Human bodies maintain their balance (homeostasis) through a series of equilibria. An important equilibrium
involves calcium ion because Ca2+ is important for muscle contractions in the heart as well as for strong bones.
Bone is a complex tissue consisting of living cells and non-living material. Calcium phosphate is part of the
non-living material and is how the body stores calcium.
a) Write the solubility product expression for the dissolution of calcium phosphate.
b) Assume all available bone material is pure calcium phosphate with a density of 3.14 g/mL. When blood
calcium ion concentration decreases, a hormone is released that causes calcium ions from the bones to be
released into the bloodstream. What effect does this have on the density of calcium phosphate in the bones?
Explain your answer.
Equations for parts (c) and (d) below.
H3PO4 + H2O ⇄ H3O1+ + H2PO41- Ka1 = 7.5 × 10-3
H2PO41- + H2O ⇄ H3O1+ + HPO42- Ka2 = 6.2 × 10-8
HPO42- + H2O ⇄ H3O1+ + PO43- Ka3 = 4.8 × 10-13
c) Blood pH is approximately 7.4 in healthy people. What are the predominant forms of phosphate in the blood at
this pH? Justify your answer.
d) Again, assume all available bone material is pure calcium phosphate. One way skeletons can be cleaned for
study is to boil the bones in a solution to remove all extraneous material, leaving just the pure bone. Based on
the equilibrium equations above and also the solubility product expression you derived in (a), would a highly
acidic or highly basic solution be best to clean the bones? Explain your answer.
a) The solubility product expression for the dissolution of calcium phosphate can be represented as follows:
Ca3(PO4)2 (s) ⇄ 3Ca2+ (aq) + 2PO4^3- (aq)
The solubility product expression is given by the product of the concentrations of the dissolved ions raised to the power of their stoichiometric coefficients:
Ksp = [Ca2+]^3 [PO4^3-]^2
b) When calcium ions are released from the bones into the bloodstream, the concentration of calcium ions in the blood increases. As a result, the density of calcium phosphate in the bones decreases. This is because the release of calcium ions disrupts the equilibrium between the dissolution of calcium phosphate in the bone and the precipitation of calcium phosphate from the bloodstream. As more calcium ions are released into the bloodstream, the equilibrium shifts towards the dissolution of calcium phosphate, leading to a decrease in its density in the bones.
c) To determine the predominant forms of phosphate in the blood at a pH of 7.4, we need to consider the dissociation constants (Ka values) of the phosphoric acid species. At a pH of 7.4, the pH is higher than the pKa values of H3PO4, H2PO41-, and HPO42-. Therefore, the predominant forms of phosphate in the blood at this pH are H2PO41- and HPO42-. H3PO4 will be mostly dissociated into its conjugate base forms.
d) To clean the bones, a highly acidic solution would be preferred. This is because the solubility product expression for the dissolution of calcium phosphate indicates that an increase in the concentration of H3O1+ ions, which corresponds to higher acidity, would shift the equilibrium towards the dissolution of calcium phosphate. By using a highly acidic solution, the equilibrium can be shifted towards the dissolution of calcium phosphate, effectively removing extraneous material from the bones during the cleaning process.