1. The Balanced Chemical Equation:
The balanced chemical equation for the reaction is:
N₂(g) + 3H₂(g) ⇌ 2NH₃(g)
2. Standard Gibbs Free Energy Change (ΔG°)
You need the standard Gibbs free energy change (ΔG°) for this reaction. You can find this value in a table of thermodynamic data. For the formation of ammonia, ΔG° is typically around -33.3 kJ/mol at 298K.
3. The Reaction Quotient (Q)
The reaction quotient (Q) is a measure of the relative amounts of reactants and products at any given time. It is calculated using the partial pressures of the gases:
Q = (P(NH₃)²) / (P(N₂) * P(H₂)³)
Plug in the given partial pressures:
Q = (2.0² ) / (2.5 * 2.75³)
4. The Gibbs Free Energy Change (ΔG)
The relationship between ΔG, ΔG°, and Q is given by:
ΔG = ΔG° + RTln(Q)
Where:
* R = Ideal gas constant (8.314 J/mol·K)
* T = Temperature in Kelvin (298K)
Now, substitute the values:
ΔG = -33.3 kJ/mol + (8.314 J/mol·K * 298 K * ln(Q))
Important Notes:
* Convert kJ/mol to J/mol for consistency in units.
* Make sure to use the correct value for ΔG° from a reliable source.
* The value of ΔG will be negative if the reaction favors product formation under the given conditions.
Calculation:
1. Calculate Q: Q = (2.0² ) / (2.5 * 2.75³) ≈ 0.16
2. Convert ΔG° to J/mol: ΔG° = -33.3 kJ/mol * 1000 J/kJ = -33300 J/mol
3. Calculate ΔG:
ΔG = -33300 J/mol + (8.314 J/mol·K * 298 K * ln(0.16)) ≈ -38422 J/mol
Therefore, the Gibbs free energy change (ΔG) for the reaction of nitrogen and hydrogen to form ammonia at 298K, given the partial pressures provided, is approximately -38.4 kJ/mol.
This negative value indicates that the reaction is spontaneous (favors product formation) under these conditions.
