# Dilution Dilemma

• Mar 21st 2009, 06:30 AM
notoobright
Dilution Dilemma
I am trying to find a formula to calculate dilution rates.

I know if I add 5 litres of a 20% solution to 15 litres of water I get a 5% solution because I have been told.

However if possible I would like the formula for the above example so I can calculate it for myself and workout for different final solution rates.

Can anyone help me please or point me in the right direction.
• Mar 21st 2009, 08:05 AM
Pim
Dilution Factor = New Volume/Old Volume

New concentration = Old Concentration/Dilution Factor
• Mar 21st 2009, 10:16 AM
notoobright
Many thanks Pim.

But as my name suggests - I am not that quick.

With the numbers I already have - would you put them into those formulae please - so I can see what values come from where.
• Mar 21st 2009, 12:01 PM
running-gag
Hi

Let $\displaystyle \tau_1$ and $\displaystyle V_1$ be the dilution factor and the volume before dilution

The quantity of I-don't-know-what inside the water is $\displaystyle \tau_1\:V_1$

When you add $\displaystyle V_2$ litres of water the dilution factor becomes
$\displaystyle \tau = \frac{\tau_1\:V_1}{V_1+V_2}$

$\displaystyle \frac{0.20\:\cdot\:5}{5+15} = 0.05$
• Mar 21st 2009, 11:21 PM
notoobright
Thank you - that really has cleared up a problem I have been trying to work out for months.