Question

Isopropyl alcohol $C_3{H}_8$, also known as rubbing alcohol, is an alcoholic mixture intended for external use as antiseptic. If the two different companies A and B are manufacturing rubbing alcohol of concentrations 47% (v/v) and 23.5% (v/v) respectively from isopropyl alcohol of density x g/mL, find the ratio of mass of isopropyl alcohol present in equal volumes of rubbing alcohol A and B.

• A. 1:2
• B. 2:1
• C. 2:3
• D. 3:2

Answer 1

The correct option is B 2:1

Let us take 100 mL each of rubbing alcohol A and B,
% (v/v) = $\frac{\text{volume of solute}}{\text{volume of solution}}\times 100$
47% (v/v) means 47 mL isopropyl alcohol is present in 100 mL of the solution.
Volume of $C_3{H}_8$ in the sanitizer of company A = 47 mL
Mass of isopropyl alcohol in the sanitizer of company A
= $volume\times density$
Mass of isopropyl alcohol,
$=47\times x=47xg$
Similarly, volume of isopropyl in the sanitizer of company B = 23.5 mL.
Mass of isopropyl alcohol in the sanitizer of company B=
$23.5\times x=23.5xg$

So, the ratio of mass of isopropyl alcohol present in sanitizer of company A and company B
$=\frac{\text{mass of isopropyl alcohol of company A}}{\text{mass of isopropyl alcohol of company B}}$ = $\frac{47x}{23.5x}$ = 2:1