Chapter 10.1, Problem 6SP

Interpretation Introduction

Interpretation: The number of carbon and hydrogen atoms in 2.12 mol of propane 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 6SP

The number of carbon and hydrogen atoms in 2.12 mol of propane is $\text{3}\text{.83}\times {10}^{24}\text{ atoms}$ and $\text{1}\text{.02}\times {10}^{25}\text{ atoms}$ respectively.

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 molecular formula of propane is ${\text{C}}_{\text{3}}{\text{H}}_{\text{8}}$ , which means there are three carbon atoms and eight hydrogen atoms in propane.

Now, the required conversion factor for determining the number of carbon atoms in 2.12 mol of propane is:

  $2.12\text{ mol}\times \left(\frac{\text{6}\text{.02}\times {10}^{23}\text{ molecules }}{1\text{ mol}}\right)\times \left(\frac{\text{3 atoms}}{1\text{ molecule}}\right)$

On solving:

  $2.12\text{ mol}\times \left(\frac{\text{6}\text{.02}\times {10}^{23}\text{ molecules }}{1\text{ mol}}\right)\times \left(\frac{\text{3 atoms}}{1\text{ molecule}}\right)\text{= 3}\text{.83}\times {10}^{24}\text{ atoms }$

Hence, the number of carbon atoms in 2.12 mol of propane is $\text{3}\text{.83}\times {10}^{24}\text{ atoms}$ .

Now, the required conversion factor for determining the number of hydrogen atoms in 2.12 mol of propane is:

  $2.12\text{ mol}\times \left(\frac{\text{6}\text{.02}\times {10}^{23}\text{ molecules }}{1\text{ mol}}\right)\times \left(\frac{\text{8 atoms}}{1\text{ molecule}}\right)$

On solving:

  $2.12\text{ mol}\times \left(\frac{\text{6}\text{.02}\times {10}^{23}\text{ molecules }}{1\text{ mol}}\right)\times \left(\frac{\text{8 atoms}}{1\text{ molecule}}\right)\text{= 1}\text{.02}\times {10}^{25}\text{ atoms }$

Hence, the number of hydrogen atoms in 2.12 mol of propane is $\text{1}\text{.02}\times {10}^{25}\text{ atoms}$ .