What is the oxidation number of cr in $C r_{2} O 7^{2}$ ?

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Solution

This is the dichromate ion, $C r_{2} O_{7}^{2 -}$
Oxygen is more electronegative than chromium, so it'll take its usual −2 charge here. There are seven oxygen atoms, so the total charge is −2⋅7=−14.
Let x be the oxidation number of two chromium atoms. So, we got:
$x + (- 14) = - 2$
$x - 14 = - 2$
$x = 12$
So, two chromium atoms have a total oxidation number of +12. Since one is not more electronegative than the other, we can divide the number by two to get one chromium's oxidation number.
$\frac{12}{2} = 6$
So, a chromium atom here has an oxidation number of +6.

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