Thermodynamic Connection

1
Thermodynamic Connection

• Q and G and letters other than K

2
Reaction Quotient

• What do you call an equilibrium constant when you
  arent at equilibrium?
• A Reaction Quotient! (Q)

3
Consider

• 1 mole of Hydrogen, 2 moles of Oxygen, and 1 mole
  of water are mixed in a 2 L flask at 800 K. The
  equilibrium constant for the formation of steam
  at 800 K is 1.6 x 10-6. Find the equilibrium
  concentrationsyada yada yada

4
Lets just set it up

• 2 H2 (g) O2 (g) ? 2 H2O (g)
• Initial
• Change
• Equilibrium
• M is preferable if Im going to solve the K
  expression for equilibrium

1 mol/2L 0.5 M 2 mol/2L 1 M 1 mol/2L 0.5 M


5
Lets just set it up

• 2 H2 (g) O2 (g) ? 2 H2O (g)
• Initial
• Change
• Equilibrium
• We dont need to know the sign, itll all come
  out in the solution, but is there a way to
  know???

0.5 M 1 M 0.5 M
2 x ??? 2x X ??? x 2 x ??? -2x

6
Q tells us where we are

• Q products NOT at equilibrium
• reactants NOT at equilibrium
• In this case
• Q H2O2 (0.5 M)2 1
• H22O2 (0.5 M)2(1 M)

7
What does the Q1 mean?

• How should we evaluate Q?
• Q is just K when I havent gotten to K, so Q is
  trying to become K.
• Compare Q to K
• K 1.6x10-6 at this temperature

8

• Q 1
• K 1.6 x 10-6
• Q is too BIG
• Q products products is too big!
• reactants
• Reaction must go left to get rid of the products
  to reach equilibrium.

9
Q vs. K

• If QgtK, too many products, reaction goes left.
• If QltK, too many reactants (too few products),
  reaction goes right.
• If Q Keverything is just right!

10
Too many products, so

• 2 H2 (g) O2 (g) ? 2 H2O (g)
• Initial
• Change
• Equilibrium
• So, we can determine the sign of the change if we
  want to!

0.5 M 1 M 0.5 M
2x x -2x

11
K in context

• Weve talked about a number of different realms
  of Chemistry.
• Kinetics How fast?
• Thermodynamics How stable? How hot?
• Equilibrium???

12
Equilibrium and Thermodynamics

• Would it surprise you to know that Equilibrium
  represents the thermodynamic balance between the
  products and the reactants?
• Equilibrium tells us what the balance should be,
  but says nothing about how fast (kinetics) it
  takes to get there.

13
Gibbs Free Energy

• Gibbs Free Energy is the most important
  thermodynamic variable it balances enthalpy and
  entropy.
• ?G ?H - T?S
• If ?G lt 0, what does that mean?
• Reaction is spontaneous as written.
• If ?G gt 0, what does that mean?
• Reaction is spontaneous in the reverse direction.

14

• ?G sounds a lot like Q!

15
K (Q) is related to ?G

• If ?G lt 0, reaction is spontaneous as written (to
  right).
• If ?G gt 0, reaction is spontaneous in the reverse
  direction (to left).
• If QgtK, reaction goes left.
• If QltK, reaction goes right.
• If Q K, were at equilibrium. At equilibrium,
  ?G 0!!!

16
As a reaction proceeds, what happens

• You make products from reactants (or make
  reactants from products) until equilibrium is
  reached.
• Assume QltK, what does that mean?
• Reaction wants to to the right. So ?G?
• ?G lt 0
• Eventually, you reach equilibrium, Q K. ?G0
• ?G must depend on concentration!!!

17
?G is naughty

• Whats the difference between ?G and ?G0?
• ?G0 is at standard conditions
• 1. 298 K
• 2. 1 atm
• 3. Stoichiometric quantities of everything
• ?G is at any arbitrary conditions

18
How does ?G depend on concentration?

• ?G ?G0 RT ln Q
• RT ln Q is the correction factor for
  concentration
• This also gives us a way to calculate K!
• When we reach equilibrium Q K!
• When we reach equilibrium ?G 0!

19
How does ?G depend on temperature?

• ?G ?G0 RT ln Q
• 0 ?G0 RT ln K
• ?G0 - RT ln K
• ?G0 ?H0 - T?S0 - RT ln K

20
Sample Problem

• What is the equilibrium constant for the
  following reaction at 250 ºC?
• CO (g) 2 H2 (g) ? CH3OH (g)
• ?H0 - T?S0 - RT ln K
• ?H0 Hf0 (products) Hf0 (reactants)
• ?S0 Sf0 (products) Sf0 (reactants)

21
Sample Problem

• What is the equilibrium problem for the following
  reaction at 250 ºC?
• CO (g) 2 H2 (g) ? CH3OH (g)
• ?H0 Hf0 (products) Hf0 (reactants)
• (-201.0 kJ) (-110.5 kJ 2(0))
• -90.5 kJ
• ?S0 Sf0 (products) Sf0 (reactants)
• (239.9 J/K) (197.7 J/K 2(130.7 J/K))
• - 219.2 J/K

22
Sample Problem

• What is the equilibrium problem for the following
  reaction at 250 ºC?
• CO (g) 2 H2 (g) ? CH3OH (g)
• ?H0 - T?S0 - RT ln K
• -90.5 kJ (250 273.15 K)(-219.2 J/K) -RT ln K
• -90.5 x 103 J 523.15 K(-219.2 J/K) -RT ln K
• 24, 174.5 - (8.314 J/mol K) (523.15 K) ln K

23
Sample Problem

• What is the equilibrium problem for the following
  reaction at 250 ºC?
• CO (g) 2 H2 (g) ? CH3OH (g)
• 24,174.5 J - (8.314 J/mol K) (523.15 K) ln K
• -5.56 ln K
• K e-5.56 3.85x10-3

24
Clicker Question

• What is the K for our favorite reaction at 25º C
• 2 H2 (g) O2 (g) ? 2 H2O (g)
• A. 9.02
• B. 1.38x1080
• C. 1.18x1040
• D. 1.20
• E. Dont know/Dont care

25
Clicker Question

• What is the K for our favorite reaction at 1000
  K
• 2 H2 (g) O2 (g) ? 2 H2O (g)
• A. 9x109
• B. 2.4404x10-21
• C. 4.0976x1020
• D. 1.0486
• E. Dont know/Dont care