The oxidation numbers of Cu and Bi in high-temperature superconductors of the type Bi₂Sr₂(Ca_0.8Y_0.2)Cu₂O_x (which could contain Cu²⁺, Cu³⁺, Bi³⁺, and Bi⁵⁺) can be measured by the following procedure. In Experiment A, the superconductor is dissolved in 1 M HCl containing excess 2 mM CuCl. Bi5+(written as BiO₃^- ) and Cu³⁺ consume Cu⁺ to make Cu²⁺:

The excess, unreacted Cu⁺ is then titrated by coulometry (described in Chapter 16). In Experiment B, the superconductor is dissolved in 1 M HCl containing excess 1 mM FeCl₂•4H₂O. Bi⁵⁺ reacts with the Fe²⁺ but Cu³⁺ does not react with Fe²⁺

The excess, unreacted Fe²⁺ is then titrated by coulometry. The total oxidation number of Cu⁺ Bi is measured in Experiment A, and the oxidation number of Bi is determined in Experiment B. The difference gives the oxidation number of Cu.

(a) In Experiment A, a sample of Bi₂Sr₂CaCu₂O_x (FM 760.37 15.999 4x) (containing no yttrium) weighing 102.3 mg was dissolved in 100.0 mL of 1 M HCl containing 2.000 mM CuCl. After reaction with the superconductor, coulometry detected 0.108 5 mmol of unreacted Cu in the solution. In Experiment B, 94.6 mg of superconductor were dissolved in 100.0 mL of 1 M HCl containing 1.000 mM FeCl₂•4H₂O. After reaction with the superconductor, coulometry detected 0.057 7 mmol of unreacted Fe₂. Find the average oxidation numbers of Bi and Cu in the superconductor and the oxygen stoichiometry coefficient, x. 

(b) Find the uncertainties in the oxidation numbers and x if the quantities in Experiment A are 102.3 (±0.2) mg and 0.108 5 (±0.000 7) mmol and the quantities in Experiment B are 94.6 (±0.2) mg and 0.057 7 (±0.000 7) mmol. Assume negligible uncertainty in other quantities.

Transcribed Image Text:

BiOS + 2Fe2+ + 4H' BiO+ + 2Fe3+ + 2H20 (3)