Question

The concentration of Ca²⁺ ions in seawater and in the vicinity of a mussel bank is 1E-2M. Assume the total concentration of inorganic carbon is seawater is 2.3E-3M. Calculate the pH of the water around the musscles so that their shell remains stable. Discuss the implication of increasing the amount of CO2 in the atmosphere on the pH of seawater and the effect of calcifying organisems. Use K_s(CaCO₃)= 9.9E-9 Mol^2*L ; K_a1= 4.3E7 Mol L ; K_a2= 4.8E-11 Mol L

Answer 1

We know,

Ksp for CaCO3 = [Ca2+][CO3^2-]

Using Ksp value of 9.9 x 10^-9, we solve for [CO3^2-]

Given, [Ca2+] = 0.01 M

Feed values,

9.9 x 10^-9 = (0.01)[CO3^2-]

[CO3^2-] = 9.9 x 10^-7 M

Let us write the first dissociation and second deissociation equations for carbonic acid.

H2CO3 <===> HCO3^- + H+ .......Ka1

Ka1 = [HCO3^-][H+]/[H2CO3]

and,

HCO3^- <===> CO3^2- + H+ ....Ka2

Ka2 = [CO3^2-][H+]/[HCO3^-]

Using the given [H2CO3] = 0.0023 M

Ka1 equation with Ka1 = 4.3 x 10^-7

assume x be the amount of disscoiation so,

[H+] = [HCO3^-] = x

Ka1 = 4.3 x 10^-7 = (x((x)/(0.0023)

x = [HCO3^-] = 3.145 x 10^-5 M

Use this value for second dissociation to find [H+] along with [CO3^2-] value calculated above

Assume x amount dissociated,

Ka2 = 4.8 x 10^-11 = (9.9 x 10^-7)[H+]/3.145 x 10^-5

[H+] = 1.523 x 10^-9 M

So, the pH of water = -log[H+] = -log(1.523 x 10^-9] = 8.817

When the amount of CO2(g) in the atmosphere is increased, carbonic acid would be formed by equation,

CO2(g) <==> CO2(aq) ---- dissolution of CO2 from atmosphere

CO2(aq) + H2O(l) <===> H2CO3(aq)

The carbonic acid would then dissociate accordiing to the equations discussed above,

The concentration of [H+] would be lower and thus the pH would would be higher.