Question

You require a solution containing 85 %v/v ethanol? You have 1350 mL of a 96 % v/v solution of ethanol. How many L of a 70 %v/v ethanol solution do you need to add to it to make the required 85 %v/v ethanol solution (2 decimal places)

Answer 1

Let us take the given solution of ethanol concentration as C₁ = 96% v/v and it’s volume as V₁ = 1350ml.

The solution to be added is of concentration 70% v/v. Let us take this concentration as C₂ and its volume which is unknown yet as V₂.

Let us take the concentration of final required solution as C_f which is = 85%v/v.

The volume of final mixture is = volume of first solution + volume of second added solution

which is 1350+V₂. Let us take this as V_f.

Now while adding two similar solutions with different concentrations, we have a formula

C_fV_f = C₁V₁ + C₂V2

This is obtained by the fact that

volume of ethanol in final solution = volume of ethanol in first solution + volume of ethanol in second solution.

which is (C_f*V_f)100 = (C₁V₁)100 + (C₂V₂)100

which gives the above formula C_fV_f = C₁V₁ + C₂V2

Now substituting the values gives us

85 * (1350 + V₂) = (96*1350) + (70 * V₂)

(85*1350) + 85V₂ = (96*1350) + 70V₂

85V₂ - 70V₂ = (96*1350)-(85*1350)

15V₂ = 11*1350

V₂ = (11*1350)/15

V₂ = 11*90 which is 990 ml or 0.99 litres

The volume of 70% v/v ethanol to be added is 0.99 litres.

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