Chapter 10, Problem 142A

Interpretation Introduction

Interpretation:

The number of molecules of ethanol in 47.0 g 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 = $\frac{\text{mass of the compound}}{\text{molar mass of the compound}}$

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

Answer to Problem 142A

Number of atoms of ethanol = $6.14\times {10}^{23}\text{ molecules}$

Explanation of Solution

Mass of ethanol = 47.0 g

Molar mass of ${\text{C}}_2{\text{H}}_5\text{OH}$ = $2\left(12.01\text{ g/mole}\right)+6\left(1.0078\text{ g/mole}\right)+1\left(15.999\text{ g/mole}\right)$

= 46.0658 g/mole

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

Put the values,

Number of moles = $\frac{\text{47}\text{.0 g}}{46.0658\text{ g/mole}}$

Number of moles of ${\text{C}}_2{\text{H}}_5\text{OH}$ = $1.0203\text{ mole}$

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

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

$1.0203\text{ mole}$ = $\text{number of molecules ×}\frac{1\text{ mole}}{6.022\times 10\text{molecules}}$

Number of atoms = $1.0203\text{ mole}\times 6.022\times 10\frac{\text{molecules}}{\text{mole}}$

Number of atoms of ethanol = $6.14\times {10}^{23}\text{ molecules}$