Question

I have 2oz concentrated 40% aqueous solution, I want to dilute it 10% , How I dilute it ??? Please I need you kind help. Thank you

Answer 1

Add `"7.2 oz"` of solvent.

Explanation:

The idea with dilution calculations is that every time you're diluting a solution, the number of moles of solute will remain constant.

In your case, you start with a `40%` solution, which I assume is the percent concentration by mass, and need to determine how much solvent you need to add to it in order to get its concentration down to `10%`.

`color(blue)("%m/m" = "mass of solute"/"mass of solution" xx 100)`

A `40%` concentration by mass will contain `"40 oz"` of solute for every `"100 oz"` of solution.

In your case, the `"2-oz"` sample will contain

`2color(red)(cancel(color(black)("oz solution"))) * "40 oz solute"/(100color(red)(cancel(color(black)("oz solution")))) = "0.80 oz solute"`

Now, when you dilute this olution, the mass of solute remains unchanged. Let's say that you add `x` grams of solvent to get the concentration down to`10%`. This means that you can write

`10% = (0.80color(red)(cancel(color(black)("oz"))))/((0.80 + x)color(red)(cancel(color(black)("oz")))) xx 100`

Solve this equation for `x` to get

`10 * (0.80 + x) = 0.80 * 100`

`8 + 10x = 80`

`10x = 72 implies x = 72/10 = 7.2`

So, if you add `"7.2 oz"` of solvent to your `"2-oz"`, `40%` solution will get a `10%` solution that has the total volume of `"9,2 oz"`.