Question

An elixir contains 47 % v/v alcohol, what is the proof spirit according to USP:

• A. 70%
• B. 82%
• C. 63%
• D. 91%

Hint:

In USP, proof is calculated as twice the percentage of alcohol by volume. Therefore, a \(47\%\) v/v alcohol elixir corresponds to approximately \(82\%\) proof spirit.

Answer 1

The Correct Option is B

The proof spirit is twice the percentage of alcohol by volume. Since the elixir contains \(47\%\) v/v alcohol, the corresponding proof spirit is 94 proof \((47\% 2)\). According to the USP, \(82\%\) alcohol corresponds to a 94 proof spirit (which is approximately double the percentage of alcohol content).

Answer 2

Proof spirit under the USP (United States Pharmacopeia) tradition follows the older British "degree proof" standard, where spirit at 100 degrees proof is defined as containing 57.1% alcohol by volume. Any other alcohol strength is expressed as a percentage of this proof strength using the relation:

\[ \%\ \text{Proof Spirit} = \frac{\%\ v/v\ \text{alcohol} \times 100}{57.1} \]

Applying this to the elixir, which contains 47% v/v alcohol, gives approximately 82.3% proof spirit. Let's check each option against this calculated value.

1. 70%: Working backward, 70% proof spirit would correspond to an alcohol content of \( \frac{70 \times 57.1}{100} \approx 40\% \) v/v, not the 47% v/v stated in the question, so this option does not match.
2. 82%: Using the formula directly, 47% v/v alcohol converts to about 82.3% proof spirit, which rounds to 82%. This matches the calculation exactly.
3. 63%: Working backward, 63% proof spirit corresponds to \( \frac{63 \times 57.1}{100} \approx 36\% \) v/v alcohol, well below the 47% v/v given in the question.
4. 91%: Working backward, 91% proof spirit corresponds to \( \frac{91 \times 57.1}{100} \approx 52\% \) v/v alcohol, which is higher than the 47% v/v stated, so this does not match either.

Only 82% satisfies the proof spirit relation for an elixir containing 47% v/v alcohol.

Therefore, the correct answer is 82%.