Consider the evaporation of methanol at 25.0 °C : CH₃OH(l) → CH₃OH(g) b. Find ΔG_r at 25.0 °C under the following nonstandard conditions: i. P_CH3OH = 150.0 mmHg ii. P_CH3OH = 100.0 mmHg iii. P_CH3OH = 10.0 mmHg

Verified step by step guidance

1. Identify the standard Gibbs free energy change (ΔG°) for the evaporation of methanol at 25.0 °C, which can be found in tables or calculated if necessary.
2. Use the equation ΔG = ΔG° + RT ln(Q) to calculate the Gibbs free energy change under nonstandard conditions, where R is the universal gas constant (8.314 J/mol·K) and T is the temperature in Kelvin.
3. Convert the temperature from Celsius to Kelvin by adding 273.15 to the Celsius temperature (25.0 °C + 273.15 = 298.15 K).
4. Calculate the reaction quotient Q for each given pressure condition using the formula Q = P_CH3OH / P° where P° is the standard pressure (1 atm or 760 mmHg).
5. Substitute the values of ΔG°, R, T, and Q into the equation ΔG = ΔG° + RT ln(Q) for each pressure condition to find ΔG for each scenario.

Key Concepts

Gibbs Free Energy (ΔG)

Gibbs Free Energy (ΔG) is a thermodynamic potential that measures the maximum reversible work obtainable from a thermodynamic system at constant temperature and pressure. It is crucial for predicting the spontaneity of a reaction; a negative ΔG indicates a spontaneous process, while a positive ΔG suggests non-spontaneity. In the context of evaporation, ΔG can change with varying conditions such as pressure.

Nonstandard Conditions

Nonstandard conditions refer to situations where the concentrations or partial pressures of reactants and products differ from standard state values (1 bar or 1 M). In this question, the partial pressure of methanol vapor is varied, affecting the Gibbs Free Energy of the evaporation process. Understanding how to adjust ΔG for nonstandard conditions is essential for accurate calculations.

Van 't Hoff Equation

The Van 't Hoff equation relates the change in the equilibrium constant of a reaction to the change in temperature and is often used to derive the Gibbs Free Energy under nonstandard conditions. It can be expressed as ΔG = ΔG° + RT ln(Q), where Q is the reaction quotient. This equation is vital for calculating ΔG at different pressures of methanol vapor during evaporation.