Temperature
dependence of K
Chemistry 201
NC State University
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Temperature
dependence of K
Chemistry 201
NC State University
N
2
O
4
(g) 2 NO
2
(g)
∆H
o
= +58.20 kJ ∆S
o
= +176.6 J/K
At what temp. does ∆G
o
(K = 1)
N
2
O
4
(g) 2 NO
2
(g)
∆H
o
= +58.20 kJ ∆S
o
= +176.6 J/K
At what temp. does ∆G
o
(K = 1)
N
2
O
4
(g) 2 NO
2
(g)
∆H
o
= +58.20 kJ ∆S
o
= +176.6 J/K
At what temp. does ∆G
o
(K = 1)
N
2
O
4
(g) 2 NO
2
(g)
∆H
o
= +58.20 kJ ∆S
o
= +176.6 J/K
What is K at 425 K?
N
2
O
4
(g) 2 NO
2
(g)
∆H
o
= +58.20 kJ ∆S
o
= +176.6 J/K
What is K at 425 K?
N
2
O
4
(g) 2 NO
2
(g)
∆H
o
= +58.20 kJ ∆S
o
= +176.6 J/K
What is K at 425 K?
Remember to convert ∆H
o
to units of J (multiply by 1000)
H 2 (g) +
/ 2 O 2 (g) H 2 O (g) ∆H o = -241.82 kJ ∆S o = -44.38 J/K At what T, if any, does K = 1?
H 2 (g) +
/ 2 O 2 (g) H 2 O (g) ∆H o = -241.82 kJ ∆S o = -44.38 J/K Evaluate K at 1500 K.
H 2 (g) +
/ 2 O 2 (g) H 2 O (g) ∆H o = -241.82 kJ ∆S o = -44.38 J/K Evaluate K at 1500 K.
H 2 (g) +
/ 2 O 2 (g) H 2 O (g) ∆H o = -241.82 kJ ∆S o = -44.38 J/K Evaluate K at 1500 K. 𝐾𝐾 = 𝑒𝑒𝑒𝑒𝑒𝑒 − ∆𝐺𝐺 𝑜𝑜 𝑅𝑅𝑅𝑅 = 𝑒𝑒𝑒𝑒𝑒𝑒 − −176,000 𝐽𝐽 8.31 𝐽𝐽 𝐾𝐾⁄ )(1500 𝐾𝐾
6
The temperature dependence of ∆G o As we have shown previously, ∆G, will decrease until it reaches 0. Then we have reached equilibrium. The equilibrium condition is ∆G o = -RT ln K Next we consider the fact that we can use the temperature dependence of the free energy to obtain information about the enthalpy. ∆H o
- T∆S o = -RT ln K If we assume that ∆H o and ∆S o are independent of temperature, then we can obtain the values of K at two temperatures as follows, ∆H o
- T 1
∆S
o = -RT 1 ln K 1 ∆H o
- T 2
∆S
o = -RT 2 ln K 2
The temperature dependence of ∆G o The subtracted equation is: ln 𝐾𝐾 2 − ln 𝐾𝐾 1 = −
𝑜𝑜 𝑅𝑅𝑅𝑅 2
𝑜𝑜 𝑅𝑅𝑅𝑅 1 Finally we factor the equation to obtain ln
𝑜𝑜 𝑅𝑅
This is known as the van’t Hoff equation. This equation says that if we plot ln(K) vs 1/T, we obtain a line, and the slope of that line is −∆H o /R.
2 NO
2
(g) 2 NO (g) + O
2
(g)
T
1
at 190 K K
1
T
2
at 200 K K
2
find ∆H
o
and ∆S
o Using equilibrium data to obtain ∆H o and ∆S o