Question

The chief compound in marble is CaCO3. Marble has been widely used for statues and ornamental work on buildings, including such structures as the Taj Mahal (Figure 1) . However, marble is readily attacked by acids via the following reaction. CaCO3(s)+H+(aq)⇌Ca2+(aq)+HCO3−(aq) Equilibrium constants at 25 ∘C are listed in the table below.

CaCO3 Ksp =4.5×10−9

H2CO3 Ka1= 4.3×10−7

H2CO3 Ka2= 5.6×10−11

Part A What is the molar solubility of marble (i.e., [Ca2+] in a saturated solution) in normal rainwater, for which pH=5.60?

Answer 1

pH = -log[H+] = 5.60

[H+] = 2.51 x 10^-6 M

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

let x be the amount of salt in solution,

4.5 x 10^-9 = [Ca2+](x) ...... (1)

x = [CO3^2-] + [HCO3-] ..... (2)

Ka for HCO3- = [H+][CO3^2-]/[HCO3]

[HCO3-] = 2.51 x 10^-6[CO3^2-]/5.6 x 10^-11 = 4.48 x 10^4 ---- (3)

substitute (3) in (2),

x = 4.48 x 10^4[CO3^2-] ---- (4)

substitute (4) in (1) with [CO3^2-] as x,

4.5 x 10^-9 = (x).4.48 x 10^4(x)

x = 3.17 x 10^-7 M

Thus molar solubility of marble in normal rainwater is 3.17 x 10^-7 M