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

1 Answer
Nov 4, 2015

Answer:

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"#.