Question

6. For an 8x10-5M methyl red solution at pH 5, A525nm is 0.92. (1cm cells were used to make this measurement.) The experimenters ascertained the following two facts about this chemical system: (1) At 525nm, absorbance by MER- is negligible, and (2) Molar absorptivity at 525nm for HMER is 23,000. What is the dissociation constant for the dye methyl red? (pKa is between 4 and 6).

Answer 1

Consider the dissociation of Methyl red in solution

             

Write the ICE table for the above equilibrium ( I = Initial concentration, C= change in concentration and E=Equilibrium concentration)

I               8x10^-5 M            10^-5 M         0                                                     Note: pH = -log[H⁺], Given pH = 5, So [H+] = 10^-5

C                -X                     +X              +X

E             8x10^-5M - X        10^-5M + X       X

Dissociation constant is calculated as

K_a = ( [H⁺] x [MER^-]) / [HMER]

      = {(10^-5M + X )(X)} / ( 8x10^-5M - X )

Beer-Lambert Law for dilute solutions is given by

A = Absorbance, Epsilon = Molar absorptivity , C= Molar Concentration and l = path length

Given A = 0.92, Epsilon = 23000 and l = 1cm                   Note: Molar Absorptivity has a unit of cm^-1Mol^-1L

Substituting in above equation, Concentration

or C = 0.00004M OR 4x10^-5M

This is the equilibrium concentration of HMER, i.e, the undissociated form form of the indicator

We can write , 8x10^-5M - X   = 4x10^-5M, so that X = 8x10^-5M - 4x10^-5M = 4x10^-5M

Now substituting this value of X in the expression for dissociation constant

To check the validity of answer calculate pka as