The reduction potential of hydrogen half-cell will be negative if:

Explanation

According to the Nernst equation, the reduction potential of a half-cell is affected by the concentration of ions and the partial pressure of gases involved. For a hydrogen half-cell, the standard reduction potential is zero at 1 atm pressure and 1M concentration of H+. Option C presents a scenario where the partial pressure of hydrogen is increased to 2 atm while maintaining the standard concentration of H+. This results in a shift in equilibrium towards oxidation, causing the reduction potential to become negative. In contrast, Option A describes standard conditions resulting in zero potential, Option B could have a balanced effect maintaining the potential near zero, and Option D increases the concentration of H+ which would increase the reduction potential, making it positive.