To determine the oxidation number of chromium in potassium dichromate (\(\text{K}_2\text{Cr}_2\text{O}_7\)), we follow a systematic approach to assign oxidation states to each element while ensuring the compound's overall charge is zero.
- Start by assigning oxidation numbers to the known elements. Potassium (\(\text{K}\)) typically has an oxidation number of +1. For \(\text{K}_2\text{Cr}_2\text{O}_7\), there are two potassium ions, contributing a total oxidation number of \(2 \times (+1) = +2\).
- Oxygen (\(\text{O}\)) usually has an oxidation number of -2. In \(\text{K}_2\text{Cr}_2\text{O}_7\), there are seven oxygen atoms, contributing a total oxidation number of \(7 \times (-2) = -14\).
- Assign the oxidation number of chromium (\(\text{Cr}\)) as \(x\). Since there are two chromium atoms present, the contribution is \(2x\).
- For the compound \(\text{K}_2\text{Cr}_2\text{O}_7\) to be electrically neutral, the sum of oxidation numbers of all atoms must be zero. Therefore:
2(+1) + 2x + 7(-2) = 0
Solving the equation:
- \(2 + 2x - 14 = 0\)
- \(2x - 12 = 0\)
- \(2x = 12\)
- \(x = 6\)
Thus, the oxidation number of chromium in potassium dichromate is +6. This matches with the correct answer option provided:
6
.