I never let my schooling get in the way of my education.

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1 Chemistry NT I never let my schooling get in the way of my education. Mark Twain Chem NT Chemical Equilibrium Module Describing Chemical Equilibrium The Equilibrium Constant Equilibrium Constant for Sums of Reactions Heterogeneous Equilibria Oscillating patterns formed by a reaction far from equilibrium

2 Chemical Equilibrium When compounds react, they eventually form a mixture of products and unreacted reactants, in a dynamic equilibrium. A dynamic equilibrium consists of a forward reaction, in which substances react to give products, and a reverse reaction, in which products react to give the original reactants. Chemical equilibrium is the state reached by a reaction mixture when the rates of the forward and reverse reactions have become equal. 4 Chemical Equilibrium Much like water in a U-shape tube, there is constant mixing back and forth through the lower portion of the tube. reactants products It s as if the forward and reverse reactions were occurring at the same rate. The system appears to static (stationary) when, in reality, it is dynamic(in constant motion). 5 Chemical Equilibrium Consider the gaseous reaction of carbon monoxide and hydrogen to produce methane and steam. CO (g) + H (g) CH 4 (g) + HO(g) Suppose you put.000 mol CO and.000 mol H into a 0.00-L container at 00. The rate of the forward reaction, which depends on reactant concentrations, is large at first but steadily decreases. 6

3 Chemical Equilibrium Consider the gaseous reaction of carbon monoxide and hydrogen to produce methane and steam. CO (g) + H (g) CH 4 (g) + HO(g) Suppose you put.000 mol CO and.000 mol H into a 0.00-L container at 00. The rate of the reverse reaction starts at zero but steadily increases. 7 Chemical Equilibrium Consider the gaseous reaction of carbon monoxide and hydrogen to produce methane and steam. CO (g) + H (g) CH 4 (g) + HO(g) Suppose you put.000 mol CO and.000 mol H into a 0.00-L container at 00. The forward rate decreases and the reverse rate increases until they eventually become equal and the reaction mixture has reached equilibrium. 8 Chemical Equilibrium Consider the gaseous reaction of carbon monoxide and hydrogen to produce methane and steam. CO (g) + H (g) CH 4 (g) + HO(g) Suppose you put.000 mol CO and.000 mol H into a 0.00-L container at 00. The next figure illustrates this approach to equilibrium. 9

4 The experiment begins with.00 mol CO and.000 mol H in a 0.00-L vessel. Note that the amounts of substances become constant at equilibrium. 0 The forward rate is large at first but steadily decreases, whereas the reverse rate starts at zero and steadily increases. Eventually, both rates become equal (at equilibrium). Chemical Equilibrium Another example is the Haber process for producing ammonia from N and H which does not go to completion. N (g) + H(g) NH (g) It establishes an equilibrium state where all three species are present. 4

5 Chemical Equilibrium Another example is the Haber process for producing ammonia from N and H which does not go to completion. N + H NH A Problem To Consider Applying Stoichiometry to an Equilibrium Mixture. Suppose we place.000 mol N and.000 mol H in a reaction vessel at 450 o C and 0.0 atmospheres of pressure. The reaction is: N (g) + H(g) NH (g) What is the composition of the equilibrium mixture if it contains mol NH? 4 A Problem To Consider Using the information given, set up the following table. Starting.000 Change -x Equilibrium.000-x N (g) + H(g) NH (g).000 -x.000-x 0 +x x = mol The equilibrium amount of NH was given as mol. Therefore, x = mol NH (x = mol). 5 5

6 A Problem to Consider Using the information given, set up the following table. Starting.000 Change -x Equilibrium.000-x N (g) + H(g) NH (g).000 -x.000-x 0 +x x = mol Equilibrium amount of N = = mol N 6 A Problem to Consider Using the information given, set up the following table. Starting.000 Change -x Equilibrium.000-x N (g) + H(g) NH (g).000 -x.000-x 0 +x x = mol Equilibrium amount of H =.000-( x 0.040) =.880 mol H 7 A Problem to Consider Using the information given, set up the following table. Starting.000 Change -x Equilibrium.000-x N (g) + H(g) NH (g).000 -x.000-x 0 +x x = mol Equilibrium amount of NH = x = mol NH 8 6

7 The Equilibrium Constant Every reversible system has its own position of equilibrium under any given set of conditions. The ratio of products produced to unreacted reactants for any given reversible reaction remains constant under constant conditions of pressure and temperature. The numerical value of this ratio is called the equilibrium constant for the given reaction. 9 The Equilibrium Constant The equilibrium-constant expression for a reaction is obtained by multiplying the concentrations of products, dividing by the concentrations of reactants, and raising each concentration to a power equal to its coefficient in the balanced chemical equation. aa + bb cc + dd For the general equation above, the equilibriumconstant expression would be: c d [C] [D] c = a [A] [B] b 0 The Equilibrium Constant The equilibrium-constant expression for a reaction is obtained by multiplying the concentrations of products, dividing by the concentrations of reactants, and raising each concentration to a power equal to its coefficient in the balanced chemical equation. aa + bb cc + dd The molar concentration of a c d [C] [D] substance is denoted by writing c = a b its formula in square brackets. [A] [B] 7

8 The Equilibrium Constant The equilibrium constant c, is the value obtained for the equilibrium-constant expression when equilibrium concentrations are substituted. Since c products reactan ts A large c indicates high concentrations of product at equilibrium. The Equilibrium Constant The equilibrium constant c, is the value obtained for the equilibrium-constant expression when equilibrium concentrations are substituted. Since c products reactan ts A small c indicates a large concentration of unreacted reactants at equilibrium. The Equilibrium Constant The law of mass action states that the value of the equilibrium constant expression c is constant for a particular reaction at a given temperature, whatever equilibrium concentrations are substituted. Consider the equilibrium established in the Haber process. N (g) + H(g) NH (g) 4 8

9 The Equilibrium Constant The equilibrium-constant expression would be: [NH c = [N ][H ] ] Note that the stoichiometric coefficients in the balanced equation have become the powers to which each concentration is raised. N (g) + H(g) NH (g) 5 A Problem To Consider Write the equilibrium-constant expression c for catalytic methanation. CO(g) + H (g) CH4(g) + HO(g) Write the concentrations of products in the top (numerator) of the equilibrium constant expression, and write the concentrations of reactants in the bottom (denominator). 6 A Problem To Consider Write the equilibrium-constant expression c for catalytic methanation. CO(g) + H (g) CH4(g) + HO(g) Raise each concentration term to the power equal to the coefficient of the substance in the chemical equation. 7 9

10 A Problem To Consider Write the equilibrium-constant expression c for catalytic methanation. CO(g) + H (g) CH4(g) + HO(g) [CH4][H c = [CO][H O] ] 8 A Problem To Consider Write the equilibrium-constant expression c for the reverse of the previous reaction. CH4 (g) + HO(g) CO(g) + H(g) c = [CO][H] [CH ][H O] 4 9 A Problem To Consider Our previous look at the Haber process led us to the equilibrium-constant expression below. N (g) + H(g) NH (g) [NH c = [N ][H ] ] 0 0

11 A Problem To Consider Write the equilibrium-constant expression c when the equation for the previous reaction is written. N (g) + H(g) NH (g) Whether coefficients are fractional or not, they still become exponents in the equilibrium-constant expression. c = [NH] [N ] [H ] Equilibrium: A inetics Argument If the forward and reverse reaction rates in a system at equilibrium are equal, then it follows that their rate laws would be equal. Consider the decomposition of N O 4, dinitrogen tetroxide. NO4(g) NO (g) If we start with some dinitrogen tetroxide and heat it, it begins to decompose to produce NO. Equilibrium: A inetics Argument If the forward and reverse reaction rates in a system at equilibrium are equal, then it follows that their rate laws would be equal. Consider the decomposition of N O 4, dinitrogen tetroxide. NO4(g) NO (g) However, once some NO is produced it can recombine to form N O 4.

12 Equilibrium: A inetics Argument NO4(g) NO (g) Call the decomposition of N O 4 the forward reaction and the formation of N O 4 the reverse reaction. These are elementary reactions, and you can immediately write the rate law for each. k f k r Rate(forward) = kf [NO4] Rate = k [NO (reverse) r ] Here k f and k r represent the forward and reverse rate constants. 4 Equilibrium: A inetics Argument k f NO4(g) NO (g) k r Ultimately, this reaction reaches an equilibrium state where the rate of the forward and reverse reactions are equal, therefore: k = f [NO 4] kr[no ] rate forward = rate reverse 5 Equilibrium: A inetics Argument NO4(g) NO (g) Combining the constants you can identify the equilibrium constant c, as the ratio of the forward and reverse rate constants. k f k r k k c = f = r [NO ] [N O ] 4 6

13 Obtaining Equilibrium Constants for Reactions Equilibrium concentrations for a reaction must be obtained experimentally and then substituted into the equilibrium-constant expression in order to calculate c. This c can then be used to define any equilibrium composition for that particular reaction. 7 Obtaining Equilibrium Constants for Reactions Consider the reaction below. CO (g) + H (g) CH 4(g) + HO(g) Suppose we started with initial concentrations of CO and H of 0.00 M and 0.00 M, respectively. 8 Obtaining Equilibrium Constants for Reactions Consider the reaction below. CO (g) + H (g) CH 4(g) + HO(g) When the system finally settled into equilibrium we determined the equilibrium concentrations to be as follows. Reactants [CO] = 0.06 M [H ] = 0.89 M Products [CH 4 ] = M [H O] = M 9

14 Obtaining Equilibrium Constants for Reactions Consider the reaction below. CO (g) + H (g) CH 4(g) + HO(g) The equilibrium-constant expression for this reaction is: [CH4][H O] c = [CO][H ] 40 Obtaining Equilibrium Constants for Reactions Consider the reaction below. CO (g) + H (g) CH 4(g) + HO(g) If we substitute the equilibrium concentrations, we obtain: (0.087M)(0.087M) = (0.06M)(0.89M) c =.9 4 Obtaining Equilibrium Constants for Reactions Consider the reaction below. CO (g) + H (g) CH 4(g) + HO(g) Note that regardless of initial concentrations (whether they be reactants or products) the law of mass action dictates that the reaction will always settle into an equilibrium where the equilibrium-constant expression equals c. 4 4

15 Obtaining Equilibrium Constants for Reactions Consider the reaction below. CO (g) + H (g) CH 4(g) + HO(g) For example, if we repeat the previous experiment, only this time, starting with initial concentrations of products: [CH 4 ] initial = M and [H O] initial = M 4 Obtaining Equilibrium Constants for Reactions Consider the reaction below. CO (g) + H (g) CH 4(g) + HO(g) We find that these initial concentrations result in the following equilibrium concentrations. Reactants [CO] = 0.06 M [H ] = 0.89 M Products [CH 4 ] = M [H O] = M 44 Obtaining Equilibrium Constants for Reactions Consider the reaction below. CO (g) + H (g) CH 4(g) + HO(g) Substituting these values into the equilibriumconstant expression, we obtain the same result. (0.087M)(0.087M) = (0.06M)(0.89M) c =.9 Whether we start with reactants initially or products, the system establishes the same ratio. 45 5

16 The Equilibrium Constant p In discussing gas -phase equilibria, it is often more convenient to express concentrations in terms of partial pressures rather than molarities. It can be seen from the ideal gas equation that partial pressure of a gas is proportional to its molarity. n P = ( ) RT = MRT V 46 The Equilibrium Constant p If we express a gas -phase equilibria in terms of partial pressures, we obtain p. Consider the reaction below. CO (g) + H (g) CH 4(g) + HO(g) The equilibrium-constant expression in terms of partial pressures becomes: p = P P CH 4 CO P P HO H 47 The Equilibrium Constant p In general, the numerical value of p is different than that of c. From the relationship n/v=p/rt, one can show Dn p = c(rt) where Dn is the sum of the moles of gaseous products in a reaction minus the sum of the moles of gaseous reactants. 48 6

17 A Problem To Consider Consider the reaction SO (g) + O (g) SO (g) The c for the reaction is.8 x 0 at 000. Calculate the p for the reaction at this temperature. Therefore, Dn = - 49 A Problem To Consider Consider the reaction SO (g) + O (g) SO (g) Since Dn p = c(rt) and from the equation we see that n = -, we can simply substitute the given reaction temperature and the value of R ( L. atm/mol. ) to obtain p. 50 A Problem To Consider Consider the reaction SO (g) + O (g) SO (g) Since Dn p = c(rt).8 0 ( Latm p = 000 ) p =.4 mol - 5 7

18 Equilibrium Constant for the Sum of Reactions Similar to the method of combining reactions we saw using Hess law in chapter 6, we can combine equilibrium reactions whose c s are known to obtain the c for the overall reaction. Just as with Hess law, when we reversed reactions or took multiples of them prior to adding them together, we had to manipulate the H s to reflect what we had done. The rules are a bit different for manipulating c s. 5 Equilibrium Constant for the Sum of Reactions. If you reverse a reaction, invert the value of c. For example, aa + bb cc + dd c [C] [D] forward = a [A] [B] d b If we reverse : cc + dd aa + bb a [A] [B] reverse = = c [C] [D] forward b d 5 Equilibrium Constant for the Sum of Reactions. If you multiply each of the coefficients in an equation by the same factor (,, ), raise the c to the same power(,, ). For example, A + B C + D [C][D] initial = [A][B] 54 8

19 Equilibrium Constant for the Sum of Reactions. If you multiply each of the coefficients in an equation by the same factor (,, ), raise the c to the same power(,, ). If we triple the reaction: A + B C + D [C] [D] tripled = ( initial ) = [A] [B] 55 Equilibrium Constant for the Sum of Reactions. If you divide each of the coefficients in an equation by the same factor (,, ) take the corresponding root of the c (i.e., square root, cube root, ). For example, A + B C + D [C][D] initial = [A][B] 56 Equilibrium Constant for the Sum of Reactions. If you divide each of the coefficients in an equation by the same factor (,, ) take the corresponding root of the c (i.e., square root, cube root, ). If we halve the reaction: A + B C+ [C] [D] halved = = (initial) = [A] [B] D initial 57 9

20 Equilibrium Constant for the Sum of Reactions 4. When you finally combine (that is, add) the individual equations together, take the product of the equilibrium constants to obtain the overall c. A + B C + D For example, C + D E + F A + B E + F overall 58 Equilibrium Constant for the Sum of Reactions 4. When you finally combine (that is, add) the individual equations together, take the product of the equilibrium constants to obtain the overall c. Simplifying: [C][D][E][F] overall = [A][B][C][D] [E][F] overall = = [A][B] 59 Equilibrium Constant for the Sum of Reactions For example, nitrogen and oxygen can combine to form either NO(g) or N O (g) according to the following equilibria. () N (g) + O (g) NO(g) c = 4. x 0 - () N (g) + O (g) N O(g) c =.4 x 0-8 Using these two equations, we can obtain the c for the formation of NO(g) from N O(g) () N O(g) + O (g) NO(g) c =? 60 0

21 Equilibrium Constant for the Sum of Reactions To combine equations () and () to obtain equation (), we must first reverse equation (). When we do we must also take the reciprocal of its c value. () (g) O (g) NO(g) c = 4. x 0 - () () N + N O(g) N(g) + O (g) c = N O(g) + O (g) NO(g) c(overall) = (4. 0 ) ( ) = Heterogeneous Equilibria A heterogeneous equilibrium is an equilibrium that involves reactants and products in more than one phase. The equilibrium of a heterogeneous system is unaffected by the amounts of pure solids or liquids present, as long as some of each is present. The concentrations of pure solids and liquids is considered to be and therefore, do not appear in the equilibrium expression. 6 Heterogeneous Equilibria Consider the reaction below. C(s) + H O(g) CO(g) + H (g) The equilibrium-constant expression contains terms for only those species in the homogeneous gas phase H O, CO, and H. c = [CO][H] [H O] 6

22 Operational Skills Applying stoichiometry to an equilibrium mixture Writing equilibrium-constant expressions Obtaining the equilibrium constant from reaction composition Determining equilibrium constants for sums of reactions Time for a few review questions