Q.2.122 - An Introduction to General, Organic, and Biological Chemistry

Question

A mouthwash is $21.6\%$ ethanol by mass. If each bottle contains $0.358 \mathrm{pt}$ of mouthwash with a density of $0.876 \mathrm{g}/\mathrm{ml}$, how many kilograms of ethanol are in $180$ bottles of the mouthwash? 

Step-by-Step Solution

Answer

$5.47 \mathrm{kg}$of ethanol are in $180$ bottles of the mouthwash 

Step 1: Given information

The quantity of matter in a sample is represented by mass. The units of mass are grams, $\mathrm{mg}$ and kilograms $\mathrm{kg}$. Mass is also the quality of stuff that causes it to resist acceleration.

Step 2: explanation

given,

percent of ethanol by mass = $26\%$ and density = $0.876 \mathrm{g}/\mathrm{ml}$

quantity of mouthwash in each bottle = $0.358 \mathrm{pt}=0.358\times 437=165.5 \mathrm{ml}$

Amount of ethanol in $180$bottles of the mouthwash,

using $\text{ Mass }=\text{ Density }\times \text{ Volume }$

$\text{ Mass }=0.876\times 165.5=144.97 \mathrm{g}=0.14497 \mathrm{kg}$

now, $180\times 0.14497=26.09 \mathrm{kg}$

by mass percent = $21.6\%$

$\Rightarrow 26.09 \mathrm{kg}\times \frac{21.6}{100}=5.47 \mathrm{kg}$