The equilibrium constant for the reaction below is Kc = 9.1 10-6 at 298 K.
2 Fe3+(aq) + Hg22+(aq) 2 Fe2+(aq) + 2 Hg2+(aq)
Calculate G when [Fe3+] = 0.21 M, [Hg22+] = 0.013 M, [Fe2+] = 0.022 M, and [Hg2+] = 0.020 M.
DG = DGo+RTlnK
At equilibrium DG = 0. YOu know Kc; therefore substitute K, R, and T, and solve for DGo.
Then use the first equation above to solve for DG at the concns listed.
To calculate the standard Gibbs free energy (ΔG°) for the reaction, you can use the formula:
ΔG° = -RT ln(Kc)
Where:
- ΔG° is the standard Gibbs free energy change for the reaction
- R is the ideal gas constant (8.314 J/mol·K)
- T is the temperature in Kelvin (298 K in this case)
- ln(Kc) is the natural logarithm of the equilibrium constant (Kc)
First, calculate ln(Kc):
ln(Kc) = ln(9.1 × 10^(-6)) = -12.10
Now, substitute the values into the formula:
ΔG° = - (8.314 J/mol·K) × (298 K) × (-12.10)
= 30,380 J/mol
Thus, the standard Gibbs free energy change (ΔG°) for the reaction is 30,380 J/mol.
To calculate the standard free energy change (ΔG) for a chemical reaction, we can use the equation:
ΔG = -RT ln(K)
Where:
- ΔG represents the standard free energy change in joules (J)
- R is the ideal gas constant, which is equal to 8.314 J/(mol·K)
- T is the temperature in Kelvin (K)
- K is the equilibrium constant of the reaction
In this case, the equilibrium constant (Kc) is given as 9.1 × 10^(-6). However, we need to convert it to Kp, which is the equilibrium constant in terms of partial pressure. For a homogeneous reaction, like the one given, Kp and Kc are related by the equation:
Kp = Kc(RT)^(∆n)
Where ∆n is the difference in the number of moles of gaseous products and gaseous reactants. In this case, the reaction does not involve any gases, so ∆n = 0.
Now, we can calculate the standard free energy change using the given concentrations of the reactants and the equation ΔG = -RT ln(K):
1. Calculate the value of Kp:
Kp = Kc(RT)^(∆n) = Kc (since ∆n = 0)
Kp = 9.1 × 10^(-6)
2. Substitute the values into the equation ΔG = -RT ln(Kp):
ΔG = -(8.314 J/(mol·K)) × (298 K) × ln(9.1 × 10^(-6))
3. Solve the equation to find ΔG:
ΔG = -(8.314 J/(mol·K)) × (298 K) × ln(9.1 × 10^(-6))
ΔG ≈ -8314 × 298 × ln(9.1 × 10^(-6)) J
Calculating this expression will provide the value of ΔG for the given reaction.