In the compound potassium dichromate, K2Cr2O7, what is the oxidation number of each chromium (Cr) atom?

Introduction / Context:
This question checks your ability to assign oxidation numbers in a polyatomic ionic compound, specifically potassium dichromate, K2Cr2O7. Understanding oxidation numbers is essential for redox reactions, balancing equations and predicting oxidising and reducing agents in inorganic chemistry.

Given Data / Assumptions:

• The compound is K2Cr2O7 (potassium dichromate).
• We need the oxidation number of chromium (Cr) in this compound.
• Standard oxidation numbers are assumed: potassium as an alkali metal and oxygen in oxides.
• The overall compound is electrically neutral, so the sum of oxidation numbers equals zero.

Concept / Approach:
Oxidation number rules are our main tool. In most compounds, potassium (K) has an oxidation number of +1, and oxygen (O) in oxides has an oxidation number of -2. For a neutral compound, the total sum of oxidation numbers of all atoms must be zero. By assigning known oxidation numbers to potassium and oxygen, we can solve for the unknown oxidation number of chromium, assuming both chromium atoms in dichromate have the same value.

Step-by-Step Solution:
1) Write down the formula K2Cr2O7 and note the number of each atom: 2 potassium, 2 chromium and 7 oxygen atoms.2) Assign oxidation numbers using standard rules: each K is +1 and each O is -2 in this type of compound.3) Let the oxidation number of chromium be x. Since there are 2 chromium atoms, their total contribution is 2x.4) Write the total sum of oxidation numbers and set it equal to zero for a neutral compound: 2*(+1) + 2*x + 7*(-2) = 0.5) Simplify: 2 + 2x - 14 = 0, which gives 2x - 12 = 0, so 2x = 12 and x = +6.6) Therefore, the oxidation number of each chromium atom in K2Cr2O7 is +6.

Verification / Alternative check:
We can check by substituting x = +6 back into the expression: total charge = 2*(+1) + 2*(+6) + 7*(-2) = 2 + 12 - 14 = 0. This satisfies the neutrality condition, confirming that +6 is correct. It also matches the fact that dichromate ion Cr2O7^2- is a strong oxidising agent where chromium typically exists in the +6 oxidation state, consistent with many qualitative and quantitative redox reactions in acidic solution.

Why Other Options Are Wrong:
-5: A negative oxidation state for chromium in dichromate contradicts both the usual chemistry of chromium and the charge balance equation.
+3: Chromium in +3 state appears in other compounds such as Cr2O3, but not in the dichromate ion.
-4: Again, a negative oxidation state is not consistent with chromium behaviour in this oxygen rich environment.
+7: This is characteristic of manganese in permanganate (MnO4^-), but chromium in K2Cr2O7 is not +7; the mathematics of charge balance disproves this value.

Common Pitfalls:
Students sometimes confuse dichromate with permanganate and guess +7 or mix up the oxidation states of chromium in different oxyanions (chromate and dichromate). Another common error is to forget to multiply the oxidation number of chromium by 2 when writing the total sum. To avoid such mistakes, always count the number of each type of atom carefully and follow the rule that the total sum of oxidation numbers equals the net charge on the species.

Final Answer:
The oxidation number of chromium in potassium dichromate, K2Cr2O7, is +6 for each chromium atom.