Question

What will be the mole fraction of ethanol in a sample of spirit containing $85$% ethanol by mass?

• A. $0.69$
• B. $0.82$
• C. $0.85$
• D. $0.60$

Answer 1

The correct option is A $0.69$

${\chi }_{C_2{H}_{5}OH}$ = $\frac{n_{C_2{H}_{5}OH}}{n_{C_2{H}_{5}OH}+n_{H_{2}O}}$

Molar mass of ethanol = $46g/mol$

Molar mass of water = $18g/mol$

Mass of ethanol =$85g$

No of moles of ethanol = $\frac{85}{46}$ = $1.85mol$

Mass of water = $100-85$ = $15g$

No of moles of water = $\frac{15}{18}$ = $0.833mol$

${\chi }_{C_2{H}_{5}OH}$ = $\frac{1.85}{1.85+0.833}$

= $\frac{1.85}{2.683}$ = $0.69$