Question

# You have synthesized a redox reagent that is a complex between cobalt and six ammonia molecules...

You have synthesized a redox reagent that is a complex between cobalt and six ammonia molecules ([Co(NH3)6] 3+/2+). It cycles between the Co(II) and Co(III) oxidation states. Unfortunately, after you complete your synthesis, you learn that your potentiostat is broken and you have no way to measure the reduction potential of your compound. Fortunately, you realize that you have sufficient information from other experiments and from data tables to determine the potential for this reagent. This information is:

The standard potential for reduction of Co3+(aq) to Co2+ (aq) is +1.82 V (see Table 11.1)

Kf for [Co(NH3)6] 3+ is 4.5 x 10^33

Kf for [Co(NH3)6] 2+ is 1.3 x 10^7

Note that the Kf for [Co(NH3)6] 3+ (for example) is defined as the equilibrium constant for the following reaction conducted in aqueous medium:

Co3+(aq) + 6 NH3 = [Co(NH3)6] 3+

To tackle this problem, set up a thermodynamic cycle and/or consider how to combine a series of reactions to give the desired reaction. Recall that you will want to identify state functions that you can easily combine to find your answer. To address this kind of problem, start by writing out the target chemical reaction and indicate the quantity being sought (here, standard reduction potential for your cobalt compound): Next, write out what relevant information is known, including chemical reactions and quantities given: Finally, consider how to combine the chemical equations with known quantities to yield a chemical equation with the unknown quantity. Then, you can consider how to combine the quantities to determine the unknown quantity. You will need to do some conversions to make this work. Use the back of the page or scratch paper to clearly lay out your approach and determine your answer. You may find setting up a thermodynamic cycle to be the best way, or you may prefer adding a series of equations explicitly.

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