The power of the equation ΔG° = –RT ln(K) is that K can be determined from tabulated values of ΔG°f. Use the tabulated values of the Gibb's energy to determine K for the reaction, 2AB(l) ↔ 2A(g) + B2(g), at 298K.
(R=8.314 J/K mol or R=0.008314 kJ/K mol)
ΔGfº (kJ/mol)
A(g)=53
B2(g)=-114
AB(l)=162
2AB(l) ↔ 2A(g) + B2(g)
I have been working on this for awhile and i can't seem to get the right answer. I have tried finding the sum of the products minus the sum of the reactants to find what ΔG. Then taking e^(-ΔG/RT) to find the value for K.
From your description I can't tell what you did wrong. If you post your work I will find the error.
A common student error is to use kJ for dGo. You must use dGo in J (unless of course you change R).
ΔG= (2x53 + -114) - (2x162)= -332
K=e^(-332/(.008314x298)= 6.36 e-59
I have also tried using 8.314 as the value for R
Isn't that e^(-dG/RT). If dG is -332,000 then the rxn should be spontaneous and K should be a large number and not a small number.
dGo = -RTlnK
-dGo = RTlnK
(332000/8.314*298)= lnK
To determine K using the tabulated values of Gibbs energy (ΔG°f), you need to follow a specific set of steps. Here's how you can solve this problem:
Step 1: Write out the balanced equation for the reaction.
2AB(l) ↔ 2A(g) + B2(g)
Step 2: Determine the values of ΔG°f for each species involved in the reaction.
ΔG°)) = 53 kJ/mol
ΔG°f(B2(g)) = -114 kJ/mol
ΔG°f(AB(l)) = 162 kJ/mol
Step 3: Calculate the Gibbs energy change (ΔG°) for the reaction.
ΔG° = (2 × ΔG°)) + ΔG°f(B2(g))) - (2 × ΔG°f(AB(l)))
= (2 × 53 kJ/mol + (-114 kJ/mol)) - (2 × 162 kJ/mol)
= (-208 kJ/mol) - (324 kJ/mol)
= -532 kJ/mol
Step 4: Convert the ΔG° value to joules and calculate the value of K.
Since R = 8.314 J/K mol, we need to convert ΔG° to joules by dividing by 1000.
ΔG° = -532 kJ/mol = -532,000 J/mol
Next, plug the values into the equation ΔG° = -RT ln(K) and solve for K.
-532,000 J/mol = -(8.314 J/K mol)(298 K) ln(K)
Now rearrange the equation to solve for K:
K = e^(-ΔG° / (RT))
K = e^(-(-532,000 J/mol) / ((8.314 J/K mol)(298 K)))
Using a scientific calculator or an online calculator, evaluate the expression to find the value of K.