Final answer:
B) High pressure and low temperature are the conditions that would most likely cause mercury to solidify, as these conditions push the particles closer together, facilitating the transition from liquid to solid state.
Step-by-step explanation:
The set of conditions that would most likely cause mercury to exist in the solid state is B. High pressure and low temperature. Mercury has a freezing point of -39°C, and when exposed to temperatures below this point, it transitions from its liquid state to a solid state. The application of high pressure can assist in this transition because as pressure increases, particles are forced closer together which facilitates the change to a denser phase, namely solid. In general, the solid-state is denser than the liquid state for most substances, and placing a liquid under great pressure often results in it turning solid. It's important to note that if mercury is brought back to room temperature, it usually reverts to its liquid form, as solid mercury is not stable at higher temperatures.