Question

18-26. A 2.00mL solution of apotransferrin was titrated as illustrated in Figure 18-11. It required 163L of 1.43 mM ferric nitrilotriacetate to reach the end point.

(a) Why does the slope of the absorbance versus volume graph change abruptly at the equivalence point?

(b) How many moles of Fe(III) (= ferric nitrilotriacetate) were required to reach the end point?

(c) Each apotransferrin molecule binds two ferric ions. Find the molar concentration of apotransferrin in the 2.00mL solution.

Short answer

$\mathrm{a})\mathrm{See}\mathrm{the}\mathrm{explanation}.\mathrm{b})\mathrm{n}\left(\mathrm{Fe}\right)=2.33.{10}^{-7}\mathrm{mol}\mathrm{c}\left)\right[\mathrm{apotransferrin}]=5.85.{10}^{-5}\mathrm{M}$

Step-by-step solution

Reason for volume graph change abruptly at the equivalence point

a) The slope of the absorbance versus volume graph changes abruptly at the equivalence point because before the equivalence point Fe binds to a protein and forms a red complex, so the absorbance increases. After the equivalence point, there are no binding sites.

Find moles

b) The moles of Fe (III) that were required to reach the end point is:

$$\begin{gathered} \mathrm{n}\left(\mathrm{Fe}\right)=\mathrm{c}.\mathrm{V}=1.43.{10}^{-3}\mathrm{M}.163.{10}^{-6}\mathrm{L} \\ \mathrm{n}\left(\mathrm{Fe}\right)=2.33.{10}^{-7}\mathrm{mol} \end{gathered}$$

Find apotransferrin

c) The n of apotransferrin is:

$$\begin{gathered} \frac{\mathrm{n}\left(\mathrm{apotransferrin}\right)}{\mathrm{n}\left(\mathrm{Fe}\right)}=\frac{\mathrm{n}\left(\mathrm{Fe}\right)}{2}=\frac{2.33.{10}^{-7}\mathrm{mol}}{2} \\ \mathrm{n}\left(\mathrm{apotransferrin}\right)=1.17.{10}^{-7}\mathrm{mol} \end{gathered}$$

The concentration of apo transferrin is:

$$\begin{gathered} \left[\mathrm{apotransferrin}\right]=\frac{\mathrm{n}\left(\mathrm{apotransferrin}\right)}{\mathrm{V}} \\ \left[\mathrm{apotransferrin}\right]=\frac{1.17.{10}^{-7}\mathrm{mol}}{2.{10}^{-3}\mathrm{L}} \\ \left[\mathrm{apotransferrin}\right]=5.85.{10}^{-5}\mathrm{M} \end{gathered}$$