Lecture 19sf

Lecture 19sf - Temperature Dependence of K o o o G = H - T...

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Temperature Dependence of K G o = H o - T S o = -RT ln K Dividing both sides by -RT and rearranging: ln K = - Τ ∆Η ο R + R S ο Compare: y = mx + b (straight line equation) where y = ln K and x = Plot ln K vs and get a straight line. The slope of the line = - R ο ∆Η and the y-intercept = R S ο This slope will be positive or negative depending on the sign of H. Suppose the plot of ln K vs gives a positive slope. Since the slope - R ο ∆Η , a positive slope implies H is negative (exothermic reaction). A positive slope also means: As ln K increases, increases As ln K increases, T decreases As K increases, T decreases As K decreases, T increases This is consistent with LeChatelier’s principle, which implies that for an exothermic reaction, a lower temperature will shift the reaction to the right leading to a higher value of K, or conversely, a higher temperature will shift the reaction to the left, leading to a lower value of K. To compare two temperatures and two equilibrium constants:
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ln K 2 = - 2 R Τ ∆Η ο + R S ο ln K 1 = - 1 R Τ ∆Η ο + R S ο Subtracting the second equation from the first: ln K 2 – ln K 1 = - R ο ∆Η ( 2 T 1 - 1 T 1 ) This is equivalent to: ln 1 2 K K = R ο ∆Η ( 1 T 1 - 2 T 1 ) or ln 1 2 K K = R ο ∆Η ( 2 1 1 2 T T T T - ) N 2 (g) + 3H 2 (g) 2NH 3 (g) K = 6.0 x 10 5 at 298.15 K. What is value of K at 600 K? For this reaction, H o = -92.22 kJ G o = -32.96 kJ S o = -198.7 J/K ln 1 2 K K = R ο ∆Η ( 1 T 1 - 2 T 1 ) ln 5 10 x 0 . 6 x = 314 . 8 220 , 92 - ( ) 15 . 298 )( 600 ( 15 . 298 600 - ) Solving: x = 4.46 x 10 -3 Alternate method:
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G o = -RT ln K G o = -32.98 kJ at 298 K. But this value will change at other temperatures. G o = H - T S o AT 600 K: G o = -92.220 -600( 1000 7 . 198 - ) = +27.0 kJ Note that reaction is spontaneous in the reverse direction at this high temperature. +27.0 = - ln K
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This note was uploaded on 04/22/2008 for the course CHEM 162 taught by Professor Siegal during the Spring '08 term at Rutgers.

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Lecture 19sf - Temperature Dependence of K o o o G = H - T...

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