Question

How many mL of 50% (v/v) alcohol should be mixed with 10% alcohol to obtain 50mL of 35% (v/v) alcohol? Round to the hundredths place.

Answer 1

The volume of 50% alcohol used to make the mixture = 31.25 L

The volume of 10% alcohol used to make the mixture = 18.75 L

Step-by-step explanation:

Let the volume of 50% alcohol used to make the mixture = x L

Let the volume of 10% alcohol used to make the mixture = y L

Total volume of the mixture = x + y = 50 L .................. (1)

For 50% alcohol:

C₁ = 50% , V₁ = x L

For 10% alcohol :

C₂ = 10% , V₂ = y L

For the resultant alcohol solution:

C₃ = 35% , V₃ = 50 L

Using

C₁V₁ + C₂V₂ = C₃V₃

50×x + 10×y = 35×50

So,

5x + y = 175 .................. (2)

Solving 1 and 2 we get,

x = 31.25 L

y = 18.75 L