Chapter 10.1, Problem 5SP

Interpretation Introduction

Interpretation: The number of atoms in 1.14 mol of sulfur trioxide should be calculated.

Concept Introduction: Factor that uses one set of units to change it to another set of units is said to be conversion factor.

Answer to Problem 5SP

The number of atoms in 1.14 mol of sulfur trioxide is $\text{ 2}\text{.74}\times {10}^{24}\text{ atoms }$ .

Explanation of Solution

The relationship between a mole and number of molecules is:

  $1\text{ mol = 6}\text{.02}\times {10}^{23}\text{ molecules}$

The total number of atoms in sulfur trioxide, ${\text{SO}}_{\text{3}}$ is 4. (One sulfur and three oxygen atoms).

Now, the required conversion factor is:

  $1.14\text{ mol}\times \left(\frac{\text{6}\text{.02}\times {10}^{23}\text{ molecules }}{1\text{ mol}}\right)\times \left(\frac{4\text{ atoms}}{1\text{ molecule}}\right)$

On solving:

  $1.14\text{ mol}\times \left(\frac{\text{6}\text{.02}\times {10}^{23}\text{ molecules }}{1\text{ mol}}\right)\times \left(\frac{4\text{ atoms}}{1\text{ molecule}}\right)\text{= 2}\text{.74}\times {10}^{24}\text{ atoms }$

Hence, the number of atoms in 1.14 mol of sulfur trioxide is $\text{ 2}\text{.74}\times {10}^{24}\text{ atoms }$ .