Calculate the equilibrium constant at 25°C and at 100.°C for each of the following reactions, using data available in Appendix 2A. Remember that the organic molecules are in a separate section behind the organic molecules in Appendix 2A.
(a) HgO(s) Hg(l) + O2(g)
at 25°C
Found to be 5.47E-11 which is correct
at 100.°C
(b) propene (C3H6, g) cyclopropane (C3H6, g)
at 25°C
Found to be 5E-8 which is correct
at 100.°C
I used text to find the Gibbs of formation for each reactant & product to find the Gibbs of reaction. I then used G=-RTlnK to solve for K. I was successful in solving for K for the 25°C temps in both cases, but for some reason the 100.°C answers were incorrect. I thought I only had to plug in the new temp (as 373K) into the equation??
I'm not positive I understand exactly; however, the delta G you are looking up is for 25 C. It is not for 100 C. I suspect that is your problem. Can you correct for that by using delta G = delta H - T*delta S.
I figured out what I was doing...I ended up using the Van't Hoff Equation and the enthalpies of formation to solve for K at 100 C. This stuff is so time consuming...
To calculate the equilibrium constant at different temperatures, you need to use the Van 't Hoff equation, which relates the equilibrium constant (K) to the change in Gibbs free energy (ΔG) with respect to temperature.
The equation is given by:
ln(K2/K1) = ΔH/R * (1/T1 - 1/T2)
Where K1 and K2 are the equilibrium constants at temperatures T1 and T2 respectively, ΔH is the enthalpy change of the reaction, R is the universal gas constant (8.314 J/(mol·K)), and T1 and T2 are the respective temperatures in Kelvin.
Now, let's apply this equation to the given reactions:
(a) HgO(s) → Hg(l) + O2(g)
First, find the Gibbs free energy change (ΔG) for the reaction using the values from Appendix 2A at 25°C (298K). The values for HgO(s), Hg(l), and O2(g) will be given in the table. Subtract the sum of the Gibbs free energies of the reactants from the sum of the Gibbs free energies of the products to calculate ΔG.
Next, rearrange the Van 't Hoff equation to solve for ln(K2/K1):
ln(K2/K1) = ΔG/R * (1/T1 - 1/T2)
Substitute the values of ΔG (calculated in the previous step), R (8.314 J/(mol·K)), T1 (298K) and T2 (373K) into the equation.
Take the natural logarithm of both sides of the equation to solve for ln(K2/K1). Then, exponentiate both sides to find K2/K1.
Finally, multiply K1 by K2/K1 to get K2.
This process will give you the equilibrium constant (K2) at 100°C for the reaction HgO(s) → Hg(l) + O2(g). Repeat the same process for the second reaction (b) propene (C3H6, g) → cyclopropane (C3H6, g).
Make sure to use the correct Gibbs free energy values for each substance at the specified temperature (25°C or 100°C) from Appendix 2A.