The two butenedioic acids are called fumaric acid(trans) and maleic acid(cis). 2,3-Dihydroxybutanedioic acid is called tartaric acid.

Show how would you convert

1. Fumaric acid to ($\mathbf{\pm }$)-tartaric acid.
2. Fumaric acid to meso-tartaric acid.
3. Maleic acid to ($\mathbf{\pm }$)-tartaric acid.
4. Maleic acid to meso-tartaric acid.

Fumaric acid is a trans-alkene and undergoes syn-hydroxylation in presence of osmium tetroxide and hydrogen peroxide. Syn-hydroxylation means, that both the incoming hydroxyl groups will be on the same side. We will get a racemic mixture of the product, that is, ()-tartaric acid. Trans alkene when undergoes syn-addition, will produce the racemic product. A racemic mixture is the mixture of equal quantities of enantiomers.

Fumaric acid is a trans-alkene. In presence of peroxy acid and water, it undergoes an epoxidation reaction at the alkene center which leads to the formation of an epoxide. On further reaction with water which acts as a nucleophile, the epoxide ring opens up in an anti-fashion, which means, water attacks from the opposite plane as epoxide and both the hydroxyl groups will be opposite to each other, meso product forms.

Maleic acid is a cis-alkene. In presence of peroxy acid and water, it undergoes an epoxidation reaction at the alkene center which leads to the formation of an epoxide. On further reaction with water which acts as a nucleophile, the epoxide ring opens up in an anti-fashion, which means, water attacks from the opposite plane as epoxide and both the hydroxyl groups will be on the opposite sides of each other. A racemic mixture of products is obtained.

Maleic acid is a cis-alkene. It undergoes syn-hydroxylation in presence of osmium tetroxide and hydrogen peroxide. Syn-hydroxylation means, that both the incoming hydroxyl groups will be on the same side. We will get a meso-product that has a plane of symmetry and two chiral centers. Cis-alkene on syn-addition gives meso product.