A solution is composed of 3.20 × 10 − 4 M Co(NO 3 ) 3 mixed with 0.200 M NH 3 . Determine the [Co 3+ ] that remains once the solution reaches equilibrium in the formation of Co(NH 3 ) 6 3+ .

Here we're told that a solution is composed of 3.20 times 10 to the negative 4 cobalt 3 nitrate, and it's mixed with 0.200 molar of ammonia. Here we need to determine the concentration of cobalt 3 ions that remains once the reaction reaches equilibrium in the form of cobalt, 3 with 6 ammonias. Here, this represents our complex ion. Alright. So this they're giving us the complex ion, so they're telling us that this is the product. So we know it's cobalt 3 ion reacting, aqueous and aqueous, and the complex ion is telling us that there are 6 molecules of ammonia involved, so it's 6 NH 3 aqueous. With this complex ion, we deal with an ICE chart. This concentration here is also equal to the concentration of the cobalt 3 ion because it's a one to one relationship. So initially we have 3.20 times 10 to the minus 4, and initially we have 0.200 molar of ammonia. We're not told anything initially about our product, so it's 0. We look on the reactant side and the smaller concentration will deduct from the larger concentration. So here we're gonna do minus 3.20 times 10 to the minus 4 molar. In here, this is really minus 6 x and the x is just the smaller molarity that's subtracting. So this is minus 6 times 3.20 times 10 to the minus 4 molar. Whatever we lose on the reactant side, we gain on the product side based on the law of conservation of mass. So it's plus 3.20 times 10 to the minus 4. Bring down everything. Now at the end at equilibrium, it may look like these totals are completely destroying each other and we should have no Cobalt 3 ion left, but in reality we don't get rid of all of the Cobalt 3 ion. There'll be some remaining. It's up to us to figure out how much that is. So at equilibrium, our cation equals x. Here we subtract 0.200 by, 6 times this concentration here, which gives us a final equilibrium concentration of 0.198 0 8 molar. We bring down this 3.20 times 10 to the minus 4 molar. Now with a complex ion, we have a formation constant attached. Here I don't give it to us, but remember in your textbooks you have appendices which have, k a values, k b values, and more importantly for this question, your formation constant value. But don't worry, on your actual exam it'll be given to you in some way within the question or formula sheet or, constants sheet. Here for this complex ion k f equals 2.3 times 10 to the 33. Now here k f, or formation constant equals products over reactants. So it equals C 0 NH 3, 6, 3 positive, divided by C 0 3 positive times NH 3 to the 6. We're looking just for this variable here because we know everyone else, so I'm just going to rearrange it where I isolate cobalt 3 ion. So here we have our complex ion divided by KF times NH3 to the 6. Here we plug in our values that we have. Kf here again is 2.3 times 10 to the 33, which I looked up within the appendix of my textbook. And then here this is 0.19808 to the 6. So when I do all that, I get the concentration of coalt 3 ion being equal to 2.3 times 10 to the minus 33 molar. Or 2.30 times 10 to the minus 33, molar. So this will represent the concentration of cobalt 3 at the end, and you can see that it's a number that's incredibly small. We get pretty close to 0, but we're just not quite there, okay? We need to kind of a plateau with this. Okay? So that's why we couldn't say that it's just 0 for the equilibrium of the metal cation. Here we have to solve for x to find out the exact value, alright? So this would be our final answer.

A solution is composed of 3.20 × 10−4 M Co(NO3)3 mixed with 0.200...

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A solution is composed of 3.20 × 10⁻⁴ M Co(NO₃)₃ mixed with 0.200 M NH₃. Determine the [Co³⁺] that remains once the solution reaches equilibrium in the formation of Co(NH₃)₆³⁺.

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A solution is composed of 3.20 × 10−4 M Co(NO3)3 mixed with 0.200 M NH3. Determine the [Co3+] that remains once the solution reaches equilibrium in the formation of Co(NH3)63+.

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Complex Ions: Formation Constant practice set

A solution is composed of 3.20 × 10⁻⁴ M Co(NO₃)₃ mixed with 0.200 M NH₃. Determine the [Co³⁺] that remains once the solution reaches equilibrium in the formation of Co(NH₃)₆³⁺.