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?

Short answer

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

Step-by-step solution

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.

explanation

given,

percent of ethanol by mass = $26\%$and density = localid="1653059279610" $0.876\mathrm{g}/\mathrm{ml}$

quantity of mouthwash in each bottle = localid="1653606426579" $0.358\mathrm{pt}=0.358\times 437=165.5\mathrm{ml}$

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

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

localid="1653059515966" $\text{Mass}=0.876\times 165.5=144.97\mathrm{g}=0.14497\mathrm{kg}$

now, localid="1653059527202" $180\times 0.14497=26.09\mathrm{kg}$

by mass percent = $21.6\%$

localid="1653059600789" $\Rightarrow 26.09\mathrm{kg}\times \frac{21.6}{100}=5.47\mathrm{kg}$