Estimate the average values of ΔH and ΔS in this temperature range

[westy6711]

1. The problem statement, all variables and given/known data

The isomerization of 1-butene and trans-2-butene occurs as shown in the table at selected temperatures. Estimate the average values of ΔH and ΔS in this temperature range.

T/Kelvins.............K
883................. 1.10
826................. 1.20
779................. 1.36
733................. 1.49
702..................1.63
686..................1.72




3. The attempt at a solution

ΔG = -RTinK

ΔG = - 8.314x883 x ln1.10 = 699.697 = 6.99697 J/mol

ΔH = ln(1.10 ÷1.72) x (1÷883)-(1/686) = 0.447014111 ,

669.697 = ΔH - TΔS

ΔG = ΔH - TΔS

Thats all ive managed so far, and im sure its wrong. Can someone help me out please, ive been trying for hours!

Many thanks

[cheme101]

You're on the right track.

You have two unknowns, ΔH & ΔS - they should remain constant at all temperatures within the given range (hence the "average" specification).

So you need two equations, at minimum. If you repeat your calculation for another temperature, that will give you (where d = delta):

dG (at T1) = dH - T1*dS
dG (at T2) = dH - T2*dS

2 equations, two unknowns. Solve for dH & dS.

To be more precise, you can do the calculation for all values (use excel or something) and graph dG vs T. The slope of that graph will be -dS, and the y-intercept will be dH. Be sure to keep your units consistent!

Edit: Actually, I think you definitely need to do the graphical method since they specify 'average'