1.1 Discuss which system has higher entropy. a. One mole of ice or one mole of liquid water at \( 0^{\circ} \mathrm{C} \). b. One mole of iodine as a solid at room temperature or one mole of iodine as a gas at room temperature. c. One mole of liquid propanol or one mole of liquid dimethyl ether. (Hint: Which of the molecule can form hydrogen bonds?)

The system with higher entropy between one mole of ice and one mole of liquid water at \( 0^{\circ} \mathrm{C} \) is the liquid water. As a liquid, the water molecules have more freedom of movement compared to the rigid structure of ice, leading to greater disorder and, therefore, higher entropy. When comparing one mole of iodine as a solid at room temperature versus one mole of iodine as a gas at room temperature, the gaseous iodine has higher entropy. The gaseous state allows iodine molecules to occupy a larger volume and move more freely, resulting in greater disorder compared to the tightly packed solid state. In the case of one mole of liquid propanol and one mole of liquid dimethyl ether, liquid propanol has higher entropy because it can form hydrogen bonds due to the presence of an -OH group. This intermolecular interaction creates more complexity and disorder in the liquid structure than dimethyl ether, which has weaker van der Waals forces, resulting in lower entropy.