# 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

Nov 4, 2015

Add $\text{7.2 oz}$ 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%.

$\textcolor{b l u e}{\text{%m/m" = "mass of solute"/"mass of solution} \times 100}$

A 40% concentration by mass will contain $\text{40 oz}$ of solute for every $\text{100 oz}$ of solution.

In your case, the $\text{2-oz}$ 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 to10%. 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

$10 \cdot \left(0.80 + x\right) = 0.80 \cdot 100$

$8 + 10 x = 80$

$10 x = 72 \implies x = \frac{72}{10} = 7.2$

So, if you add $\text{7.2 oz}$ of solvent to your $\text{2-oz}$, 40% solution will get a 10% solution that has the total volume of $\text{9,2 oz}$.