Two solutions of different concentrations of acid are mixed creating 40 mL of a solution that is 32% acid. One-quarter of the so
lution is made up of a 20% acid solution. The remaining three-quarters is made up of a solution of unknown concentration, c. Which equation can be used to determine c, the unknown concentration? 30c + 10(0.2) = 40(0.32) (c) + (0.2) = 40(0.32) (c)( (0.2)) = 40(0.32) 30(c)(10(0.2)) = 40(0.32)
In order to construct this equation, we will use the variables: V to represent mixture volume (40 ml) C to represent mixture concentration (0.32) v₁ to represent volume of first solution (40 / 4 = 10 ml) c₁ to represent concentration of first solution (0.2) v₂ to represent the volume of the second solution (40 * 3/4 = 30 ml) c₂ to represent the concentration of the second solution
We know that the total amount of substance, product of the volume and concentration, in the final solution is equal to the individual amounts in the two given solutions. Thus: VC = v₁c₁ + v₂c₂ 40(0.32) = 10(0.2) + 30c
If we take the value of t to be 15 and then we perform the calculations of 2 times t divided by 3, we can express it all by two equations substituting the value given for t like so: t = 15 2t/3 = 2(15)/3 = 30/3 = 10
