Question

Имеются два раствора кислоты с концентрациями 10% и 90% соответственно. Сколько литров второго раствора нужно добавить к 10 л первого раствора чтобы получить раствор с концентрацией 80%

Answer 1

В 10 л 10% раствора содержится 10*0.1 = 1 л вещества (кислоты)
в (х) л 90% раствора будет содержаться (х*0.9) л кислоты
если их смешать --- получим (х+10) л 80% рствора
1 + 0.9х = (х+10)*0.8
1 + 0.9х = 0.8х + 8
0.1х = 7
х = 70 л второго раствора нужно добавить)))
ПРОВЕРКА:
в 70 л 90% раствора --- 70*0.9 = 63 л кислоты
смешали 10 л + 70 л = 80 л раствора, содержащего 63 л + 1 л = 64 л кислоты
80 л --- 100%
64 л ---   ? %
64*100 / 80 = 8*10 = 80(%)

Answer 2

Calculating the Amount of 90% Acid Solution Needed

To calculate the amount of 90% acid solution needed to be added to 10 liters of 10% acid solution to obtain a solution with a concentration of 80%, we can use the method of mixtures.

Let's denote: - V1 = volume of 10% acid solution (given as 10 liters) - V2 = volume of 90% acid solution to be added - C1 = concentration of 10% acid solution (given as 10% or 0.1) - C2 = concentration of 90% acid solution (given as 90% or 0.9) - C3 = concentration of the final 80% acid solution

We can use the following equation to solve for V2: C1 * V1 + C2 * V2 = C3 * (V1 + V2)

Substitute the given values: 0.1 * 10 + 0.9 * V2 = 0.8 * (10 + V2)

Solving for V2: 1 + 0.9V2 = 8 + 0.8V2 0.1V2 = 7 V2 = 70 liters

So, 70 liters of the 90% acid solution need to be added to 10 liters of the 10% acid solution to obtain a solution with a concentration of 80%.

Final Calculation

Therefore, to obtain a solution with a concentration of 80%, 70 liters of the 90% acid solution should be added to 10 liters of the 10% acid solution.