Chapter 6, Problem 7A

Interpretation Introduction

Interpretation: The number of sulfur atoms in a sample of mass 8274 amu needs to be determined. Also, the mass of a given number of atoms of sulfur needs to be determined.

Concept introduction: The molar mass is defined as the mass of a substance in 1 mol. The number of units of the substance in 1 mol is $6.02\times {10}^{23}$ . This is Avogadro’s number and is denoted by the symbol $N_A$ .

Answer to Problem 7A

258 and 277.7 g.

Explanation of Solution

The average atom of sulfur has mass 32.07 amu. The number of atoms of sulfur with mass 8274 amu will be:

  $N=\frac{8274\text{ amu}}{32.07\text{ amu}}=258$

Now, the 1 mol of sulfur has $6.02\times {10}^{23}$ atoms. Also, the mass of 1 mol of S is 32.07 g/mol thus, the mass of 1 atom of sulfur will be:

  $m=\frac{32.07\text{ g/mol}}{6.02\times {10}^{23}{\text{ mol}}^{-1}}=5.327\times {10}^{-23}\text{ g}$

If the mass of 1 atom is $5.327\times {10}^{-23}\text{ g}$ thus, the mass of $5.213\times {10}^{24}\text{ atoms}$ will be:

  $m=\left(5.213\times {10}^{24}\times 5.327\times {10}^{-23}\right)\text{ g}=277.7\text{ g}$

Thus, the mass of sulfur atoms is 277.7 g.

Conclusion

Thus, the number of sulfur atoms is 258 and the mass of $5.213\times {10}^{24}\text{ atoms}$ of sulfur is 277.7 g.