Calculate the pH of a 0.060 M carbonic acid solution,H₂CO₃₍_aq_),that has the stepwise dissociation constants K_a1 = 4.3 × 10^-7 and K_a2 = 5.6 × 10^-11. A)1.22 B)3.79 C)6.37 D)10.25

Question

Quizplus · Accepted Answer

The first dissociation of carbonic acid is:

HS1U1B12S1U1B0COS1U1B13(S1U1B0S1U1B1aqS1U1B0S1U1B1)S1U1B0+H2OS1U1B0→H3O+S1U1B0+HS1U1B1O3S1U1B12-S1U1B0+H2OS1U1B0

Using the equilibrium constant expression for this reaction and given Ka1 value, we can calculate the concentration of H3O+ ion:

Ka1=(H3O+S1U1B0)(HS1U1B12S1U1B0COS1U1B13(S1U1B0S1U1B1))([H2OS1U1B0])
4.3 × 10S1U1P1-7S1S1P0=(x)(0.060-x)/(0.060)
x=9.73 × 10S1U1P1-4S1S1P0

Now, we can use the second dissociation of carbonic acid which occurs in two steps:

HS1U1B1O3S1U1B12-S1U1B0+H2OS1U1B0⇌H3O+S1U1B0+HS1U1B1O3-S1U1B1O2S1U1B13-(S1U1B0.

Ka2=([H3O+S1U1B0]×[HS1U1B1O3-S1U1B1O2S1U1B13-])/(HS1U1B1O3S1U1B12-S1U1B0)

In the first step, the concentration of H3O+ is 9.73 × 10S1U1P1-4S1S1P0, and the initial concentration of HS1U1B1O3S1U1B12-S1U1B0 is 0.060 M.

Ka2=[H3O+S1U1B0]×[HS1U1B1O3-S1U1B1O2S1U1B13-])(HS1U1B1O3S1U1B12-S1U1B0)
5.6 × 10S1U1P1-11S1S1P0=(9.73 × 10S1U1P1-4S1S1P0)(x)/(0.060-x)
x=1.73 × 10S1U1M1S1U1M13S1S1P0

So the concentration of H3O+ ion in the solution is 9.73 × 10S1U1P1-4S1S1P0 + 1.73 × 10S1U1M1S1U1M13S1S1P0 = 1.10 × 10S1U1P1-3S1S1P0

Using the definition of pH:

pH=−log([H3O+S1U1B0])
pH=−log(1.10 × 10S1U1P1-3S1S1P0)
pH=3.79

Calculate the PH of a 0