Concentration of Solutions
Percent by Volume
Problem 4. What is the volume of alcohol in 500 mL of wine that contains 12% alcohol by volume? What is its proof number?
Answer
1. Known: volume of wine = 500 mL; % alcohol (v/v) = 12%
2. Unknown: proof number and volume of alcohol
3. Process: Use the equation:
\[
\begin{aligned}
\% \left( \frac{v}{v} \right)
&=
\frac{
\text{volume of alcohol}
}{
\text{volume of wine}
}
\times 100
\end{aligned}
\]
Manipulating this equation, we have:
\[
\begin{aligned}
\text{volume of alcohol} &= \frac{12\% \times 500\,\text{mL}}{100} \\
&= 60\,\text{mL}
\end{aligned}
\]
The proof number is given by the equation: proof number = %(v) × 2 = 12 × 2 = 24
4. Answer: The wine contains 60 mL of ethyl alcohol, which is 24 proof.
