Calculating Kc and Kp for the Reaction between Iron and Oxygen

Understanding and calculating the equilibrium constants (Kc and Kp) for a chemical reaction is essential for predicting the progress of the reaction. In this article, we will discuss the reaction between iron (Fe) and oxygen (O?) to form iron(III) oxide (Fe?O?) and how to calculate the corresponding equilibrium constants.

Reaction Stoichiometry and Mole Calculation

The balanced chemical equation for the reaction between iron and oxygen to form iron(III) oxide is:

4Fe 3O? rarr; 2Fe?O?

To calculate the number of moles of iron (Fe) from its mass, we use the molar mass of iron, which is approximately 55.845 g/mol. Given 16.7 g of Fe:

16.7 g Fe × (1 mol Fe/55.845 g Fe) 0.2990 mol Fe

Based on the stoichiometry of the reaction, we can determine the amount of O? required to completely react with Fe:

0.2990 mol Fe × (3 mol O?/4 mol Fe) 0.2243 mol O?

To convert the moles of O? to grams, we use the molar mass of O? (31.998 g/mol):

0.2243 mol O? × 31.998 g O?/mol 7.18 g O?

The Equilibrium Constants Kc and Kp

The equilibrium constants Kc and Kp are essential for understanding the extent of the reaction. Kc is the concentration-based equilibrium constant, and Kp is the pressure-based equilibrium constant. For the reaction:

4Fe(s) 3O?(g) ? 2Fe?O?(s)

The expression for Kc is:

Kc [Fe?O?]^2 / ([Fe]^4 [O?]^3)

Since pure solids do not affect the equilibrium constant (as their concentration remains constant), we can simplify:

Kc 1 / [O?]^3

The expression for Kp is related to Kc through the ideal gas law:

Kp 1 / (P?O?)^3 Kc (RT)^-3

For the given reaction, the values for Kc and Kp are:

Kc 1.0 x 10^-14, Kp 9.8 x 10^-7

These values indicate that the forward reaction is highly favored under standard conditions, with a very low probability of the reverse reaction occurring.

The Thermodynamics of the Reaction

The reaction between iron and oxygen to form iron(III) oxide is also analyzed from a thermodynamic perspective, considering the change in Gibbs free energy (ΔG20°C) and enthalpy (ΔH20°C) at 20°C:

ΔG20°C -111.3 kJ (negative, indicating a spontaneous reaction)

ΔH20°C -123.3 kJ (negative, indicating an exothermic reaction)

Absolutely, 16.7 g of Fe, which is 0.299 mol, would form 0.150 mol of Fe?O?. The reaction requires 0.224 mol (7.177 g) of O? to proceed. At standard temperature and pressure (STP), 0.224 mol of O? would occupy 5.027 L.

Key Takeaways:

Kc and Kp: These are the equilibrium constants that help predict the extent of a chemical reaction. Stoichiometry: The balanced equation and molar masses are crucial for determining the amount of reactants and products. Thermodynamics: Gibbs free energy (ΔG) and enthalpy (ΔH) provide insights into the spontaneity and energy changes of the reaction.

Understanding these concepts is vital for anyone interested in chemical engineering, materials science, and related fields.