Multiple choice

Dr. Anderson has a 20-litre solution that currently contains 30% ethanol. To achieve optimal conditions for her research, Dr. Anderson needs to adjust the solution to precisely 50% ethanol concentration. How many litres of pure ethanol should she add to achieve this targeted concentration?

  1. 4

  2. 6

  3. 8

  4. 12

  5. a
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C Correct answer
Explanation

Let x be the amount of pure ethanol added. The initial amount of ethanol is 0.30 * 20 = 6 litres. After adding x litres of pure ethanol, the total volume becomes 20 + x, and the new amount of ethanol is 6 + x. Setting the new concentration to 50% gives (6 + x) / (20 + x) = 0.5. Solving this, 6 + x = 10 + 0.5x, so 0.5x = 4, which means x = 8.

AI explanation

The initial 20-litre solution contains 30% ethanol, which means there are 6 litres of ethanol and 14 litres of water. The amount of water remains constant at 14 litres, so to reach a 50% ethanol concentration, the 14 litres of water must represent 50% of the new total volume. This means the new total volume must be 28 litres. The amount of pure ethanol to add is the difference between the new total volume and the initial volume, which is 28 minus 20, resulting in 8 litres.

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