Harris H. answered • 08/04/18

Tutor

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Hi Esme,

GOAL: Find the volume of each solution needed, that is 2 variables, V(A) and V(B)

This is essentially a simultaneous equations problem, so you need to formulate two equations to solve two variables.

Assume the the 20% acid Solution as A and 40% acid solution as B.

CLUE 1: Your final solution volume is 28 L, which is a combination of V(A) and V(B). Makes sense?

V(A) + V(B) = 28 (Equation 1)

CLUE 2: Your final concentration is 25% (or 0.25).

Note: Concentration is not additive, means you can't just add them together to give a new concentration. It's like speed or rate. So you need to multiply it by the volume to tell you how much ACTUAL ACID is in there (compare that to distance = speed x time, where time is like volume and distance is like the ACTUAL ACID).

So, we formulate the second equation:

0.20 V(A) + 0.40 V(B) = 0.25 * 28 => 0.20 V(A) + 0.40 V(B) = 7 (Equation 2)

This equation tells us that using V(A) amount of Acid A (20% solution) and V(B) amount of Acid B (40% solution), you should get 28 L of acid with concentration of 25%.

Solving it:

Solve V(B) or V(A) first:

From Equation 1: V(B) = 28 - V(A)

Substitute into Equation 2:

0.20 V(A) + 0.40 (28 - V(A)) = 7

=> V(A) = 21

Substitute V(A) back into Equation 1:

=> V(B) = 7

Conclusion: You need 21 L of 20% acid solution and 7 L of 40% acid solution.