for the haber process for the synthesis of ammonia: N2(g)+ 3H2(g)= 2NH3(g), what is ΔG (kJ/mol) at298 K for a reaction mixture that consists of 1.5 atm N2,3 atm H2 and 1.8 atm NH3?
[ΔG° f(NH3)= -16.66kJ/mol]
To calculate ΔG (Gibbs free energy) for the given reaction mixture, we can use the formula:
ΔG = ΔG° + RT * ln(Q)
Where:
- ΔG is the Gibbs free energy of the reaction mixture.
- ΔG° is the standard Gibbs free energy change.
- R is the gas constant, which is 8.314 J/(mol·K) or 0.008314 kJ/(mol·K).
- T is the temperature in Kelvin.
- Q is the reaction quotient, which can be calculated using the given partial pressures.
Step 1: Convert the given pressures from atm to kPa:
1 atm = 101.325 kPa
Partial pressures:
P(N2) = 1.5 atm = 1.5 * 101.325 kPa = 151.9875 kPa
P(H2) = 3 atm = 3 * 101.325 kPa = 303.975 kPa
P(NH3) = 1.8 atm = 1.8 * 101.325 kPa = 182.385 kPa
Step 2: Convert the temperatures to Kelvin:
Given temperature = 298 K
Step 3: Calculate Q:
Q = (P(NH3))^2 / (P(N2) * (P(H2))^3)
= (182.385)^2 / (151.9875 * (303.975)^3)
Step 4: Calculate ΔG:
ΔG = ΔG° + RT * ln(Q)
= -16.66 kJ/mol + (0.008314 kJ/(mol·K)) * (298 K) * ln(Q)
Now, substitute the value of ln(Q) and perform the calculation to find ΔG.