the question: given M_1 at V_1 and M_2 at V_2, where M is molarity
and V is volume and M_1 > M_2.
M_1 is diluted by M_2 to M_f such that, M_1 > M_f > M_2 and M_f is at
V_f
known: M_1, M_2, M_f, and V_2
find: V_1 and V_f
Here is my solution:
conservation of mass implies that V_1 + V_2 = V_f
some other rule of chem that I think is right implies (M_1) * (V_1) =
(M_f) * (V_f)
here I have a pair of coupled linear equations in two variables, easy
to solve.
Is this right?
That depends, I think you are missing part of the problem, or I am.
M1*V1 is the number of moles in v1.
M2*V2 is the number of moles in v2
Mf*Vf is the number of moles in vf
If V1 + V2 = Vf, then
M1*V1 + M2*V2 = Mf*Vf
If only some small portion, x, of V2 was used to create Vf, then you have
M1*V1 + x*M2*V2 = Mf*Vf
V1 + x*V2 = Vf
It appears that all of the second solution was used, so the first set of
equations works.
You can't add concentrations. You need to add volumues and moles, then
refigure the concentration from that.
Michael