Question

An octahedral complex with the formula \(\text{CoCl}_3n\text{NH}_3\) upon reaction with excess of \(\text{AgNO}_3\) solution gives 2 moles of \(\text{AgCl}\). Consider the oxidation state of Co in the complex is \(x\). The value of "x + n" is ______.

• A. 3
• B. 6
• C. 8
• D. 5

Answer 1

The Correct Option is C

To solve the problem, we need to determine the oxidation state of cobalt (Co) in the complex \(\text{CoCl}_3n\text{NH}_3\) and use the information provided to find the value of \(x + n\).

1. Given the complex formula is \(\text{CoCl}_3n\text{NH}_3\), it is an octahedral complex. This means that in the coordination sphere of cobalt, a total of six ligands are present (since octahedral coordination implies coordination number six).
2. We know that ammonia (\(\text{NH}_3\)) acts as a neutral ligand, and chlorine (\(\text{Cl}^-\)) acts as an anion with a -1 charge.
3. The formula \(\text{CoCl}_3n\text{NH}_3\) suggests that the complex contains three \(\text{Cl}^-\) ions outside the coordination sphere, which participate in precipitating \(\text{AgCl}\) upon reaction with \(\text{AgNO}_3\).
4. When 2 moles of \(\text{AgCl}\) are formed, it implies that two of the \(\text{Cl}^-\) ions are free or outside the coordination sphere. This means the complex should be \([\text{Co}( \text{NH}_3)_n \text{Cl}](\text{Cl})_2\), where one Cl is within the coordination sphere and two Cls outside.
5. To determine the oxidation state \(x\) of Co:
   • The complex charge can be written as:
     \(text{Co}^{x} (\text{NH}_3)_n \text{Cl}^-]^{2+}\), canceling two negative charges from the outside \(\text{Cl}^-\) ion\)
   • Since ammonia is neutral, it does not affect the oxidation state, only the chlorines change it.
   • The overall equation for charge balance in the coordination sphere is:
     \(x - 1 = +1\)
   • Simplifying, \(x = +3\).
6. Since the complex is octahedral, having 6 coordination sites, we get:
   \(n + 1 (\text{for Cl}) = 6\)
7. Simplifying for \(n\):
   \(n = 5\)
8. Therefore, \(x + n = 3 + 5 = 8\).

Hence, the value of "x + n" is 8, which is the correct answer.

Answer 2

The reaction of $[\text{Co}(\text{NH}_3)_5\text{Cl}]\text{Cl}_2$ with excess AgNO$_3$ is as follows:
\[[\text{Co}(\text{NH}_3)_5\text{Cl}]\text{Cl}_2 + \text{excess AgNO}_3 \rightarrow 2\text{AgCl (2 moles)}\]
In the complex $[\text{Co}(\text{NH}_3)_5\text{Cl}]\text{Cl}_2$:
The inner coordination sphere contains 1 Cl ligand.
The outer coordination sphere contains 2 Cl$^-$ ions, which react with AgNO$_3$ to give 2 moles of AgCl.
Let $x$ be the oxidation state of Co. The total charge on the complex is neutral. Therefore:
\[x + 0 \text{ (from 5 NH}_3\text{)} + (-1 \text{ from 1 Cl}) + (-2 \text{ from 2 Cl}^-) = 0\]
\[x - 1 - 2 = 0\]
\[x = +3\]
Here, $n = 5$ (the number of NH$_3$ ligands). Thus:
\[x + n = 3 + 5 = 8\]
Final Answer: $x + n = 8$