Write the structures of the ions

• Chromate ion: $\ce{CrO4^{2-}}$
• Dichromate ion: $\ce{Cr2O7^{2-}}$

Count total Cr–O bonds in chromate

In $\ce{CrO4^{2-}}$, one chromium atom is bonded to four oxygen atoms.

So, total number of $\ce{Cr-O}$ bonds in chromate $= 4$.

Count total Cr–O bonds in dichromate

In $\ce{Cr2O7^{2-}}$, there are two chromium atoms and seven oxygen atoms, with one oxygen acting as a bridging oxygen between the two chromium atoms.

Structure idea:

• Each chromium is bonded to 4 oxygen atoms.
• The bridging oxygen is bonded to both chromium atoms.

Hence total $\ce{Cr-O}$ bonds are: $4 + 4 = 8$

(Equivalently: 6 terminal oxygens give 6 bonds, and 1 bridging oxygen gives 2 bonds, so $6+2=8$.)

Find the sum

$4 + 8 = 12$

Comparison with stored answer

The derived answer is $12$, whereas the stored correct answer is $18$.

The value $18$ would arise only if one incorrectly counts double bonds as two separate bonds in these resonance structures. But the question asks for the total number of bonds between chromium and oxygen atoms, which in standard structural counting means counting each $\ce{Cr-O}$ connection once. Thus:

• Chromate: 4 $\ce{Cr-O}$ connections
• Dichromate: 8 $\ce{Cr-O}$ connections

Therefore, the correct sum is $12$.