In the equilibrium ratio [OAc-] / [HOAc], the units of the numerator and denominator are moles / L. Since everything is in the same container, the volume L is the same in the numerator and denominator, so the value of the ratio in molarity units is the same value as moles of OAc- / moles of HOAc.
To make a solution containing a specific number of moles of OAc- and HOAc from inital solutions of OAc- and HOAc at molarities M1 and M2, remember
moles of OAc- = V1 X M1 and
moles of HOAc = V2 X M2
where V1 is the volume of OAc- solution and V2 is the volume of HOAc solution.
Therefore,
moles OAc- = V1 M1
moles HOAc V2 M2
But since M1 = M2 = 0.500 M, M1 and M2 cancel to give
moles OAc- = V1
moles HOAc V2
If VT = the total volume V1 + V2,
moles OAc- / VT = [OAc-] = V1
moles HOAc / VT [HOAc] V2
because the VT terms can cancel.
Steve
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