Question

What are the oxidation numbers in the compound $KCl$?

Answer 1

The oxidation number of $K$ is $+1$. The oxidation number of $Cl$ is $-1$.
You assign oxidation numbers to the elements in a compound by using the Rules for Oxidation Numbers. The important rules for this problem are:

1. The oxidation number of a monatomic ion equals the charge of the ion.
2. The oxidation number of a Group 1 element in a compound is +1.
3. The oxidation number of a Group 17 element in a binary compound is -1.
4. The sum of the oxidation numbers of all the atoms in a neutral compound is 0.

In your case, $KCl$ is an ionic compound. It consists of $K^{+}$ ions and $C{l}^{-}$ ions.
The oxidation number of $K$ is $+1$ (Rules 1 and 2).
The oxidation number of $Cl$ is $-1$ (Rules 1 and 3).
Note that Rule 4 also applies: +1 + (-1) = 0. KCl is a neutral compound. It has no charge.