A student accidentally poured 2 liters of 20% acid solution into a container having 10 liters of 15% acid solution. What is the concentration of the new solution?

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Answer 1 · 2015-08-24T21:25:36

The concentration of the new solution is 15.83 %.

A 15 % concentration means

$15 % = \frac{15 L acid}{100 L solution}$ $15 % = "15 L acid"/"100 L solution"$

So the volume of acid in 10 L of solution is

$"Volume of acid" = 10 color(red)(cancel(color(black)("L soln"))) × "15 L acid"/(100 color(red)(cancel(color(black)("L soln")))) = "1.5 L acid"$

So you have $"1.5 L acid"/"10 L soln"$ .

And in 2 L of 20 % acid,

$"Volume of acid" = 2 color(red)(cancel(color(black)("L soln"))) × "20 L acid"/(100 color(red)(cancel(color(black)("L soln")))) = "0.4 L acid"$

After mixing, the new solution contains 1.5 L + 0.4 L = 1.9 L of acid and has a total volume of 2 L + 10 L = 12 L.

Then

$1.9/12 = x/100$

$190=12x$

$x=190/12 = 95/6$

$x ≈ 15.83$

The new concentration is 15.83 %.