Atomic Structure and Properties

3.a. Write the ground-state electron configuration of the $Fe^{2+}$ ion.

3.b. The radii of the ions are given in the table above. Using principles of atomic structure, explain why the radius of the $Fe^{2+}$ ion is larger than the radius of the $Fe^{3+}$ ion.

3.c. $Fe^{3+}$ ions interact more strongly with water molecules in aqueous solution than $Fe^{2+}$ ions do. Give one reason for this stronger interaction, and justify your answer using Coulomb’s law.

3.d. A student obtains a solution that contains an unknown concentration of $Fe^{2+}(aq)$. To determine the concentration of $Fe^{2+}(aq)$ in the solution, the student titrates a sample of the solution with $MnO_4^-(aq)$, which converts $Fe^{2+}(aq)$ to $Fe^{3+}(aq)$, as represented by the following equation.

$5 Fe^{2+}(aq) + MnO_4^-(aq) + 8 H^+(aq) \rightarrow 5 Fe^{3+}(aq) + Mn^{2+}(aq) + 4 H_2O(l)$

Write the balanced equation for the half-reaction for the oxidation of $Fe^{2+}(aq)$ to $Fe^{3+}(aq)$.

3.e. The student titrates a 10.0 mL sample of the $Fe^{2+}(aq)$ solution. Calculate the value of $[Fe^{2+}]$ in the solution if it takes 17.48 mL of added 0.0350 M $KMnO_4(aq)$ to reach the equivalence point of the titration.

3.f. To deliver the 10.0 mL sample of the $Fe^{2+}(aq)$ solution in part (e), the student has the choice of using one of the pieces of glassware listed below.

• 25 mL buret
• 25 mL beaker
• 25 mL graduated cylinder
• 25 mL volumetric flask

Explain why the 25 mL volumetric flask would be a poor choice to use for delivering the required volume of the $Fe^{2+}(aq)$ solution.

3.g. In a separate experiment, the student is given a sample of powdered Fe(s) that contains an inert impurity. The student uses a procedure to oxidize the Fe(s) in the sample to $Fe_2O_3(s)$. The student collects the following data during the experiment.

3.g.i. Calculate the number of moles of Fe in the $Fe_2O_3(s)$ produced.

3.g.ii. Calculate the percent by mass of Fe in the original sample of powdered Fe(s) with the inert impurity.

3.g.iii. If the oxidation of the Fe(s) in the original sample was incomplete so that some of the 7.531 g of product was FeO(s) instead of $Fe_2O_3(s)$, would the calculated mass percent of Fe(s) in the original sample be higher, lower, or the same as the actual mass percent of Fe(s)? Justify your answer.

7.a. Identify the element.

7.b. A radioactive isotope of the element decays with a half-life of 10. minutes.

7.b.i. Calculate the value of the rate constant, $k$, for the radioactive decay. Include units with your answer.

7.b.ii. If 64 atoms of the radioactive isotope are originally present in a sample, what is the expected amount of time that will pass until only one atom of the isotope remains? Show how you arrived at your answer.

5.a.i. $1s^22s^22p^63s^23p^4$

5.a.ii. Sulfur

5.b. E = 1.0 x $10^{-18}$ J

E = $\frac{hc}{\lambda}$

$\lambda = \frac{hc}{E}$

$\lambda = \frac{6.626 \times 10^{-34} \times 3.0 \times 10^8}{1.0 \times 10^{-18}}$ = 1.99 x $10^{-7}$ m