Equilibrium and Concentration

Equilibrium and Concentration Vocabulary: chemical equilibrium, concentration, equilibrium, equilibrium constant, reaction quotient, reversible reaction Prior Knowledge Questions (Do these BEFORE using the Gizmo.) [Note: The purpose of these questions is to activate prior knowledge and get students thinking. Students are not expected to know the answers to the Prior Knowledge Questions.] Gary has $5,000 in his bank account and earns a modest salary. Every month he pays for rent, food, utilities, and entertainment. A. How will Gary’s account change if he saves more than he spends? It will increase. B. How will Gary’s account change if he spends more than he saves? It will decrease. C. What happens if Gary spends exactly as much as he saves? It will stay the same. Gizmo Warm-up If Gary spends exactly as much as he earns, his savings will be in equilibrium. Equilibrium occurs when two opposing processes occur at the same rate, leading to no net change. In the Equilibrium and Concentration Gizmo™, you will investigate how equilibrium can occur in chemical reactions. To begin, check that Reaction 1 is selected. Set Moles NO2 to 8 and Moles N O to 0. 2 1. Click Play ( 4 ) and observe the colliding molecules. What do you notice? Sample answer: The molecules move and collide. Occasionally there is a blue or red flash. In the Gizmo, a blue flash appears every time two reactants combine to form a product. A red flash appears every time a product dissociates into reactants. 2. Click Reset ( ), and set Moles NO to 0 and Moles N O to 8. Click Play. 2 2 4 What do you notice now? Sample answer: At first, there are more red flashes than blue flashes. 3. When a reaction can proceed in either direction, it is a reversible reaction. Based on what you have observed, is the synthesis of NO into N O a reversible reaction? Explain. 2 2 4 I know the synthesis of NO into N O is a reversible reaction because both the forward reaction (blue flashes) and the reverse reaction (red flashes) are observed. 2 Activity A: Reversible reactions 2 4 Get the Gizmo ready: • Click Reset. Reaction 1 should be selected. • Set Moles NO to 8 and Moles N O to 0. • Move the Sim. speed slider all the way to the right. 2 2 4 Question: What are the characteristics of reversible reactions? 1. Predict: Suppose you began with 8 moles of NO in the chamber. What do you think will 2 happen if you let the reaction go for a long time? Predictions will vary. 2. Test: Click Play. Select the BAR CHART tab and check that Moles is selected. Observe the bar chart for about 30 seconds. As time goes by, what do you notice about the bars representing moles NO and moles N O ? 2 2 4 After a while, the bars don’t move as much as at first. 3. Observe: Click Pause ( ). Select the GRAPH tab. Click the (–) zoom control on the horizontal axis until you can see the whole graph. What do you notice? At first, the amounts of NO and N O change rapidly. After a while the amounts do not change as much. 2 2 4 This situation, in which the overall amounts of reactants and products does not change significantly over time, is called a chemical equilibrium. 4. Record: On the BAR CHART tab, turn on Show data values. How many moles of NO and 2 N O are there right now? Moles NO ~4.0 Moles N O ~2.0 [Exact values will vary.] 2 4 2 2 4 5. Calculate: Suppose all the NO molecules were synthesized into N O . Given the equation 2 2 4 2NO ⇌ N O , how many moles of N O would be produced? 4 moles of N O4 2 2 4 2 4 2 6. Experiment: Click Reset. On the INITIAL SETTINGS tab, set Moles NO to 0 and Moles N O to 4. Click Play. Click Pause when the bars of the bar chart stop moving very much. 2 2 4 A. List the current amounts of each substance: Moles NO ~4.0 Moles N O ~2.0 B. 2 2 4 How do these results compare to starting with 8 moles of NO ? 2 The resulting amounts of NO and N O in this experiment are very similar to the results obtained when starting with 8 moles NO and 0 moles N O . 2 2 4 2 2 4 (Activity A continued on next page) Activity A (continued from previous page) 7. Summarize: In each trial, you started with the same amounts of nitrogen and oxygen. In this situation, did the equilibrium amounts change depending on the direction of the reaction? The equilibrium amounts were about the same in both situations. 8. Set up the Gizmo: Click Reset and select the EXPERIMENT tab on the left. On the INITIAL SETTINGS tab on the right, select Reaction 2. Set Moles NO to 5, Moles NO to 5, and Moles N O to 0. What are the reactants and product of this reaction? 2 2 3 Reactants: NO NO Product: N O3 2 2 (Note: In this reaction, some of the NO reactants combine to form N O , as in reaction 1.) 2 2 4 9. Observe: Recall that a blue flash appears every time two reactants combine to form a product. A red flash appears every time a product dissociates into reactants. Click Play. A. At first, do you notice more blue flashes or red flashes? Blue flashes B. What do you notice about the frequency of blue and red flashes as time goes by? After a while, the frequency of blue and red flashes is about the same. C. Click Reset. This time, start the experiment with 0 moles of NO and NO and 5 moles of N O . Click Play. What do you notice about the red and blue flashes now? 2 2 3 At first, there are more red flashes than blue flashes. Later, the frequencies are even. 10. Explain: Think about how the numbers of blue and red flashes reflect the rates of the forward (reactants 🡪 products) and reverse (products 🡪 reactants) reactions. A. What happens to the rate of the forward reaction as the reactants are consumed? The rate of the forward reaction decreases as reactants are consumed. B. What happens to the rate of the reverse reaction as the products are produced? The rate of the reverse reaction increases as products are produced. C. Why do reversible reactions always result in chemical equilibria? Sample answer: Chemical equilibrium occurs when the rates of the forward and reverse reactions are equal. If there is an excess of reactants, the forward reaction will occur more quickly than the reverse reaction until there is no longer an excess of reactants. At this point the rates of the forward and reverse reactions are equal and equilibrium is reached. The same thing occurs when there is an excess of products. Activity B: Get the Gizmo ready: • Click Reset. Select Reaction 1. • Set Moles NO to 2 and Moles N O to 7. The equilibrium constant 2 2 4 Introduction: When investigating the rates of reactions, it often is useful to consider the concentrations of reactants rather than the total number of moles. Concentrations are often expressed in moles per liter, or mol/L. Brackets are used to signify concentration. For example, “[H ] = 5.0 M” means the concentration of hydrogen gas in a chamber is 5.0 moles per liter. 2 Question: What are the characteristics of reactions in equilibrium? 1. Record: On the BAR CHART tab, select Concentration. Check that Show data values is on. If necessary, use the arrows to adjust the scale of the chart. A. What are the current concentrations of each compound? [NO ] 4.00 M [N O ] 14.00 M 2 2 4 Note: “M” is equivalent to “mol/L” B. Click Play and wait for equilibrium to become established. Click Pause. What are the approximate equilibrium concentrations? [NO ] ~12 M [N O ] ~6 M 2 2 4 2. Calculate: The value K represents the ratio of products to reactants in a reaction at equilibrium. The greater the amount of products relative to reactants, the higher the resulting value of K . For a general reaction between gases: aA(g) + bB(g) ⇌ cC(g) + dD(g), K is calculated as follows: c c c cd [C] [D] = Kc [A] [B] ab For the current reaction, 2NO ⇌ N O , we have: 2 2 4 [N O ] K= c 24 [NO ] 2 2 Based on the current concentrations of NO and N O , what is K ? ~0.042 2 2 4 c [N O ] 6.0 0.042 Show your work here: 24 22 K = == [NO ] 12.0 c 2 [Note: The value of K may vary from 0.025 to 0.065. This variation occurs because the Gizmo model uses a limited number of molecules.] c (Activity B continued on next page) Activity B (continued from previous page) 3. Gather data: Experiment with a variety of initial concentrations of NO and N O . For each set of initial concentrations, use the Gizmo to determine the equilibrium concentrations of each substance. In the last column, find K for that trial. Run three trials for each set of initial conditions. 2 2 4 c Initial [NO ] 2 Initial [N O ] 2 4 Equilibrium [NO ] 2 Equilibrium [N O ] 2 Kc 4 Chosen by student Chosen by student Values will vary Values will vary Chosen by student Chosen by student Values will vary Values will vary ~0.042 ~0.042 Chosen by student Chosen by student Values will vary Values will vary ~0.042 4. Calculate: Find the average value of K for each set of three trials. Check calculations. Trials 1-3: c __________ Trials 4-6: __________ Trials 7-9: __________ 5. Analyze: What do you notice about the values of K ? c No matter what initial concentrations are chosen, the value of K stays relatively constant. c In general, the value of K will be constant for a given reaction at a constant temperature, no matter the starting concentrations. That is why K is known as the equilibrium constant. In this Gizmo, the values of K will vary somewhat because there is a very limited number of molecules in the chamber. c c c 6. On your own: Use the Gizmo to find K for Reaction 4: H + I ⇌ 2HI. Collect data at least 10 times and average your results to get the best approximation of K . Show your data and work on a separate sheet of paper. c 2 2 c (Hint: Because of the coefficient “2” in front of HI, you will have to square the concentration of HI to find K .) c K = ~40 [Check student work. For this reaction, you can expect values of K to vary between 20 and 60.] c c 7. Activity C: Reaction direction Get the Gizmo ready: • Click Reset. Check that Reaction 4 is selected. • Set Moles H to 5, Moles I to 5, and Moles HI to 3. 2 2 Introduction: For a reversible reaction with equilibrium constant K , it often is useful to know in which direction the reaction will proceed given the starting amounts of reactants A and B and products C and D. This is done by calculating the reaction quotient, Q : c c cd [C] [D] = Qc [A] [B] ab Question: How can you predict the direction of a reversible reaction? 1. List: Select the BAR CHART tab. What are the initial concentrations of each substance? [H ] 9.23 M [I ] 2 2 9.23 M [HI] 5.54 M 2. Calculate: Use the equation above to find Q for the current reaction. A. c What is the current value of Q ? 0.36 c B. In activity B, what value of K did you arrive at for this reaction? ~40 [Check student results] c C. How does Q compare to K ? Q is less than K . c c c c 3. Analyze: Recall that Q is equal to the ratio of product concentrations to reactant concentrations. c A. If there is an excess of products, will Q be greater than or less than K ? Greater c c B. If there is an excess of reactants, will Q be greater than or less than K ? Less C. c c In the current situation, is there an excess of products or reactants? Reactants Explain: Q is less than K , so there is an excess of reactants. c c D. When the reaction begins, do you expect [HI] to increase or decrease? Increase Explain: There is an excess of reactants. HI is a product, so it will increase as the reaction proceeds. 4. Test: Click Play. What happens to [HI]? [HI] increases. [Note: [HI] may decrease in the first instant but will eventually increase.] Extension: Get the Gizmo ready: Equilibrium calculations • Click Reset. Select Reaction 1. • Set Moles NO to 0 and Moles N O to 6. 2 2 4 Goal: Given K and initial concentrations, calculate equilibrium concentrations. 1. List: c Select the BAR CHART. What is the initial concentration N O ? [N O ] 2 4 2 4 initial = 18.00 M 2. Experiment: Click Play and wait for a few seconds. Click Pause before equilibrium is reached. Note: Student results will vary. Sample answers are shown to illustrate the relationship. A. What is the current concentration of N O ? [N O ] = 11.93 M 2 4 2 4 B. How much has the concentration of N O gone down? 6.07 M 2 4 C. What is the current concentration of NO ? [NO ] = 6.07 M 2 2 D. In general, if [N O ] is reduced by x, how much does [NO ] increase? x 2 4 2 This result may be surprising. It is true because at constant pressure, the overall density of particles in the container remains constant. So, if the concentration of one substance is reduced by x, the concentration of the other substance increases by x. cd [C] [D] 3. Manipulate: Begin with the general equation for K : c =. ab Kc [A] [B] [N O ] O ⇌NO? K = 2 2 4 c 24 2 [NO ] 2 B. In this experiment, the initial concentration of NO is zero. If the concentration of N O is reduced by x at equilibrium, the equilibrium concentration of NO is equal to x. Substitute the following values into the equation you wrote in step A: 2 2 4 2 [N O ] = ([N O ] 2 4 2 4 initial – x) [NO ] = x 2 − [N O ] x initial K= c 24 2 x C. In activity A, you discovered that K for this reaction was close to 0.042. Substitute this value and the initial concentration of N O into your equation. c 2 4 18.00 x 0.042 = x − 2 D. Rearrange the terms of your equation to form a quadratic equation in the form ax + bx + c = 0. 0.042 x + x – 18.00 = 0 2 2 (Extension continued on next page) Extension (continued from previous page) 4. Solve: Because the equation is in the form ax + bx + c = 0, you can use the quadratic formula (shown below) to solve for x. Ignore negative solutions because the concentrations cannot be negative. Show your work. 2 x 4 2 2− ±− = a = 0.042, b = 1, c = -18.00 b b ac a 2 1 1 4 0.042 ( 18.0) 1 1 3.024 1 4.024 1 2.006 11.98 x− ± − ⋅ ⋅− −± + −± −+ = = = == ⋅ 2 0.042 0.084 0.084 0.084 5. Predict: Based on the value for x, what do you expect the equilibrium concentrations of NO2 and N O to be? 2 4 [NO ] 11.98 M [N O ] 6.02 M 2 2 4 [N O ] K = K = 0.042 c c 24 Check your work by solving for K using c 2 [NO ] 2 If you don’t get the correct value of K , recheck your work. c 6. Test: Click Play and wait for equilibrium to be established. What are the actual equilibrium values of each substance? Sample results: [NO ] 12.18 M [N O ] 5.82 M 2 2 4 How close were these results to your predicted results? Answers will vary. [Results should be relatively close to predicted results given the variation in the Gizmo.] 7. Challenge: Suppose you begin with 6 moles of NO and 5 moles of N O . Assuming a value for K of 0.042, predict the equilibrium concentrations of NO and N O . (Use the Gizmo to determine the initial concentrations.) Show your work on a separate sheet of paper. After you have made your predictions, click Play and record the experimental results. 2 2 c 2 2 4 Predicted: [NO ] 11.98 M [N O ] 6.02 M 2 2 4 Experimental: [NO ] Answers will vary [N O ] Answers will vary 2 [Solution is shown on next page.] 2 4 4 Initial concentrations: [NO ] = 9.82 M, [N O ] = 8.18 M x x x KOx x x 2 2 4 x − − − == = = + + + + [N O ] 8.18 8.18 0.042[N ] 9.82 96.4324 19.64 initial c 24 22 2 ()() 2 initial 2 0.042(96.4324 19.64 ) 8.18 + += − x x x 2 4.050 0.825 0.042 8.18 + + =− x x x 2 0.042 1.825 4.13 0 x x + −= a = 0.042, b = 1.825, c = -4.13 Using the quadratic formula, we have: 2 1.825 1.825 4 0.042 ( 4.13) 1.825 3.331 0.694 x− ± − ⋅ ⋅− −± + = = ⋅ 2 0.042 0.084 −± −+ = == 1.825 4.025 1.825 2.006 2.16 0.084 0.084 Recall the initial concentrations: [NO ] = 9.82 M, [N O ] = 8.18 2 M If x = 2.16, then: Equilibrium [NO ] = 9.82 + 2.16 = 11.98 M 2 Equilibrium [N O ] = 8.18 – 2.16 = 6.02 M 2 4 2 4