Question

A chemist needs to strengthen a 34% alcohol solution with a 50% solution to obtain a 44% solution. How much of the 50% solution should be added to 285 millilitres of the 34% solution? Round your final answer to 1 decimal place.

Answer 1

Answer: 475 ml of 50% solution is needed

Step-by-step explanation:

Let x represent the volume of the 50% solution needed.

From the information given,

volume of 34% alcohol solution = 285

Volume of the mixture of 34% solution and 50% solution = x + 285

Concentration of 44% mixture = 44/100 * (x + 285) = 0.44(x + 285)

Concentration of 34% alcohol solution = 34/100 * 285 = 96.9

Concentration of 50% solution = 50/100 * x = 0.5x

Thus,

96.9 + 0.5x = 0.44(x + 285)

By multiplying the terms inside the parentheses with the term outside, we have

96.9 + 0.5x = 0.44x + 125.4

0.5x - 0.44x = 125.4 - 96.9

0.06x = 28.5

x = 28.5/0.06

x = 475