Question

Ethanol, is the substance commonly called alcohol. The density of liquid alcohol is $0.7893g\text{ m}{\text{l}}^{-1}$ $293K$. If $1.2$ moles of ethanol are needed for a particular experiment, what volume of ethanol should be measured out?
(a) $55\text{ ml}$
(b) $58\text{ ml}$
(c) $\text{70 ml}$
(d) $\text{79 ml}$

Answer 1

Hint: First we have to find the mass of ethanol by using the formula as $givenmass=mole\times molecularmass$ and after finding the mass we can easily calculate the volume of ethanol by applying the density formula as; $density={\displaystyle \frac{mass}{volume}}$. Now solve it.

Complete answer:
First of all, let’s discuss ethanol. Ethanol is a member of the alcohol family and consists of two carbon atoms along with the -OH group and its common name is ethyl alcohol and has a high boiling point and is readily soluble in water. The chemical formula of ethanol is as $C{H}_{3}C{H}_{2}OH$.
Now considering the statement as;
We can find the volume of the ethanol by using the formula as;
$\begin{array}{rl}& density={\displaystyle \frac{mass}{volume}}\\ & volume={\displaystyle \frac{mass}{density}}\end{array}$ (1)
First, we have to find the mass of the ethanol.
We have been moles of ethanol as $1.2$ and
Molecular mass of ethanol i.e. $C_2{H}_{5}OH=12\times 2+5+16+1=46g$
Then, we can find the mass of the ethanol by using the formula as;
$\begin{array}{rl}& mole={\displaystyle \frac{givenmass}{molecularmass}}\\ & givenmass=mole\times molecularmass\\ & ⟹\text{ =1}\text{.2}\times \text{ 46}\\ & ⟹\text{ =55}\text{.2 g}\end{array}$
And density of the ethanol is as$0.7893g\text{ m}{\text{l}}^{-1}$ (given)
Then, put these in equation (1),we get;
$\begin{array}{rl}& volume={\displaystyle \frac{mass}{density}}\\ & ⟹{\displaystyle \frac{55.2}{0.7893}}\\ & ⟹\text{ 70 ml}\end{array}$

So, if the density of liquid alcohol is $0.7893g\text{ m}{\text{l}}^{-1}$ $293K$ and If $1.2$ moles of ethanol are needed for a particular experiment then the volume of ethanol measured is $70\text{ ml}$.

Note: While doing the calculations, always keep in mind that the units of all should be same i.e. if density is in $gm{l}^{-1}$ , then the mass should also be in gram not in kilogram and the volume should be in milliliters and not in liters.