Final answer:
B, 1 mol of H₂(g) at 100°C and 0.5 atm, The system with the greatest entropy is option due to its higher temperature and lower pressure compared to the other options, which make the gas molecules more spread out.
Step-by-step explanation:
The student has asked which system has the greatest entropy among the following options: A. 1 mol of H₂(g) at STP, B. 1 mol of H₂(g) at 100°C 0.5 atm, C. 1 mol of H₂O(s) at 0°C, D. 1 mol of H₂O(l) at 25°C.
Entropy is a measure of the disorder or randomness in a system, and tends to increase with temperature, phase changes from solid to liquid to gas, and with the increase of volume or decrease of pressure.
Comparing the options, B. 1 mol of H₂(g) at 100°C 0.5 atm has the highest entropy because it has both a higher temperature and lower pressure than option A, which make the gas molecules more spread out, increasing their entropy.
Options C and D have lower entropy than A and B because they are not in the gas phase; with option C being a solid and thus having the lowest entropy of the four options.