Which state in each of the following pairs has the higher entropy per mole of substance? 1. Ice at - 40 degrees C or ice at 0 degrees C.
2. N2 at STP or N2 at 0 degrees C and 10 atm.
3. N2 at STP or N2 at 0 degrees C in a volume of 50 L.
4. Water vapor at 150 degrees C and 1 atm or water vapor at 100 degrees C and 2 atm.

1. Ice at 0 degrees C.

2. N₂ at STP.

3. N₂ at STP.

4. Water vapor at 150 degrees C and 1 atm.

Explanation:

First, we need to remember that entropy (S) is a measure of how spread out or dispersed the energy of a system is among the different possible ways that system can contain energy. The greater the dispersal, the greater is the entropy.

When the temperature is increased, the energies associated with all types of molecular motion increase. Consequently, the entropy of a system always increases with increasing temperature.

With this in mind, we consider the pairs:

1. Since the ice at 0ºC has a greater temperature than the ice at -40 ºC, the first has the higher entropy.

2. The N₂ at STP (that is, 1 atm and 25 ºC) has higher entropy than N₂ at 0ºC and 10 atm because it has a higher temperature and less pressure, which allows a greater dispersal of energy by the molecules of the gas.

3. The N₂ at STP has a higher entropy since it has a higher temperature than N₂ at 0ºC, even though it the first has a lower volume (24,4 L vs. 50 L).

4. The water vapor at 150 ºC and 1 atm have a higher temperature and a lower pressure. This means that its molecules will have an increased molecular motion than the molecules of water vapor at a lower temperature and higher pressure. Therefore, the first has the highest entropy.