substance is the mass of one mole of the substance and is numerically equal to the molecular weight of the substance expressed in the unit of g.mol-1.