You are studying the formation of HI(g) from its gaseous elements H2(g) and I2(g). The free energy of formation of HI(g) is –10.10 kJ/mol at 500 K. When the free energy change of the process at 500 K is zero, the reaction mixture shows partial pressures of HI and I2 as 10.0 atm and 0.001 atm, respectively. What must be the partial pressure of H2 at this time?
I would do this.
dG = -RTlnK
Substitute and solve for K.
Then K = p^2HI/pH2*pI2
Substitute and solve for pH2
Okay, I did the equation and I got P H2 : 881.06 atm. That seems very high. Where did I make a mistake?
Thank you for your help.
To determine the partial pressure of H2 in the reaction mixture, we need to use the equation for the free energy change of a reaction, which relates the free energy change (ΔG), the equilibrium constant (K), and the gas constant (R) to the temperature (T) and the partial pressures of the reactants and products.
ΔG = -RT * ln(K)
Here, ΔG is the free energy change, R is the gas constant (8.314 J/K·mol), T is the temperature in Kelvin (500 K in this case), ln(K) is the natural logarithm of the equilibrium constant, and K is the ratio of the products' concentrations to the reactants' concentrations.
The equilibrium constant (K) can be determined using the partial pressures of the reactants and products:
K = (P_HI / P_H2 * P_I2)
Given that P_HI = 10.0 atm and P_I2 = 0.001 atm, we need to find the partial pressure of H2 (P_H2) when ΔG = 0.
First, let's calculate the equilibrium constant (K) using the given partial pressures:
K = (10.0 atm) / (P_H2 * 0.001 atm)
Now, substitute this expression for K into the equation for ΔG:
0 = - (8.314 J/K·mol) * (500 K) * ln((10.0 atm) / (P_H2 * 0.001 atm))
Next, let's simplify the equation:
0 = - (8.314 J/K·mol) * (500 K) * ln(10000 / P_H2)
Now, we can solve for P_H2. Divide both sides of the equation by (-8.314 J/K·mol) * (500 K):
0 / [(-8.314 J/K·mol) * (500 K)] = ln(10000 / P_H2)
Take the exponential of both sides to remove the natural logarithm:
exp(0 / [(-8.314 J/K·mol) * (500 K)]) = 10000 / P_H2
Simplifying further:
1 = 10000 / P_H2
Rearrange the equation and solve for P_H2:
P_H2 = 10000 atm
Therefore, the partial pressure of H2 at the time when the free energy change of the process is zero is 10000 atm.