Hydroxylation of cis-but-2-ene with basic potassium manganate yields a different product than hydroxylation of trans-but-2-ene. Draw the structure, show stereochemistry of each product and explain?

The hydroxylation of cis-but-2-ene with basic potassium manganate yields a 2,3-diol product, while the hydroxylation of trans-but-2-ene yields a 1,2-diol product.

Here are the structures and stereochemistry of each product:

Cis-but-2-ene hydroxylation product (2,3-diol):
```
OH
|
H3C ─ C ─ CH3
|
OH
```

Trans-but-2-ene hydroxylation product (1,2-diol):
```
OH
|
H3C ─ C ─ CH3
|
OH
```

The difference in products can be explained by the different orientations of the double bond in cis-but-2-ene and trans-but-2-ene.

In cis-but-2-ene, the two methyl groups are on the same side of the double bond. When hydroxylation occurs, the hydroxyl groups are added to the same face of the molecule, resulting in the formation of a 2,3-diol. This is due to the syn addition of the hydroxyl groups to the same face of the double bond.

In trans-but-2-ene, the two methyl groups are on opposite sides of the double bond. When hydroxylation occurs, the hydroxyl groups are added to opposite faces of the molecule, resulting in the formation of a 1,2-diol. This is due to the anti addition of the hydroxyl groups to opposite faces of the double bond.

Therefore, the different products obtained from the hydroxylation of cis-but-2-ene and trans-but-2-ene can be attributed to the different orientations of the double bond and the resulting syn or anti addition of the hydroxyl groups.