Answer:
(a) 4 stereoisomers: (1R,2S) 4,4-dimethylcyclopentane1,2-diol; (1R,2S) 4,4-dimethylcyclopentane1,2-diol; (1S,2S) 4,4-dimethylcyclopentane1,2-diol; (1R,2R) 4,4-dimethylcyclopentane1,2-diol. (b) (1R,2S) 4,4-dimethylcyclopentane1,2-diol; (1R,2S) 4,4-dimethylcyclopentane1,2-diol (c) No, they are optically inactive.
Explanation:
(a) The stereoisomers possible for 4,4-dimethyl-1, 2-cyclopentanediol are (1R,2S) 4,4-dimethylcyclopentane1,2-diol; (1R,2S) 4,4-dimethylcyclopentane1,2-diol; (1S,2S) 4,4-dimethylcyclopentane1,2-diol; (1R,2R) 4,4-dimethylcyclopentane1,2-diol. Their structures are shown in the attached file.
(b) The oxidation reaction that occurs between 4,4-dimethylcyclopentene and osmium tetroxide produces (1R,2S) 4,4-dimethylcyclopentane1,2-diol; (1R,2S) 4,4-dimethylcyclopentane1,2-diol. Their structures are also shown in the attached file.
(c) The products of the oxidation reaction in (b) are optically inactive because the compounds contain plane of symmetry that makes them optically inactive compound.
![[OH^{-}] = 10^{-pOH}= 10^{-8.43}= 3.72*10^{-9} [OH^{-}]= 3.72*10^{-9}](https://tex.z-dn.net/?f=%5BOH%5E%7B-%7D%5D%20%3D%2010%5E%7B-pOH%7D%3D%2010%5E%7B-8.43%7D%3D%203.72%2A10%5E%7B-9%7D%0A%0A%20%5BOH%5E%7B-%7D%5D%3D%203.72%2A10%5E%7B-9%7D)