Consider the equilibrium A(g)=2B(g)+3C(g) at 25 degrees Celsius. When A is loaded into a cylinder at 10 atm and the system is allowed to come to equilibrium, the final pressure is found to be 12.13 atm. What is the standard gibbs free energy of reaction for this reaction.
To calculate the standard Gibbs free energy of reaction (ΔrG°), you can use the equation:
ΔrG° = -RTln(K)
Where:
- ΔrG° represents the standard Gibbs free energy of reaction
- R is the ideal gas constant (8.314 J/mol·K)
- T is the temperature in Kelvin
- K is the equilibrium constant for the reaction at the given temperature
Given:
- The reaction is A(g) = 2B(g) + 3C(g)
- The equilibrium pressure is found to be 12.13 atm
- The initial pressure of A is 10 atm
To find K, you need to calculate the ratio of the equilibrium concentrations of the products to the reactant, raised to their stoichiometric coefficients. However, we are given pressures instead of concentrations, so we need to convert the pressures to concentrations using the ideal gas law.
The ideal gas law equation is:
PV = nRT
Where:
- P is the pressure
- V is the volume
- n is the number of moles
- R is the ideal gas constant (which is the same as in the Gibbs equation)
- T is the temperature in Kelvin
We'll start by converting the initial and final pressures to concentrations and then using them to calculate K.
Step 1: Convert the initial pressure to concentration
Using the ideal gas law, rearrange the equation to solve for n (number of moles):
n = PV / RT
For A(g):
n_A = (10 atm) * V_A / (R * 298 K) (using 25 degrees Celsius = 298 K)
Step 2: Convert the final pressure to concentration
For each gas component:
n_B = (P_B - P_A) * V / (R * 298 K)
n_C = (P_C - P_A) * V / (R * 298 K)
Step 3: Calculate K
Since K is defined as the ratio of products to reactants, raised to their stoichiometric coefficients, we have:
K = (n_B^2 * n_C^3) / n_A
Step 4: Calculate ΔrG°
Now that you have calculated K, you can use the equation ΔrG° = -RTln(K) to find the standard Gibbs free energy of reaction.
Plug in the values for R (8.314 J/mol·K), T (298 K), and K into the equation to obtain ΔrG°.
ΔrG° = - (8.314 J/mol·K) * (298 K) * ln(K)
Calculate the natural logarithm (ln) of K and multiply it by the remaining values to get ΔrG°.
Note: Make sure to express pressure in the same units when plugging into the equations (e.g., atm).
Please note that this is a general method, and you need to specify the volume and other specific conditions to get a precise value for ΔrG°.
..........A ==> 2B + 3C
I.........10.....0.....0
C.........-x.....2x...3x
E........10-x....2x...3x
Ptotal = 12.13 = 10-x+3x+2x
Solve for x and find pressures of A, B, C; substitute into Kp expression below and solve for Kp.
Kp = p^3C*p^2B/pA
Then dG = -RT*ln*Kp
T is 25C (from standard temperature in the problem.)