The solution to this problem is given by the formula C1V1 x C2V2 = C3V3
where C = Concentration, and V = Volume
Basically, the 5% solution will be used to dilute the 14% solution to make 5L of 10% solution.
To simplify, we will convert the % figures to decimals, so 5% = .05, 10% = .1, and 14% = .14
Let x = V1. since the total volume will be 5L, then V2 = 5L - x
So, our equation will be .14x + .05(5L - x) = .10 · 5L
expanding, we get .14x + .25 - .05x = .5L
combining like terms, we get 0.09x = .25L
x = 2.777L
So, we will need 2.777L of 14% acid which will be diluted with 2.222L of 5% acid to make 5L of 10% acid.
Proof: 2.777L · .14 = 0.388L of pure acid; 2.222L · .05 = .1111L of pure acid; and 5L · .10 = .5L of pure acid
0.388L + 0.111L = 0.5L
