# 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?

Aug 24, 2015

The concentration of the new solution is 15.83 %.

#### Explanation:

A 15 % concentration means

15 % = "15 L acid"/"100 L solution"

So the volume of acid in 10 L of solution is

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

So you have $\text{1.5 L acid"/"10 L soln}$.

And in 2 L of 20 % acid,

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

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

$\frac{1.9}{12} = \frac{x}{100}$

$190 = 12 x$

$x = \frac{190}{12} = \frac{95}{6}$

x ≈ 15.83

The new concentration is 15.83 %.