Chapter 10.2, Problem 28SSC

Interpretation Introduction

Interpretation: A concept map needs to be designed to show the conversion factors that convert mass, number of moles and number of particles to each other.

Concept introduction: The relation between the number of moles and the mass of a substance is represented as follows:

  $n=\frac{m}{M}$

Here, m is mass and M is molar mass.

Also, the number of moles is related to Avogadro’s number and the number of units as follows:

  $N=n\times {\text{N}}_{\text{A}}$

Thus, the relation between the number of units and mass will be:

  $\begin{array}{l}\frac{N}{{\text{N}}_{\text{A}}}=\frac{m}{M}\\ \text{or,}\\ m=\frac{N}{{\text{N}}_{\text{A}}}\times M\end{array}$

Answer to Problem 28SSC

  

Explanation of Solution

1 mol of any substance has $6.022\times {10}^{23}$ units. These units are also known as representative particles. For an element, these represented particles are atoms and for compounds these are molecules.

To start a concept map, the number of moles can be considered to be known.

Let the number of moles of a substance be n mol.

Now, for all the substances, 1 mol contains $6.022\times {10}^{23}$ representative particles.

Also, the mass of 1 mol of a substance is known as molar mass. The relation between the number of moles, mass and molar mass is as follows:

  $n=\frac{m}{M}$

Here, the number of moles can be written in terms of the number of particles as follows:

  $n=\frac{N}{{\text{N}}_{\text{A}}}$

Thus,

  $\begin{array}{l}\frac{m}{M}=\frac{N}{{\text{N}}_{\text{A}}}\\ \text{Or,}\\ m=\frac{N}{{\text{N}}_{\text{A}}}\times M\end{array}$