Concept:
In coordination compounds, the oxidation state of the central metal ion can be determined using the charges of ligands and the overall charge of the complex.
Important points:
\begin{itemize}
\item \(NH_3\) is a neutral ligand.
\item \(Cl^{-}\) carries a charge of \(-1\).
\item The compound \([Co(NH_3)_6]Cl_3\) contains three chloride ions outside the coordination sphere.
\end{itemize}
Step 1: {\color{red}Determine the charge on the complex ion.}
Since there are \(3\) chloride ions \((Cl^-)\), the complex ion must have a charge of:
\[
[Co(NH_3)_6]^{3+}
\]
Step 2: {\color{red}Let the oxidation state of cobalt be \(x\).}
\[
x + 6(0) = +3
\]
Step 3: {\color{red}Solve the equation.}
\[
x = +3
\]
Thus, the oxidation state of cobalt is:
\[
\boxed{+3}
\]
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