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

First we have to find the mass of ethanol by using the formula as $given\text{ }mass=mole\times molecular\text{ }mass$ and after finding the mass we can easily calculate the volume of ethanol by applying the density formula as; $density=\dfrac{mass}{volume}$. 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;
$\begin{aligned} & density=\dfrac{mass}{volume} \\\ & volume=\dfrac{mass}{density} \\\ \end{aligned}$ (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;
$\begin{aligned} & mole=\dfrac{given\text{ }mass}{molecular\text{ }mass} \\\ & given\text{ }mass=mole\times molecular\text{ }mass \\\ &\implies \text{ =1}\text{.2}\times \text{ 46} \\\ &\implies \text{ =55}\text{.2 g} \\\ \end{aligned}$
And density of the ethanol is as$0.7893g\text{ m}{{\text{l}}^{-1}}$ (given)
Then, put these in equation (1),we get;
$\begin{aligned} & volume=\dfrac{mass}{density} \\\ &\implies \text{ }\dfrac{55.2}{0.7893} \\\ &\implies \text{ 70 ml} \\\ \end{aligned}$

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 $g\text{ }m{{l}^{-1}}$ , then the mass should also be in gram not in kilogram and the volume should be in milliliters and not in liters.