Some words to dilution else.
Sorry if this is described somewhere in a depth of the forum.
I anticipate what is problem. The cross rule or the crisscross method.
It is published in many handbooks, for example in Anchell's The Darkroom Cookbook (the 3rd) on page 168.
Is it correct? We will see.
Let's image mixing two solutions (of one compound; e.g. H2SO4). This procedure gives the third solution.
The first solution can be described by mass, which enter to mixture, let's mark m(1) and composition described by mass fraction of compound, w(1).
The second solution similarly. Mass m(2) and its composition w(2).
The third desired solution, mass m(3) and w(3).
According to the law of conservation of mass, the sum of mass of particular parts before dilution of solution is equal to mass after that. We can balance both total mass of the system and mass of concrete compounds.
[eq. 1]
m(1) + m(2) = m(3)
[eq. 2]
m(1)×w(1) + m(2)×w(2) = m(3)×w(3)
From above:
[eq. 3]
m(1)×w(1) + m(2)×w(2) = [m(1) + m(2)]×w(3)
Let's continue
[eq. 4]
m(1)×w(1) + m(2)×w(2) = m(1)×w(3) + m(2)×w(3)
[eq. 5]
m(1)×w(1) - m(1)×w(3) = m(2)×w(3) - m(2)×w(2)
[eq. 6]
m(1)×[w(1) - w(3)] = m(2)×[w(3) - w(2)]
[eq. 7]
m(1)/m(2) = [w(3) - w(2)]/[w(1) - w(3)]
Equation 7 is proof of the cross rule. (Mass fraction can be replaced by mass percentage in ratio on the right of equation.)
But! But! But!
The cross rule is (generally) valid only for mass!!!
(For volume only with the important limitations, below)
And volume?
The example solutions above can be described by volumes; V(1), V(2) and V(3) and by the density given solutions (I use symbol "d") d(1), d(2) and d(3).
Eq. 2 can be arranged:
[eq. 8]
d(1)×V(1)×w(1) + d(2)×V(2)×w(2) = d(3)×V(3)×w(3)
Or arranging eq. 3
[eq. 9]
d(1)×V(1)×w(1) + d(2)×V(2)×w(2) = [d(1)×V(1) + m(2)]×w(3)
If the second solutions is water, w(2) is zero and some equations become more simply.
Eq. 9 is basic equation for correct calculation of dilution.
When densities at concentrations w(1) and w(2) are significantly different (this is case of H2SO4!!!) we can't use the principle ("law") of conservation of volume.
And what Steve Anchell with his example? Concentrated (glacial) acetic acid has density 1,05 g/mL and that's why the mistake can be neglected. Similarly for solutions let's say under 10 %.
The principle ("law") of conservation of volume can be applied only in the cases of such dilute solutions or for unusual volume fractions.
I recommend to be more careful with dilution of H2SO4.
Note: As I told, densities are published in many chemical handbooks, for example legendary CRC Handbook of Chemistry and Physics
http://en.wikipedia.org/wiki/CRC_Handbook_of_Chemistry_and_Physics
It can be reached in every technical (and I think not only technical) libraries and table for H2SO4 is only on one or two pages.
) priority.
