1. 1 “ICE” CALCULATIONS

2. 2 THE EQUILIBRIUM CONSTANT a A + b B ---> c C + d D (at a given T). Pure substances are not included in equation.

3. 3 H + (aq)+ OH - (aq)  H 2 O(l) WRITE THE EQUILIBRIUM CONSTANT EXPRESSION CaO (s) + CO 2 (g)  CaCO 3 (s) K =

4. 4 Typical Calculations PROBLEM: Place 1.00 mol each of H 2 and I 2 in a 1.0 L flask. Calc. equilibrium concentrations. H 2 (g) + I 2 (g)  2 HI(g) X X  2 X Q = 0/1 2 = 0 --+

5. 5 H 2 (g) + I 2 (g)  2 HI(g) K c = 55.3 Step 1. Set up ICE table [H 2 ][I 2 ][HI] Initial 1.001.000 Change Equilib

6. 6 [H 2 ][I 2 ][HI] Initial 1.001.000 Change-x-x+2x Equilib1.00-x1.00-x2x where x is defined as am’t of H 2 and I 2 consumed on approaching equilibrium. Step 2. define “X”

7. 7 H 2 (g) + I 2 (g) e 2 HI(g) K c = 55.3 Step 3. Put equilibrium concentrations into K c expression.

8. 8 [H 2 ] = [I 2 ] = 1.00 - x = 0.21 M [HI] = 2x = 1.58 M [H 2 ] = [I 2 ] = 1.00 - x = 0.21 M [HI] = 2x = 1.58 M Step 4. Solve K c expression - take square root of both sides. x = 0.79 Therefore, at equilibrium H 2 (g) + I 2 (g) ---> 2 HI(g) K c = 55.3

9. 9 Pg 132 CPSC

10. 10 Nitrogen Dioxide Equilibrium N 2 O 4 (g) ---> 2 NO 2 (g)  X 2X

11. 11 Nitrogen Dioxide Equilibrium N 2 O 4 (g) ---> 2 NO 2 (g) If initial concentration of N 2 O 4 is 0.50 M, what are the equilibrium concentrations? Step 1. Set up an ICE table [N 2 O 4 ][NO 2 ] Initial0.500 Change Equilib

12. 12 Step 2. Define “X” [N 2 O 4 ] [NO 2 ] Initial 0.50 0 Change-x+2x Equilib 0.50 - x 2x Nitrogen Dioxide Equilibrium N 2 O 4 (g) ---> 2 NO 2 (g)

13. 13 Step 2. Define “X” [N 2 O 4 ] [NO 2 ] Initial 0.50 0 Change-x+2x Equilib 0.50 2x APPROXIMATE: K is small: x will be small

14. 14 Step 3. Substitute into K c expression and solve. Rearrange: 0.0059 (0.50) = 4x 2 0.0029 = 4x 2 0.0029/4 = x 2 X = 0.027 Step 4. check if assumption is correct 0.50 – 0.027 = 0.47 same?

15. 15 Step 3. Substitute into K c expression and solve. Rearrange: 0.0059 (0.50 - x) = 4x 2 0.0029 - 0.0059x = 4x 2 4x 2 + 0.0059x - 0.0029 = 0 This is a QUADRATIC EQUATION ax 2 + bx + c = 0 a = 4b = 0.0059 c = -0.0029

16. 16 Solve the quadratic equation for x. ax 2 + bx + c = 0 a = 4b = 0.0059 c = -0.0029 x = -0.00074 ± 1/8(0.046) 1/2 = -0.00074 ± 0.027 = -0.00074 ± 0.027

17. 17 Nitrogen Dioxide Equilibrium N 2 O 4 (g) ---> 2 NO 2 (g) x = 0.026 or -0.028 negative value is not reasonable. Conclusion: x = 0.026 M [N 2 O 4 ] = 0.050 - x = 0.47 M [NO 2 ] = 2x = 0.052 M x = -0.00074 ± 1/8(0.046) 1/2 = -0.00074 ± 0.027

18. 18 Solving Quadratic Equations Recommend you solve the equation exactly on a calculator