Time—1 hour and 45 minutes, 7 Questions
Questions 1–3 are long free-response questions that require about 23 minutes each to answer and are worth 10 points each. Questions 4–7 are short free-response questions that require about 9 minutes each to answer and are worth 4 points each.
For each question, show your work for each part in the space provided after that part. Examples and equations may be included in your responses where appropriate. For calculations, clearly show the method used and the steps involved in arriving at your answers. You must show your work to receive credit for your answer. Pay attention to significant figures.
10 points, suggested time 23 minutes
Answer the following questions related to cobalt compounds.
(a) Cobalt has several common oxidation states.
(i) Write the complete electron configuration for a Co atom in the ground state.
(ii) When cobalt forms cations, electrons are lost from which subshell first? Identify both the number and letter associated with the subshell.
A student performs an experiment to produce a cobalt salt of unknown composition, CoxBry(aq), and determine its empirical formula. The student places a sample of Co(s) in a beaker containing excess HBr(aq), as represented by the following equation:
x Co(s) + y HBr(aq) → CoxBry(aq) + (y/2) H2(g)
The student heats the resulting mixture until only CoxBry(s) remains in the beaker. The data are given in the following table:
| Mass of empty beaker | 58.204 g |
| Mass of beaker and Co(s) | 59.383 g |
| Mass of beaker and CoxBry after heating to constant mass | 62.579 g |
(b) Calculate the mass of Br in the sample of CoxBry(s) remaining in the beaker.
(c) Calculate the number of moles of Br in the sample of CoxBry(s) remaining in the beaker.
(d) The student determines that 0.0200 mol of Co was used in the experiment. Use the data to determine the empirical formula of the CoxBry(s).
(e) The student repeats the experiment using the same amounts of Co and HBr and notices that some of the CoxBry splatters out of the beaker as it is heated to dryness. Will the number of moles of Br calculated for this trial be greater than, less than, or equal to the number calculated in part (c)? Justify your answer.
(f)Another compound of cobalt-group chemistry, NiO(OH), is used in rechargeable nickel–cadmium batteries, represented by the following diagram.
Some half-reactions are given in the table:
| Reduction Half-Reaction | E° (V) |
|---|---|
| Cd2+(aq) + 2e−→ Cd(s) | −0.40 |
| Cd(OH)2(s) + 2e− → Cd(s) + 2 OH−(aq) | −0.81 |
| 2 NiO(OH)(s) + 2 H2O(l) + 2e− → 2 Ni(OH)2(s) + 2 OH−(aq) | +0.49 |
(i) Based on the half-reactions given in the table, write the balanced net ionic equation for the reaction that has the greatest thermodynamic favorability.
(ii) Calculate the value of E°cell for the overall reaction.
(iii) Calculate the value of ΔG° in kJ/molrxn.
(iv)A student claims that the total mass of a sealed Ni–Cd battery decreases as the battery operates because the anode loses mass. Do you agree with the student’s claim? Justify your answer.
Answer all parts of Question 1. Show your work for each part, including calculations and justifications where required.
10 points, suggested time 23 minutes
In the gas phase, GaCl3 is a molecular substance. A reaction of gaseous GaCl3 at high temperature is represented by the following balanced equation.
Reaction 1: GaCl3(g) → Ga(g) + 3 Cl(g) ΔH1° = ?
(a) How many grams of Cl(g) can be formed from 0.875 mol of GaCl3(g)?
Additional reactions that involve Ga or Cl are shown in the following table:
| Reaction Number | Equation | ΔH° (kJ/molrxn) |
|---|---|---|
| 2 | Ga(s) + (3/2)Cl2(g) → GaCl3(g) | −525 |
| 3 | Ga(s) → Ga(g) | +272 |
| 4 | Cl2(g) → 2 Cl(g) | +243 |
(b) Calculate the value of ΔH1°, in kJ/molrxn, for reaction 1 above using reactions 2, 3, and 4.
(c) A potential energy diagram for Cl2 is shown in the following graph.
(i) Based on the graph, what is the bond length, in picometers, for Cl2?
(ii)A student finds that the average Ga–Cl bond length is 210 picometers and the average bond energy is 354 kJ/mol. Draw the potential energy curve for the average Ga–Cl bond on the preceding graph. (In this text-only interface, describe the curve you would draw — e.g., give the internuclear distance at its minimum, the minimum energy value, and how the curve behaves at short and long distances.)
(d) Three proposed Lewis diagrams for the GaCl3(g) molecule are shown.
(i) The GaCl3(g) molecule has a trigonal planar geometry. Which diagram (1, 2, or 3) can be eliminated based on geometry? Justify your choice based on VSEPR theory.
(ii) Which of the three diagrams is the best representation for the bonding in GaCl3? Justify your choice based on formal charges.
GaCl3 is known to dimerize reversibly in the gas phase. The dimerization equilibrium is represented by the following equation.
2 GaCl3(g) ⇌ Ga2Cl6(g)
(e) Write the expression for the equilibrium constant, Kp, for this reaction.
A particle-level diagram of an equilibrium mixture of GaCl3(g) and Ga2Cl6(g) at 400°C in a 25 L closed container is shown.
(f) Using the particle-level diagram, calculate the value of Kp for the reaction if the total pressure in the container is 18.0 atm.
Answer all parts of Question 2. Show your work for each part, including calculations and justifications where required.