Chapter 10.3, Problem 45PP

Interpretation Introduction

Interpretation:

The mass of sodium chloride needs to be determined if number of formula units is $4.59\times {10}^{24}$.

Concept introduction:

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

$n=\frac{m}{M}$

Here, m is mass and M is molar mass.

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

$N=n\times N_A$

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

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

Explanation of Solution

Given Information:

The number of formula units or molecules of NaCl is $4.59\times {10}^{24}$.

Calculation:

The first step is to convert the given formula unit in terms of mass.

The mass can be calculated using the following formula:

$m=\frac{N}{N_A}\times M$

The molar mass of NaCl can be calculated as follows:

1 mol of NaCl contains 1 mol of Na and 1 mol of Cl, the molar mass of Na and Cl atom is 23 g/mol and 35.45 g/mol respectively. The molar mass of NaCl will be:

$M=23+35.45=58.45\text{ g/mol}$

Putting the values,

$m=\frac{4.59\times {10}^{24}}{6.022\times {10}^{23}}\times 58.45\text{ g/mol}=\text{445}\text{.5 g}$

Thus, mass of NaCl is $\text{445}\text{.5 g}$.

Conclusion

Therefore, the mass of NaCl is $\text{445}\text{.5 g}$.