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Calculating Equilibrium Concentrations from Initial Concentrations

Calculating Equilibrium Concentrations from Initial Concentrations. Part 1: Perfect Squares Method. Learning Goals. Students will: Determine the equilibrium concentrations of a chemical equilibrium reaction given the initial concentrations. Success Criteria. Students will:

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Calculating Equilibrium Concentrations from Initial Concentrations

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  1. Calculating Equilibrium Concentrations from Initial Concentrations Part 1: Perfect Squares Method

  2. Learning Goals • Students will: • Determine the equilibrium concentrations of a chemical equilibrium reaction given the initial concentrations

  3. Success Criteria • Students will: • Apply a problem solving methodology • Know if they need to determine the reaction quotient (Q) to solve the question • Apply appropriate algebraic skills to solve the problem

  4. Steps in the Process 1) Write the equation and state the K value 2) Determine reaction quotient, Q (if required) 3) Set up an ICE table a) enter initial concentrations b) determine changes in concentration 4) Write K equation 5) Solve for K by entering initial concentrations 6) Use “perfect squares method” to solve for x 7) Find equilibrium concentrations 8) Check answer by plugging calculated equilibrium concentrations into K equation (values should match)

  5. Sample Question • Carbon monoxide reacts with water vapour to produce carbon dioxide and hydrogen. At 900℃, K is 4.200. calculate the concentrations of all entities at equilibrium if 4.000 mol of each entity are initially placed in a 1.000-L closed container.

  6. 1) Write the equation and state the K value • CO(g) + H2O(g)⇔ CO2(g) + H2(g) K = 4.200

  7. 2) Determine reaction quotient, Q (if required) • CO(g) + H2O(g)⇔ CO2(g) + H2(g) K = 4.200 [CO(g)]=[H2O(g)]=[CO2(g)]=[H2(g)] = 4.000mol/L Q = [CO2(g)][H2(g)] = (4.000)(4.000) = 1.000 [CO(g)][H2O(g)] (4.000)(4.000) Q < K ∴ the reaction must move forward to reach equilibrium.

  8. 3) Set up an ICE table a) enter initial concentrations b) determine changes in concentration • Since this reaction must proceed forward to reach equilibrium, the concentrations of CO(g) and H2O(g) must decrease

  9. 4) Write K equation K = [CO2(g)][H2(g)]= 4.200 [CO(g)][H2O(g)]

  10. 5) Solve for K by entering initial concentrations K = [CO2(g)][H2(g)] = 4.200 [CO(g)][H2O(g)] (4.000+x)(4.000+x)= 4.200 (4.000-x)(4.000-x)

  11. 6) Use “perfect squares method” to solve for x (4.000+x)(4.000+x) = 4.200 (4.000-x)(4.000-x) (4.000+x)2= 4.200 (4.000-x)2 (4.000+x)= 2.050 (4.000-x) 4.000+x= 2.050(4.000-x) 4.000+x= 8.200-2.050x 3.050x= 4.200 x= 1.377

  12. 7) Find equilibrium concentrations @ equilibrium: [CO(g)]= 4.000 – x = 4.000 – 1.377 = 2.623 mol/L [CO(g)]=[H2O(g)]= 2.623mol/L CO2(g)]= 4.000 + x = 4.000 + 1.377 = 5.377 mol/L CO2(g)]=[H2(g)] = 5.367mol/L

  13. 8) Check answer • plug calculated equilibrium concentrations into K equation (values should match) K = [CO2(g)][H2(g)] = 4.200 [CO(g)][H2O(g)] K = [5.377][5.377] [2.623][2.623] K = 4.200

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