Calculate The Standard-State Entropy for The Following Reaction Ch4 H20

Introduction

The standard-state entropy change (ΔS°) for a reaction is calculated using the standard entropies of the products and reactants. The formula for the standard-state entropy change is:

Where:

• ΔS° is the standard-state entropy change (J/mol·K)
• S°(products) is the sum of the standard entropies of the products
• S°(reactants) is the sum of the standard entropies of the reactants

This calculation is essential in chemical thermodynamics for understanding the spontaneity of reactions and the energy changes involved.

Formula

The standard-state entropy change for a reaction is calculated using the following formula:

Where:

• ΔS° is the standard-state entropy change (J/mol·K)
• S°(products) is the sum of the standard entropies of the products
• S°(reactants) is the sum of the standard entropies of the reactants

This formula is derived from the second law of thermodynamics, which states that the total entropy of an isolated system can never decrease over time, and is constant if the system is in equilibrium.

Calculation

To calculate the standard-state entropy change for the reaction CH4 + H2O, you need the standard entropies of the products and reactants. The standard entropy is the entropy of a substance at 1 bar pressure and a specified temperature (usually 298 K).

For the reaction CH4 + H2O, the standard entropies are typically provided in thermodynamic tables. Using these values, you can calculate the standard-state entropy change as follows:

However, in this case, the reaction is written as CH4 + H2O, which implies that the products are not specified. If the reaction is CH4 + H2O → CO2 + 2H2, then the calculation would be:

Using typical standard entropy values:

• S°(CO2) = 213.6 J/mol·K
• S°(H2) = 130.6 J/mol·K
• S°(CH4) = 186.3 J/mol·K
• S°(H2O) = 69.95 J/mol·K

The calculation would be:

This result indicates that the reaction leads to an increase in entropy, which is consistent with the second law of thermodynamics.

Interpretation

The standard-state entropy change (ΔS°) provides valuable information about the spontaneity and direction of a chemical reaction. A positive ΔS° indicates that the reaction leads to an increase in entropy, which is often associated with spontaneous reactions at constant temperature and pressure.

For the reaction CH4 + H2O → CO2 + 2H2, the positive ΔS° of 218.55 J/mol·K suggests that the reaction is spontaneous under standard conditions. This is because the increase in entropy due to the formation of more molecules (CO2 and 2H2) outweighs the decrease in entropy due to the formation of fewer molecules (CH4 and H2O).

However, it's important to note that the spontaneity of a reaction is also influenced by the enthalpy change (ΔH°) and the temperature. The Gibbs free energy change (ΔG°) is a more comprehensive measure of spontaneity and is calculated using the formula:

Where:

• ΔG° is the standard-state Gibbs free energy change (kJ/mol)
• ΔH° is the standard-state enthalpy change (kJ/mol)
• T is the temperature in Kelvin
• ΔS° is the standard-state entropy change (J/mol·K)

If ΔG° is negative, the reaction is spontaneous under standard conditions. If ΔG° is positive, the reaction is non-spontaneous under standard conditions.