Question 22.6: The protein transferrin is involved in the transport of iron...
The protein transferrin is involved in the transport of iron into cells. Iron accumulation in the human body has been implicated in diseases such as Parkinson’s, Alzheimer’s, and thalassemia. The chelating ligand deferoxamine (DFO) is used to treat thalassemia; the complex between iron and DFO is eliminated from the body. Given the formation constants for the complexation of iron(III) by transferrin (Equation 1) and the reaction of DFO with iron (Equation 2), calculate the equilibrium constant for the ligand exchange reaction between DFO and transferrin (Equation 3).
Fe^{3+}(aq) + transferrin(aq) \rightleftharpoons Fe(transferrin)^{3+}(aq)
K_{f,1} = 4.7 \times 10^{20} (1)
Fe^{3+}(aq) + DFO(aq) \rightleftharpoons Fe(DFO)^{3+}(aq)
K_{f,2} = 4.0 \times 10^{30} (2)
Fe(transferrin)^{3+}(aq) + DFO(aq) \rightleftharpoons Fe(DFO)^{3+}(aq) + transferrin(aq)
K_{3} =? (3)
Collect and Organize We are given the formation constants of two reactions involving iron and different ligands and are asked to calculate the equilibrium constant for the ligand exchange reaction. You may wish to refer to Chapter 16 for calculations involving formation constants of complexes, as well as to Chapters 14 and 15, where we manipulated equilibrium constants.
Analyze Transferrin is a reactant in Equation 1 and a product in the exchange reaction (3). Therefore we need to reverse Equation 1 before adding it to Equation 2 to obtain Equation 3. Reversing a reaction means taking the reciprocal of its equilibrium constant. Combining the reverse of Equation 1 with Equation 2 to obtain Equation 3 means multiplying (1/K_{f,1}) and K_{f,2} together to obtain K_{3}. The reciprocal of K_{f,1} has a value of about 10^{-20}. Therefore the value of K_{3} should be about 10^{-20} \times 10^{30}, or about 10^{10}.
Solve Multiplying (1/K_{f,1})by K_{f,2} to obtain K_{3}:
K_{3}=\frac{1}{4.7 \times 10^{20}} \times (4.0 \times 10^{30})=8.5 \times 10^{9}
Think About It The equilibrium constant for the ligand exchange between the Fe(transferrin)^{3+} complex and DFO is indeed \sim 10^{10} and illustrates why DFO is an effective treatment for thalassemia— the large value for the equilibrium constant means that the equilibrium in Equation 3 lies toward the products (to the right), removing iron from the blood.