What is the stereochemical designation of the following molecule? (The roman numerals, I-IV are just used to indicate the different attachments NOT to designate priority).

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All four attached groups are carbons, which have the same priority. When you have groups with the same atomic , especially carbon, you proceed to the other attached groups to the carbon. In this case we have a CH₃, CH₂, CH₂, CH at I, II, III and IV respectively. This means IV is highest priority and I is lowest priority. II is CH₂CH₃, III is CH₂CH₂CH₃. If you look at each one's second carbon you are comparing a CH₃ to a CH₂, CH₂ has less hydrogen so is higher priority. This means II is third in priority and III is second in priority. Going from the highest priority, IV, to the second highest priority, III, you move clockwise. But since the lowest priority is facing you, the correct designation is S.

What Is the Stereochemical Designation of the Following Molecule? (The