Question

What quantities of 95% and 45% v/v alcohol are to be mixed to make 200 mL of 65% v/v alcohol?

• A. \( 120 \text{ mL of 95\% and } 80 \text{ mL of 45\% alcohol} \)
• B. \( 40 \text{ mL of 95\% and } 160 \text{ mL of 45\% alcohol} \)
• C. \( 160 \text{ mL of 95\% and } 40 \text{ mL of 45\% alcohol} \)
• D. \( 80 \text{ mL of 95\% and } 120 \text{ mL of 45\% alcohol} \)

Hint:

You can quickly check your answer by plugging the volumes back into the concentration equation: \((0.95 \times 80) + (0.45 \times 120) = 76 + 54 = 130\), and \(130 / 200 = 0.65\) or 65%.

Answer 1

The Correct Option is D

We can solve this problem using the principle of alligation or by setting up a system of equations. Let \( V_{95} \) be the volume of 95% alcohol and \( V_{45} \) be the volume of 45% alcohol required. We have two conditions: 1. The total volume of the mixture should be 200 mL: $$ V_{95} + V_{45} = 200 $$ 2. The final concentration of alcohol in the mixture should be 65% v/v: $$ 0.95 V_{95} + 0.45 V_{45} = 0.65 \times 200 $$ $$ 0.95 V_{95} + 0.45 V_{45} = 130 $$ Now we can solve these two equations simultaneously. From the first equation, we can express \( V_{45} \) as: $$ V_{45} = 200 - V_{95} $$ Substitute this into the second equation: $$ 0.95 V_{95} + 0.45 (200 - V_{95}) = 130 $$ $$ 0.95 V_{95} + 90 - 0.45 V_{95} = 130 $$ $$ (0.95 - 0.45) V_{95} = 130 - 90 $$ $$ 0.50 V_{95} = 40 $$ $$ V_{95} = \frac{40}{0.50} = 80 \text{ mL} $$ Now, substitute the value of \( V_{95} \) back into the first equation to find \( V_{45} \): $$ 80 + V_{45} = 200 $$ $$ V_{45} = 200 - 80 = 120 \text{ mL} $$ So, 80 mL of 95% alcohol and 120 mL of 45% alcohol are required to make 200 mL of 65% v/v alcohol.