Chemistry long HW help

Question

Reaction. E°red (V)

H3BO3 (aq) / B (s). -0.8698

BiO+ (aq) / Bi (s) 0.320

1.Find the overall reaction that will be occurring between the H3BO3 / B and BiO+ / Bi half cells in acidic conditions.

2. What is the standard cell voltage of this electrochemical cell?

3. What is the standard free energy of this reaction?

4.What is the equilibrium constant of this reaction at 25 °C?

5. After 56.0 hours at 1.04 A, how many moles of electrons have been used in this reaction?

6.Predict the sign of the entropy (🔼Srxn) for this electrochemical reaction. Explain your reasoning.

Answer 1

Yes, this is a long question/answer. The balanced redox equation is obtained by standard procedures for balancing redox in acid medium. If not sure how to do this, submit separate question.

(1). Bi³⁺(aq) + 3e- ==> Bi(s) .. reduction at cathode (0.320 V)

B(s) + 3H₂O ==> B(OH)₃ + 3H⁺ + 3e- .. oxidation at anode (-0.8698 V)

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Bi³⁺(aq) + B(s) + 3H₂O ==> Bi(s) + B(OH)₃ + 3H⁺ .. balanced redox equation

(2). Eº_cell = cathode - anode = 0.320 - (-0.8698) = 1.19 V

(3). ∆Gº = -nFEº_cell = -(3)(96500)(1.19) = -345 kJ

(4). ∆Gº = -RT ln K

-345 kJ = -(0.008314 kJ/Kmol)(298K) ln K

ln K = 139

K = 3.0x10⁶⁰

(5). 1.04 A = 1.04 C/sec and 56 hrs = 56 hr x 3600 sec/hr = 201,600 sec

1.04 C/sec x 201,600 sec = 209,664 C

209,664 C x 1 mol e- / 96500 C = 2.17 moles e-

(6). The sign of ∆S_rxn will be negative.

Reasoning: Eº_cell is positive and ∆Gº is negative, both indicating the reaction is spontaneous. For a spontaneous reaction, ∆H should also be negative (exothermic), and thus from ∆G =∆H - T∆S, the value for ∆S_rxn would be negative.