Understanding Entropy and Vaporization
* Entropy (ΔS) is a measure of disorder or randomness in a system. When a substance changes state from liquid to gas, the molecules become more spread out and disordered, leading to an increase in entropy.
* Vaporization (or boiling) is the process where a liquid changes into a gas.
Calculations
1. Find the enthalpy of vaporization (ΔHvap):
* The enthalpy of vaporization of water at 100°C is approximately 40.7 kJ/mol.
2. Use the Clausius-Clapeyron equation:
* The Clausius-Clapeyron equation relates enthalpy of vaporization (ΔHvap) to the change in entropy (ΔSvap) during vaporization:
```
ΔSvap = ΔHvap / T
```
* Where:
* ΔSvap is the entropy change of vaporization
* ΔHvap is the enthalpy of vaporization (in J/mol)
* T is the temperature in Kelvin (K)
3. Convert temperature to Kelvin:
* 100°C + 273.15 = 373.15 K
4. Calculate the entropy change:
* ΔSvap = (40.7 kJ/mol) / (373.15 K)
* ΔSvap = 0.109 kJ/(mol·K)
* Convert to J/(mol·K): ΔSvap = 109 J/(mol·K)
5. Calculate the entropy change for 1.8 mol of water:
* ΔS_total = ΔSvap * n
* ΔS_total = (109 J/(mol·K)) * (1.8 mol)
* ΔS_total = 196.2 J/K
Therefore, the entropy change for the vaporization of 1.8 mol of water at 100°C and 1 atm is approximately 196.2 J/K.
