The Equilibrium State

Transcription

1 15.1 The Equilibrium State All reactions are reversible and under suitable conditions will reach a state of equilibrium. At equilibrium, the concentrations of products and reactants no longer change because the rates of the forward and reverse reactions are equal. At equilibrium: rate forward = rate reverse Chemical equilibrium is a dynamic state because reactions continue to occur, but because they occur at the same rate, no net change is observed on the macroscopic level. 15-1

2 Figure 15.1 Reaching equilibrium on the macroscopic and molecular levels. 15-2

3 The Equilibrium Constant Consider the reaction N 2 O 4 (g) 2NO 2 (g) At equilibrium rate fwd = rate rev so k[n 2 O 4 ] eq = k[no 2 ] 2 eq then k fwd 2 = [NO 2 ] eq k rev [N 2 O 4 ] eq The ratio of constants gives a new constant, the equilibrium constant: K = k fwd 2 eq = [NO 2 ] k rev [N 2 O 4 ] eq 15-3

4 K and the extent of reaction K reflects a particular ratio of product concentrations to reactant concentrations for a reaction. K therefore indicates the extent of a reaction, i.e., how far a reaction proceeds towards the products at a given temperature. A small value for K indicates that the reaction yields little product before reaching equilibrium. The reaction favors the reactants. A large value for K indicates that the reaction reaches equilibrium with very little reactant remaining. The reaction favors the products. 15-4

5 Figure 15.2 The range of equilibrium constants 15-5 small K The reaction mixture contains mostly reactants. large K The reaction mixture contains mostly products. intermediate K

6 15.2 The Reaction Quotient Q For the general reaction the reaction quotient Q = [C]c [D] d [A] a [B] b Q gives the ratio of product concentrations to reactant concentrations at any point in a reaction. At equilibrium: Q = K For a particular system and temperature, the same equilibrium state is attained regardless of starting concentrations. The value of Q indicates how close the reaction is to equilibrium, and in which direction it must proceed to reach equilibrium. 15-6

7 Figure 15.3 The change in Q during the N 2 O 4 -NO 2 reaction. 15-7

8 Table 15.1 Initial and Equilibrium Concentration Ratios for the N 2 O 4 -NO 2 System at 200 C (473 K) Initial Equilibrium Expt [N 2 O 4 ] [NO 2 ] Q, [NO 2 ] 2 [N 2 O 4 ] eq [NO 2 ] eq K, [N 2 O 4 ] 2 [NO 2 ] eq [N 2 O 4 ] eq

9 Sample Problem 15.1 Writing the Reaction Quotient from the Balanced Equation Problem:Write the reaction quotient, Q, for each of the following reactions: (a) The decomposition of dinitrogen pentoxide, N 2 O 5(g) NO 2(g) + O 2(g) (b) The formation of cobalt hexamine in solution, Co 3+ (aq) + 6 NH 3(aq) Co(NH 3 )3+ (aq) (c) The reaction between fluorine gas and tin ion in solution: F 2(g) +Sn 2+ (aq) 2F- (aq) +Sn 4+ (aq) PLAN: Write balance the equations and then construct the reaction quotient. SOLUTION: (a) N 2 O 5(g) NO 2(g) + O 2(g ) (b) Co 3+ (aq) + 6 NH 3(aq) Co(NH 3 )3+ (aq) Q = P NO2.P O2 P N2O5 Q = [Co(NH 3 ) 3+ ] [Co 3+ ][NH 3 ] 6 (c) F 2(g) +Sn 2+ (aq) 2F- (aq) +Sn 4+ (aq) Q = [F - ] 2 [Sn 4+ ( ] [P F2 ][Sn 2+ ] 15-9

10 Forms of K and Q For an overall reaction that is the sum of two more individual reactions: Q overall = Q 1 x Q 2 x Q 3 x.. and K overall = K 1 x K 2 x K 3 x The form of Q and K depend on the direction in which the balanced equation is written: Q c(rev) = 1 Q c(fwd) K c(rev) = 1 K c(fwd) 15-10

11 Forms of K and Q If the coefficients of a balanced equation are multiplied by a common factor, Q' = Q n = [C] c [D] d [A] a [B] b n and K' = K n 15-11

12 Sample Problem 15.2 Writing the Reaction Quotient and Finding K for an Overall Reaction PROBLEM: Nitrogen dioxide is a toxic pollutant that contributes to photochemical smog. The following sequence is one way it forms, N 2(g) + O 2(g) 2NO (g) K 1 = NO (g) + O 2(g) 2NO 2(g) K = (a) Show that the overall Q for this reaction sequence is the same as the product of the Q's of the individual reactions. (b) Given that both reactions occur at the same temperature, find K for the overall reaction. PLAN: We first write the overall reaction by adding the individual reactions and then write the overall Q. Then we write the Q for each step. We add the steps and multiply their Q's, canceling common terms. We can then calculate the overall K

13 Sample Problem 15.2 SOLUTION: (a) N 2(g) + O 2(g) 2NO (g) (1) 2NO (g) + O 2(g) 2NO 2(g) N 2(g) + 2O 2(g) 2NO 2(g) (2) Q 1 = P 2 NO P N 2 P O 2 Q 2 = P 2 NO2 P 2 NO P O 2 Q overall = Q l x Q 2 = P 2 NO P N 2 P O 2 x P 2 NO2 P 2 NO P O 2 = P 2 NO2 P N 2 P 2 O2 (b) K overall = K 1 x K 2 = (4.3x10-25 ) x (2.6x10 8 ) = 1.1x

14 Sample Problem 15.3 Finding the Equilibrium Constant for an Equation Multiplied by a Common Factor PROBLEM: For the ammonia formation reaction, the reference equation is K is 3.6x10-7 at 1000 K. What are the values of K for the following balanced equations: (a) (b) PLAN: We compare each equation with the reference equation to see how the direction and/or coefficients have changed. SOLUTION: (a) The reference equation is multiplied by ⅓, so K c(ref) will be to the ⅓ power. K = [K (ref) ] 1/3 = (3.6x10-3 ) 1/3 = 7.1x

15 Sample Problem 15.3 (b) This equation is one-half the reverse of the reference equation, so K c is the reciprocal of K c(ref) raised to the ½ power. K c = [K c(ref) ] -1/2 = (3.6x10-7 ) -1/2 = 1 [ ] 1/2 = (3.6x10-7 ) 15-15

16 K and Q for hetereogeneous equilibrium A hetereogeneous equilibrium involves reactants and/ or products in different phases. A pure solid or liquid always has the same concentration, i.e., the same number of moles per liter of solid or liquid. The expressions for Q and K include only species whose concentrations change as the reaction approaches equilbrium. Pure solids and liquids are omitted from the expression for Q or K.. For the above reaction, Q = [CO 2 ] 15-16

17 Figure 15.4 The reaction quotient for a heterogeneous system depends only on concentrations that change. solids do not change their concentrations 15-17

18 Table 15.2 Ways of Expressing Q and Calculating K 15-18

19 15.3 Expressing Equilibria with Pressure Terms K and K c K for a reaction may be expressed using partial pressures of gaseous reactants instead of molarity. The partial pressure of each gas is directly proportional to its molarity. Q = P P 2 NO 2 2 NO x P O 2 Q c = [NO 2 ] 2 [NO] 2 [O 2 ] K = K c (RT)Δn(gas) If the amount (mol) of gas does not change in the reaction, Δn gas = 0 and K = K c

20 Sample Problem 15.4 Converting Between K c and K p PROBLEM: A chemical engineer injects limestone (CaCO 3 ) into the hot flue gas of a coal-burning power plant for form lime (CaO), which scrubs SO 2 from the gas and forms gypsum (CaSO 4 2H 2 O). Find K c for the following reaction. CaCO 3(s) CaO (s) +CO 2(g) K = (at K) PLAN: We know K, so to convert between K and K c, we must first determine Δn gas from the balanced equation before we calculate K c. Assuming pressure is in bar or atmospheres, R = bar.l.mol -1 K-1. SOLUTION: Δn gas = 1-0 since there is one gaseous product and no gaseous reactants. K = K c (RT)Δn(gas) rearranging K c = K(RT)- Δn = (2.1x10-4 )( x1000) -1 = 2.5x

21 15.4 Determining the Direction of Reaction The value of Q indicates the direction in which a reaction must proceed to reach equilibrium. If Q < K, the products must increase and the reactant decrease; reactants products until equilibrium is reached. If Q > K, the reactants must increase and the products decrease; products reactants until equilibrium is reached. If Q = K, the system is at equilibrium and no further net change takes place

22 Figure 15.5 Reaction direction and the relative sizes of Q and K. Q < K Q = K Q > K 15-22

23 Sample Problem 15.5 Using Molecular Scenes to Determine Reaction Direction PROBLEM: For the reaction A(g) B(g), the equilibrium mixture at 175 C is [A] = 2.8x10-4 mol/l and [B] = 1.2x10-4 mol/l. The molecular scenes below represent mixtures at various times during runs 1-4 of this reaction (A is red; B is blue). Does the reaction progress to the right or left or not at all for each mixture to reach equilibrium? PLAN: We must compare Q c with K c to determine the reaction direction, so we use the given equilibrium concentrations to find K c. Then we count spheres and calculate Q for each mixture

24 Sample Problem 15.5 SOLUTION: K c = [B] [A] = 1.2x x10-4 = 0.43 Counting the red and blue spheres to calculate Q c for each mixture: 1. Q c = 8/2 = Q c = 3/7 = Q c = 4.6 = Q c = 2/8 = 0.25 Comparing Q c with K c to determine reaction direction: 1. Q c > K c ; reaction proceeds to the left. 2. Q c = K c ; no net change. 3. Q c > K c ; reaction proceeds to the left. 4. Q c < K c ; reaction proceeds to the right

25 Sample Problem 15.6 Using Concentrations to Determine Reaction Direction PROBLEM: For the reaction N 2 O 4 (g) 2NO 2 (g), K c = 0.21 at 100 C. At a point during the reaction, [N 2 O 4 ] = 0.12 mol/l and [NO 2 ] = 0.55 mol/l. Is the reaction at equilibrium? If not, in which direction is it progressing? PLAN: We write an expression for Q c, find its value by substituting the giving concentrations, and compare the value with the given K c. SOLUTION: Q c = [NO 2 ]2 [N 2 O 4 ] = (0.55)2 (0.12) = 2.5 Q c > K c, therefore the reaction is not at equilibrium and will proceed from right to left, from products to reactants, until Q c = K c

26 15.5 Solving Equilibrium Problems If equilibrium quantities are given, we simply substitute these into the expression for K c to calculate its value. If only some equilibrium quantities are given, we use a reaction table to calculate them and find K c. A reaction table shows the balanced equation, the initial quantities of reactants and products, the changes in these quantities during the reaction, and the equilibrium quantities

27 Example: In a study of carbon oxidation, an evacuated vessel containing a small amount of powdered graphite is heated to 1080 K. Gaseous CO 2 is added to a pressure of atm and CO forms. At equilibrium, the total pressure is atm. Calculate K p. CO 2 (g) + C(graphite) 2CO(g) Pressure ( atm) CO 2 ( g ) + C(graphite) 2CO( g ) Initial Change Equilibrium x - +2 x x - 2 x The amount of CO 2 will decrease. If we let the decrease in CO 2 be x, then the increase in CO will be +2x. Equilibrium amounts are calculated by adding the change to the initial amount

28 Once we have the equilibrium amounts expressed in terms of x, we use the other information given in the problem to solve for x. The total pressure at equilibrium is atm = P CO 2 (eq) atm = x + 2x (from reaction table) atm = x x = = atm At equilibrium P CO 2 (eq) + P CO(eq) = x = = atm P CO = 2x = 2(0.299) = atm K p = P CO 2 2 (eq) = P CO(eq) =

29 Sample Problem 15.7 Calculating K c from Concentration Data PROBLEM: To study hydrogen halide decomposition, a researcher fills an evacuated 2.00-L flask with mol of HI gas and allows the reaction to proceed at 453 C. 2HI(g) H 2 (g) + I 2 (g) At equilibrium, [HI] = mol/l. Calculate K c. PLAN: To calculate K c we need equilibrium concentrations. We can find the initial [HI] from the amount and the flask volume, and we are given [HI] at equilibrium. From the balanced equation, when 2x mol of HI reacts, x mol of H 2 and x mol of I 2 form. We use this information to set up a reaction table. SOLUTION: Calculating [HI]: [HI] = mol = mol/l 2.00 L

30 Sample Problem 15.7 Concentration (M) 2HI(g) H 2 (g) + I 2 (g) Initial Change Equilibrium x + x + x x x x [HI] = = x; x = mol/l K c = [H 2 ] [I 2 ] [HI] 2 = (0.011)(0.011) (0.078) 2 = = K c 15-30

31 Sample Problem 15.8 Determining Equilibrium Concentrations from K c PROBLEM: In a study of the conversion of methane to other fuels, a chemical engineer mixes gaseous CH 4 and H 2 O in a 0.32-L flask at 1200 K. At equilibrium the flask contains 0.26 mol of CO, mol of H 2, and mol of CH 4. What is the [H 2 O] at equilibrium? K c = 0.26 for this process at 1200 K. PLAN: First we write the balanced equation and the expression for Q c. We calculate the equilibrium concentrations from the given numbers of moles and the flask volume. We then use the value of K c to solve for [H 2 O]. SOLUTION: CH 4 (g) + H 2 O(g) CO(g) + 3H 2 (g) [CH 4 ] eq = mol 0.32 L = 0.13 mol/l [CO] eq = mol [H 2 ] eq = 0.32 L 0.26 mol 0.32 L = 0.28 mol/l = 0.81 mol/l 15-31

32 Sample Problem 15.8 K c = [CO][H 2 ] 3 [CH 4 ][H 2 O] [H 2 O] = [CO][H 2 ]3 [CH 4 ] K c = (0.81)(0.28) 3 (0.13)(0.26) = 0.53 mol/l 15-32

33 Sample Problem 15.9 Determining Equilibrium Concentrations from Initial Concentrations and K c PROBLEM: Fuel engineers use the extent of the change from CO and H 2 O to CO 2 and H 2 to regulate the proportions of synthetic fuel mixtures. If mol of CO and mol of H 2 O are placed in a 125-mL flask at 900 K, what is the composition of the equilibrium mixture? At this temperature, K c is PLAN: We have to find the concentrations of all species at equilibrium and then substitute into a K c expression. First we write a balanced equation, calculate initial concentrations and set up a reaction table. SOLUTION: CO(g) + H 2 O(g) CO 2 (g) + H 2 (g) Calculating initial concentrations,[co] = [H 2 O] = mol L = 2.00 mol/l 15-33

34 Sample Problem 15.9 Concentration (M) CO(g) + H 2 O(g) CO 2 (g) + H 2 (g) Initial Change Equilibrium x - x + x + x x x x x Q c = K c = [CO 2 ][H 2 ] [CO][H 2 O] = (x) (x) ( x) ( x) (x) = 2 ( x) 2 x = x = 1.25 x = 1.11 mol/l x = 0.89 mol/l [CO] = [H 2 O] = 0.89 mol/l [CO 2 ] = [H 2 ] = 1.11 mol/l 15-34

35 Sample Problem Making a Simplifying Assumption to Calculate Equilibrium Concentrations PROBLEM: Phosgene is a potent chemical warfare agent that is now outlawed by international agreement. It decomposes by the reaction COCl 2 (g) CO(g) + Cl 2 (g); K c = 8.3x10-4 at 360 C. Calculate [CO], [Cl 2 ], and [COCl 2 ] when the following amounts of phosgene decompose and reach equilibrium in a 10.0-L flask. (a) 5.00 mol COCl 2 (b) mol COCl 2 PLAN: We know from the balanced equation that when x mol of COCl 2 decomposes, x mol of CO and x mol of Cl 2 form. We calculate initial concentrations, define x, set up a reaction table, and substituted the values into the expression for Q c. Since K c is very small, we can assume that x is negligible, which simplifies the expression. We must check this assumption when we have solved for x

36 Sample Problem SOLUTION: (a) Calculating initial concentrations,[cocl 2 ] = Let x = amount of COCl 2 that reacts: L = mol/l Concentration (M) COCl 2 (g) CO(g) + Cl 2 (g) Initial Change Equilibrium x + x + x x x x K c = [CO][Cl 2 ] [COCl 2 ] = x x = 8.3x

37 Sample Problem Since K c is very small, the reaction does not proceed very far to the right, so let's assume that x can be neglected when we calculate [COCl 2 ] eqm : x 2 K c = 8.3x10-4 x 2 (8.3x10-4 )(0.500) so x 2.0x10-2 At equilibrium, [COCl 2 ] = x10-2 =.480 mol/l and [Cl 2 ] = [CO] = 2.0x10-2 mol/l Check that the assumption is justified: x x 100 = 2.0x10-2 [COCl 2 ] init x 100 = 4%, which is < 5%, so the assumption is justified

38 Sample Problem mol (b) Calculating initial concentrations,[cocl 2 ] = 10.0 L [CO][Cl 2 ] x K c = 2 = [COCl 2 ] x = 8.3x10-4 If we assume that x x 2 then K c = 8.3x10-4 and x 2.9x Checking the assumption: 2.9x = mol/l x 100 = 29%, which is > 5%, so the assumption is not justified

39 Sample Problem Using the quadratic formula we get x 2 + (8.3x10-4 )x (8.3x10-6 ) = 0 x = 2.5x10-3 and x = 7.5x10-3 mol/l [CO] = [Cl 2 ] = 2.5x10-3 mol/l [COCl 2 ] = 7.5x10-3 mol/l 15-39

40 The Simplifying Assumption We assume that x([a] reacting can be neglected if K c is relatively small and/or [A] init is relatively large. If [A] init K c > 400, the assumption is justified; neglecting x introduces an error < 5%. If [A] init K c < 400, the assumption is not justified; neglecting x introduces an error > 5%

41 Sample Problem Predicting Reaction Direction and Calculating Equilibrium Concentrations PROBLEM: The research and development unit of a chemical company is studying the reaction of CH 4 and H 2 S, two components of natural gas: CH 4 (g) + 2H 2 S(g) CS 2 (g) + 4H 2 (g) In one experiment, 1.00 mol of CH 4, 1.00 mol of CS 2, 2.00 mol of H 2 S, and 2.00 mol of H 2 are mixed in a 250-mL vessel at 960 C. At this temperature, K c = (a) In which direction will the reaction proceed to reach equilibrium? (b) If [CH 4 ] = 5.56 mol/l at equilibrium, what are the equilibrium concentrations of the other substances? PLAN: (a) To find the direction of reaction we determine the initial concentrations from the given amounts and volume, calculate Q c and compare it with K c. (b) Based on this information, we determine the sign of each concentration change for the reaction table and hence calculate equilibrium concentrations.

42 Sample Problem SOLUTION: (a) Calculating initial concentrations,[ch 4 ] = 1.00 mol L = 4.00 mol/l [H 2 S] = 8.00 mol/l, [CS 2 ] = 4.00 mol/l and [H 2 ] = 8.00 mol/l Q c = [CS 2 ][H 2 ] 4 [CH 4 ][H 2 S] 2 = (4.0)(8.0)4 (4.0)(8.0) 2 = 64 Since Q c > K c, the reaction will proceed to the left. The reactant concentrations will decrease and the product concentrations will increase

43 Sample Problem (b) We use this information to construct our reaction table. Concentration (M) CH 4 (g) + 2H 2 S(g) CS 2 (g) + 4H 2 (g) Initial Change Equilibrium x +2x - x -4x x x x x At equilibrium [CH 4 ] = 5.56 M, so x = 5.56 and x = 1.56 [H 2 S] = x = mol/l [CS 2 ] = x = 2.44 mol/l [H 2 ] = x = 1.76 mol/l 15-43

44 Figure 15.6 Steps in solving equilibrium problems. PRELIMINARY SETTING UP 1. Write the balanced equation. 2. Write the reaction quotient, Q. 3. Convert all amounts into the correct units (M or atm). WORKING ON THE REACTION TABLE 4. When reaction direction is not known, compare Q with K. 5. Construct a reaction table. ü Check the sign of x, the change in the concentration (or pressure)

45 Figure 15.6 continued SOLVING FOR x AND EQUILIBRIUM QUANTITIES 6. Substitute the quantities into Q. 7. To simplify the math, assume that x is negligible: 8. Solve for x. ([A] init x = [A] eq [A] init ) ü Check that assumption is justified (<5% error). If not, solve quadratic equation for x. 9. Find the equilibrium quantities. ü Check to see that calculated values give the known K

46 15.6 Le Châtelier s Principle When a chemical system at equilibrium is disturbed, it reattains equilibrium by undergoing a net reaction that reduces the effect of the disturbance. A system is disturbed when a change in conditions forces it temporarily out of equilibrium. The system responds to a disturbance by a shift in the equilibrium position. A shift to the left is a net reaction from product to reactant. A shift to the right is a net reaction from reactant to product

47 The Effect of a Change in Concentration If the concentration of A increases, the system reacts to consume some of it. If a reactant is added, the equilibrium position shifts to the right. If a product is added, the equilibrium position shifts to the left. If the concentration of B decreases, the system reacts to consume some of it. If a reactant is removed, the equilibrium position shifts to the left. If a product is removed, the equilibrium position shifts to the right. Only substances that appear in the expression for Q can have an effect. A change in concentration has no effect on the value of K

48 Figure 15.7 The effect of a change in concentration

49 Table 15.3 The Effect of Added Cl 2 on the PCl 3 -Cl 2 -PCl 5 System Concentration (M) PCl 3 (g) + Cl 2 (g) PCl 3 (g) Original equilibrium Disturbance New initial Change -x -x +x New equilibrium x x * Experimentally determined value x (0.637) * 15-49

50 Figure 15.8 The effect of added Cl 2 on the PCl 3 -Cl 2 -PCl 5 system. PCl 3 (g) + Cl 2 (g) PCl 5 (g) When Cl 2 (yellow curve) is added, its concentration increases instantly (vertical part of yellow curve) and then falls gradually as it reacts with PCl 3 to form more PCl 5. Equilibrium is re-established at new concentrations but with the same value of K

51 Sample Problem Predicting the Effect of a Change in Concentration on the Equilibrium Position PROBLEM: To improve air quality and obtain a useful product, chemists often remove sulfur from coal and natural gas by treating the contaminant hydrogen sulfide with O 2 : 2H 2 S(g) + O 2 (g) What happens to (a) [H 2 O] if O 2 is added? (c) [O 2 ] if H 2 S is removed? 2S(s) + 2H 2 O(g) (b) [H 2 S] if O 2 is added? (d) [H 2 S] if sulfur is added? PLAN: We write the reaction quotient to see how Q c is affected by each disturbance, relative to K c. This effect tells us the direction in which the reaction proceeds for the system to reattain equilibrium and how each concentration changes

52 Sample Problem SOLUTION: Q c = [H 2 O]2 [H 2 S] 2 [O 2 ] (a) When O 2 is added, Q decreases and the reaction proceeds to the right until Q c = K c again, so [H 2 O] increases. (b) When O 2 is added, Q decreases and the reaction proceeds to the right until Q c = K c again, so [H 2 S] decreases. (c) When H 2 S is removed, Q increases and the reaction proceeds to the left until Q c = K c again, so [O 2 ] increases. (d) The concentration of solid S is unchanged as long as some is present, so it does not appear in the reaction quotient. Adding more S has no effect, so [H 2 S] is unchanged

53 The Effect of a Change in Pressure (Volume) Changes in pressure affect equilibrium systems containing gaseous components. Changing the concentration of a gaseous component causes the equilibrium to shift accordingly. Adding an inert gas has no effect on the equilibrium position, as long as the volume does not change. This is because all concentrations and partial pressures remain unchanged. Changing the volume of the reaction vessel will cause equilibrium to shift if Δn gas 0. Changes in pressure (volume) have no effect on the value of K

54 Figure 15.9 The effect of a change in pressure (volume) on a system at equilibrium

55 Sample Problem Predicting the Effect of a Change in Volume (Pressure) on the Equilibrium Position PROBLEM: How would you change the volume of each of the following reactions to increase the yield of the products? (a) CaCO 3 (s) CaO(s) + CO 2 (g) (b) S(s) + 3F 2 (g) (c) Cl 2 (g) + I 2 (g) SF 6 (g) 2ICl(g) PLAN: Whenever gases are present, a change in volume causes a change in concentration. For reactions in which the number of moles of gas changes, a decrease in volume (pressure increase) causes an equilibrium shift to lower the pressure by producing fewer moles of gas. A volume increase (pressure decrease) has the opposite effect

56 Sample Problem SOLUTION: (a) CO 2 is the only gas present. To increase its yield, we should increase the volume (decrease the pressure). (b) There are more moles of gaseous reactants than products, so we should decrease the volume (increase the pressure) to shift the equilibrium to the right. (c) The number of moles of gas is the same in both the reactants and the products; therefore a change in volume will have no effect