Chapter 10, Problem 145A

Interpretation Introduction

Interpretation:

The number of molecules of acetic acid should be determined which is present in 25.0 g of vinegar.

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 145A

Number of molecules of acetic acid = $1.25\times {10}^{22}\text{ molecules}$

Explanation of Solution

It is given that; vinegar contains 5.0 % of acetic acid.

The molecular formula of acetic acid = ${\text{CH}}_{\text{3}}\text{COOH}$

The molar mass of ${\text{CH}}_{\text{3}}\text{COOH}$ = $2\left(12.01\text{ g/mole}\right)+4\left(1.0078\text{ g/mole}\right)+2\left(15.999\text{ g/mole}\right)$

= $60.0492\text{ g/mole}$

Mass of acetic acid = $\frac{5.0}{100}\times 25.0\text{ g}$

= $1.25\text{ g}$

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

Number of moles of acetic acid = $\frac{\text{1}\text{.25 g}}{\text{60}\text{.0492 g/mole}}$

= $0.0208\text{ mole}$

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

Number of molecules of acetic acid = $0.0208\text{ mole}\times \text{6}\text{.022 }\times {\text{10}}^{23}\frac{\text{molecules}}{\text{mole}}$

Number of molecules of acetic acid = $1.25\times {10}^{22}\text{ molecules}$