Question

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?

Answer 1

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

`"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 %.