1. Chemical Equilibrium Some more complicated applications

2. The ICE chart is a powerful tool for many different equilibrium problems But you can’t always make a simplifying assumption, and that means that you may need to do a little algebra

3. A Quadratic Equation A quadratic equation is a 2 nd order polynomial of the general form: a x 2 + b x + c = 0 Where a, b, and c represent number coefficients and x is the variable

4. The Quadratic Formula

5. Equilibrium & the Quadratic Formula If you cannot make a simplifying assumption, many times you will end up with a quadratic equation for an equilibrium constant expression. You can end up with a 3 rd, 4 th, 5 th, etc. order polynomial, but I will not hold you responsible for being able to solve those as there is no simple formula for the solution.

6. A sample problem. A mixture of 0.00250 mol H 2 (g) and 0.00500 mol of I 2 (g) was placed in a 1.00 L stainless steel flask at 430 °C. The equilibrium constant, based on concentration, for the creation of HI from hydrogen and iodine is 54.3 at this temperature. What are the equilibrium concentrations of all 3 species?

7. Determining the concentrations ICE - ICE - BABY - ICE – ICE The easiest way to solve this problem is by using an ICE chart. We just need a BALANCED EQUATION

8. An ICE Chart H 2 (g) + I 2 (g)  2 HI (g)

9. An ICE Chart H 2 (g) + I 2 (g)  2 HI (g) I C E 0.00250 M0.00500 M0 M -x-x-x+2x 0.00250 – x0.00500 – x2x

10. Plug these numbers into the equilibrium constant expression.

11. Assuming x is small…

12. We’re going to have to use the quadratic formula

13. Using the quadratic formula

14. There are 2 roots… All 2 nd order polynomials have 2 roots, BUT only one will make sense in the equilibrium problem x = 0.005736 OR 0.002356 Which is correct? Look at the ICE chart and it will be clear.

15. x = 0.005736 OR 0.002356 H 2 (g) + I 2 (g)  2 HI (g) I C E If x = 0.005736, then the equilibrium concentrations of the reactants would be NEGATIVE! This is a physical impossibility. 0.00250 M0.00500 M0 M -x-x-x+2x 0.00250 – x0.00500 – x2x

16. SO x = 0.002356 H 2 (g) + I 2 (g)  2 HI (g) I C E And you are done! 0.00250 M0.00500 M0 M - 0.002356 +2(0.002356) 0.000144 M0.002644 M0.00471 M

17. ` X IS NOT THE ANSWER X IS A WAY TO GET TO THE ANSWER