Is the osmium oxidised or reduced during the formation of the osmate ester?
The osmium is reduced during the formation of the osmate ester.
A typical equation for the reaction is:
Let's look at the oxidation numbers.
In cyclopentane, the oxidation number of each alkene carbon is 0. In the ester, the oxidation numbers are +1. The total oxidation number change in cyclopentane is +2.
The cyclopentane is oxidized, so the Os must have been reduced.
The cyclopentane loses two electrons. The Os gains two electrons — the new lone pair.
This decreases the oxidation number of Os from +8 to +6. Os is reduced.