Question

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

• A. 70%
• B. 82%
• C. 63%
• D. 91%

Answer 1

The Correct Option is B

The correct option is (B): 82%.

Answer 2

This question is really about converting an alcohol percentage into the older "proof spirit" scale that pharmacy calculations still use for elixirs and tinctures. Since only one route to that number exists, let's build it and then confirm it lands on the right listed value.

1. 70%: This would follow only if the conversion factor from percent alcohol to percent proof were about 1.49, which is not the accepted proof spirit conversion factor. It is too low to be reached with the correct ratio.
2. 82%: Proof spirit is defined so that 57.1% alcohol by volume equals exactly 100 degrees proof, which fixes the conversion factor at \( \frac{100}{57.1} \approx 1.75 \). Applying it to 47% v/v: \[ \text{Proof strength} = 47 \times \frac{100}{57.1} \approx 47 \times 1.75 \approx 82.3\% \] which rounds to 82%.
3. 63%: This value would need a conversion factor near 1.34, well below the 1.75 factor fixed by the proof spirit definition, so it does not come out of a correct calculation.
4. 91%: Reaching 91% would require a conversion factor of roughly 1.94, higher than the true 1.75 factor, so this overshoots what 47% v/v alcohol actually converts to.

Working the standard proof spirit conversion through gives approximately 82%, matching one option exactly.

The correct answer is 82%.