Question

What is the oxidation state of $Cr$ in ${{K}_{2}}C{{r}_{2}}{{O}_{7}}$

Answer 1

Hint: Think about what the term oxidation state means. Determine the fixed oxidation states of $K$ and $O$, and also the net charge present on this molecule.

Complete step by step solution:
The oxidation state is the number of electrons that are lost, gained, or shared by a certain atom with other atoms in the same molecule.
Here, we will focus on all the fixed components and then work out the oxidation state of $Cr$
- The net charge on the molecule is 0. Therefore, all the oxidation states will add up to 0 after they are multiplied by the number of molecules.
\[(2\times \text{oxidation state of }K)+(2\times \text{oxidation state of }Cr)+(7\times \text{oxidation state of }O)=0\]
- We know that the oxidation state of $O$ is considered to be -2 in almost all cases. This changes only if a bond with a more electronegative element is formed. This is not the case in this example; hence we will assume that the oxidation state of $O$ is -2.
- We know that almost all elements from group 1A have an oxidation state of +1. This rule never changes. Thus, we will assume that the oxidation state of $K$ is +1.
Now plugging in the numbers in the equation given above, we get:
\[[2\times (+1)]+[2\times \text{oxidation state of }Cr]+[7\times (-2)]=0\]
\[2+(2\times \text{oxidation state of }Cr)-14=0\]
\[2\times \text{oxidation state of }Cr=12\]
Oxidation state of $Cr$= $\dfrac{+12}{2}$
Oxidation state of $Cr$= +6

Thus, the oxidation state of $Cr$ is +6 when the oxidation states of $K$ and $O$ are +1 and -2 respectively.

Note: Always check what the net charge on the given ion or molecule is, this will change the number present on the R.H.S. of the equation. For example, if we consider the ion $C{{O}_{3}}^{2-}$then to calculate the oxidation state of $C$, we need to consider the equation:
\[(\text{oxidation state of }C)+(3\times \text{oxidation state of }O)=-2\]
Here the oxidation state of $C$ will be +4. If we do not pay attention to the net charge, the answer will turn out to be +6, which is not possible.