Which state in each of the following pairs has the higher entropy per mole of substance? (b) N₂ at STP or N₂ at 0 °C and 10 atm

Verified step by step guidance

1. Entropy is a measure of the disorder or randomness in a system. In general, gases have higher entropy than liquids, and liquids have higher entropy than solids.
2. For gases, entropy increases with an increase in volume or a decrease in pressure, as the molecules have more space to move around.
3. STP (Standard Temperature and Pressure) is defined as 0 °C and 1 atm.
4. Compare the two conditions: N_2 at STP (0 °C, 1 atm) and N_2 at 0 °C and 10 atm.
5. Since the temperature is the same in both cases, focus on the pressure: lower pressure (1 atm) at STP means higher volume and thus higher entropy compared to 10 atm.

Key Concepts

Entropy

Entropy is a measure of the disorder or randomness in a system. It quantifies the number of microscopic configurations that correspond to a thermodynamic system's macroscopic state. Higher entropy indicates greater disorder and more available microstates, which typically occurs in gases compared to liquids and solids.

Ideal Gas Law

The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of an ideal gas through the equation PV = nRT. This law helps predict how gases behave under different conditions, including changes in temperature and pressure, which directly affect the entropy of the gas.

Standard Temperature and Pressure (STP)

Standard Temperature and Pressure (STP) is defined as a temperature of 0 °C (273.15 K) and a pressure of 1 atm. At STP, gases behave ideally, and their properties, including entropy, can be compared more easily. Deviations from STP, such as increased pressure or decreased temperature, can significantly alter a gas's entropy.