Chapter 10.1, Problem 14SSC

Interpretation Introduction

Interpretation:

The given samples need to be arranged from smallest to largest in terms of number of representative particles.

Concept introduction:

In 1 mol of any substance, there are $6.022\times {10}^{23}$ units of that substance. These units can be atoms and molecules. The number of units in 1 mol of any substance is known as Avogadro’s number. It is denoted by symbol N_A.

Answer to Problem 14SSC

The order of samples from smallest to largest is as follows:

$6.78\times {10}^{22}$ molecules of glucose $\left({\text{C}}_{\text{6}}{\text{H}}_{\text{12}}{\text{O}}_{\text{6}}\right)\text{<}$

$\text{3}\text{.56 mol}$ of iron (Fe) $<1.25\times {10}^{25}$ atoms of zinc

Explanation of Solution

Given information:

$1.25\times {10}^{25}$ atoms of zinc (Zn)

$3.56\text{ mol}$ of iron (Fe)

$6.78\times {10}^{22}$ molecules of glucose $\left({\text{C}}_6{\text{H}}_{12}{\text{O}}_6\right)$

The number of representative units in Zn, Fe and glucose is atoms, atoms and molecules respectively. The number of atoms of Zn and glucose are given thus, to compare number of moles of Fe should be converted into number of atoms of Fe.

This can be calculated using the following equation:

$N=n\times N_A$

Putting the values,

$\begin{array}{l}N=\left(3.56\text{ mol}\right)\left(6.022\times {10}^{23}\text{ atoms/mol}\right)\\ =2.14\times {10}^{24}\text{ atoms}\end{array}$

Now, the given number of atoms of Zn and number of molecules of glucose $\left({\text{C}}_6{\text{H}}_{12}{\text{O}}_6\right)$ is $1.25\times {10}^{25}$ and $6.78\times {10}^{22}$ respectively.

On comparing, the number of atoms of Zn will be largest followed by number of atoms of Fe and number of molecules of glucose $\left({\text{C}}_6{\text{H}}_{12}{\text{O}}_6\right)$ is smallest.

Conclusion

Thus, the order from smallest to largest in terms of number of representative particles will be:

$6.78\times {10}^{22}$ molecules of glucose $\left({\text{C}}_{\text{6}}{\text{H}}_{\text{12}}{\text{O}}_{\text{6}}\right)\text{<}$

$\text{3}\text{.56 mol}$ or $2.14\times {10}^{24}\text{ atoms}$ of iron (Fe) $<1.25\times {10}^{25}$ atoms of zinc.