A plot of ln(Keq) vs 1/T had the following parameters: slope = 8744 K-1 y-intercept = -61.91 Determine the value of Δ Δ Horxn and Δ Δ Gorxn for this reaction at 298 K.

Question

The reaction ClO(g) + ClO(g) ⟷ ⟷ ClOOCl(g) is important in polar stratospheric chemistry because the ClO dimer sequesters chlorine in the polar vortex that forms over Antarctica during the southern winter. When the sun comes up in the austral Spring, ClO dimer photolyzes, releasing chlorine atoms which then react rapidly with ozone to form the Antarctic ozone hole in mid-September. The value of the equilibrium constant for the above reaction was measured over a range of temperatures.

Answer 1

The plot of ln (K_eq) vs 1/T provides you with two important pieces of information: the enthalpy of the reaction, ΔH_rxn, and the entropy of the reaction, ΔS_rxn. The slope of this plot will give you -ΔH_rxn/R while the y-intercept will give you ΔS_rxn/R. Equipped with both of those values and the temperature, you can find ΔG_rxn pretty quickly using the formula ΔG_rxn = ΔH_rxn - TΔS_rxn. Try it first given the information I just provided, and then continue along if you get stuck.

1. First let's find the enthalpy, ΔH_rxn. The slope of the plot will give you -ΔH_rxn/R, where R is the constant 8.314 J/mol·K. If the slope is 8744 K^-1, we can plug in like this:

8744 K^-1 = -ΔH_rxn/8.314 J/mol·K

Next, we can use algebra to rearrange the equation to get ΔH_rxn alone,

8744 K^-1 x 8.314 J/mol·K = -ΔH_rxn

Then we can see how the K will cancel out, and if we divide both sides by -1 to really isolate a

value for ΔH_rxn, we get:

-72,697.616 J/mol = ΔH_rxn

*If the question is asking us to stop and report an answer here, we should probably change the

unit to kJ so it's not so large. Just divide by 1000 to get this, as -72.697 kJ/mol. If we want to

round for significant figures, we should use 4 sig figs, so -72.70 kJ/mol would be the ΔH_rxn.

1. Next, let's find the entropy, ΔS_rxn. The y-intercept of the plot will give you ΔS_rxn/R, where R is the constant 8.314 J/mol·K. If the y-intercept value is -61.91, we can plug in like this:

-61.91 = ΔS_rxn/8.314 J/mol·K

Doing similar algebra from step 1, we find that:

-61.91 x 8.314 J/mol·K = ΔS_rxn

And thus, ΔS_rxn = -514.719 J/mol·K

1. Lastly, let's find the ΔG_rxn. Using the values found in the previous steps plus the temperature given in the problem, we can plug into the equation ΔG_rxn = ΔH_rxn - TΔS_rxn like this:

First, let's make sure all the units are the same for the enthalpy, entropy, and temperature values.

ΔH_rxn = -72,697.616 J/mol *keep this one in J to match the entropy)

ΔS_rxn = -514.719 J/mol·K

and T = 298 K (given in the question)

Now we can plug in to get ΔG_rxn!

ΔG_rxn = ΔH_rxn - TΔS_rxn

ΔG_rxn = (-72,697.616 J/mol) - (298 K)(-514.719 J/mol·K)

ΔG_rxn = 80,688.646 J/mol (the K canceled out)

If we want to represent our answer in units that make a little more sense, we can change J to kJ. So ΔG_rxn becomes 80.688646 kJ/mol. And if we want to round to 4 significant figures due to the given values, we can use 80.69 kJ/mol as our ΔG_rxn.

Note: The significant figures are perhaps a little more complicated than that due to the subtraction, but for any multiple-choice question or most instructors, 4 should be fine here.