[Dolphinsiu]

The equilibrium constant for the reaction

2CrO4 2- + 2H + <=> Cr2O7 2- + H2O

is 4.2 x 10^14 The molar absorptivities for the two principle species in solution of K2CrO7 are

Wavelength          CrO4 2-                   Cr2O7 2-
345 nm                1.84 x10^7              10.7 x10^2
370 nm                4.81 x 10^3             7.28 x10^2
400 nm                1.88 x 10^3             1.89 x10^2

Four solutions were prepared by dissolving 4.00 x10^-4, 3.00 x10^-4,2.00x10^-4,1.00 x10^-4 moles of K2Cr2O7 in water and diluting to 1.00 L with a pH 5.60 buffer. Derive theoretical absorbance values (1cm cells) for each solution.

The book answers says

[Cr2O7 2-] / [CrO4 2-]^2[H +]^2 = 4.2 x10^14

Then I don't understand why

[Cr2O72-] = [K2Cr2O7] - [CrO4 2-]/2

The first question I want to raise is: Why the concentration of Cr2O72- is not same as that of K2Cr2O7?
Is it because of this equation K2Cr2O7 <---> 2K+ + Cr2O72- has equilibrium relationship?

Also why it is not [Cr2O72-] = [K2Cr2O7] - 2[CrO4 2-], but [Cr2O72-] = [K2Cr2O7] - [CrO4 2-]/2 ?

[Borek]

Why the concentration of Cr2O72- is not same as that of K2Cr2O7?

You have already answered your own question with reaction equation. Some Cr₂O₇^2- reacted with water.

Also why it is not [Cr2O72-] = [K2Cr2O7] - 2[CrO4 2-], but [Cr2O72-] = [K2Cr2O7] - [CrO4 2-]/2 ?

Think about reaction stoichiometry, think about chromium mass balance.