Chapter 10, Problem 118A

Interpretation Introduction

Interpretation:

Whether 10.0 mole of C or 10.0 mole of $\text{Ca}$ contains more atoms should be determined. Number of atoms of 10.0 mole of C and 10.0 mole of $\text{Ca}$ should be calculated.

Concept introduction:

The number of moles of a compound is defined as the ratio of the given mass of the compound to the molar or molecular mass of the compound.

The mathematical expression is given by:

Number of moles = $\frac{\text{given mass of the compound}}{\text{molar mass of the compound}}$

The one mole of any substance is equal to the Avogadro number, i.e., $6.022\times {10}^{23}$ atoms.

Answer to Problem 118A

The number of atoms of 10.0 mole of carbon is equal to the number of atoms of 10.0 mole of calcium.

Number of atoms of $\text{C}$ = $\text{60}\text{.22}\times {\text{10}}^{23}\text{ atoms}$

Number of atoms of $\text{Ca}$ = $\text{60}\text{.22}\times {\text{10}}^{23}\text{ atoms}$

Explanation of Solution

Number of moles of carbon = 10.0 mole

Number of moles of calcium = 10.0 mole

Since one mole of any substance is equal to the Avogadro number, i.e., $6.022\times {10}^{23}$ atoms.

Number of moles = $\text{number of molecules ×}\frac{1\text{ mole}}{6.022\times 10\text{atoms}}$

Put the values,

$\text{10}\text{.0 mole}$ = $\text{Number of atoms ×}\frac{1\text{ mole}}{6.022\times 10\text{atoms}}$

$\text{Number of atoms }=\text{10}\text{.0 mole}\times 6.022\times {10}^{23}\frac{\text{atoms}}{\text{mole}}$

Number of atoms of $\text{C}$ = $\text{60}\text{.22}\times {\text{10}}^{23}\text{ atoms}$

Number of moles of calcium = 10.0 mole

$\text{10}\text{.0 mole}$ = $\text{Number of atoms ×}\frac{1\text{ mole}}{6.022\times 10\text{atoms}}$

$\text{Number of atoms }=\text{10}\text{.0 mole}\times 6.022\times {10}^{23}\frac{\text{atoms}}{\text{mole}}$

Number of atoms of $\text{Ca}$ = $\text{60}\text{.22}\times {\text{10}}^{23}\text{ atoms}$

The number of atoms of 10.0 mole of carbon is equal to the number of atoms of 10.0 mole of calcium.