Equilibrium Constants Quiz

PDF page 735: The status of a reversible reaction is conveniently assessed by evaluating its reaction quotient (Q). For a reversible reaction described by mA + nB + ⇌ xC + yD the reaction quotient is derived directly from the stoichiometry of the balanced equation as x y [C] [D] Qc = m n [A] [B] where the subscript c denotes the use of molar concentrations in the expression. If the reactants and products are gaseous, a reaction quotient may be similarly derived using partial pressures: x y P P C D Q p = m n P P A B Note that the reaction quotient equations above are a simplification of more rigorous expressions that use relative values for concentrations and pressures rather than absolute values. These relative concentration and pressure values are dimensionless (they have no units); consequently, so are the reaction quotients. For purposes of this introductory text, it will suffice to use the simplified equations and to disregard units when computing Q. In most cases, this will

PDF page 735: The status of a reversible reaction is conveniently assessed by evaluating its reaction quotient (Q). For a reversible reaction described by mA + nB + ⇌ xC + yD the reaction quotient is derived directly from the stoichiometry of the balanced equation as x y [C] [D] Qc = m n [A] [B] where the subscript c denotes the use of molar concentrations in the expression. If the reactants and products are gaseous, a reaction quotient may be similarly derived using partial pressures: x y P P C D Q p = m n P P A B Note that the reaction quotient equations above are a simplification of more rigorous expressions that use relative values for concentrations and pressures rather than absolute values. These relative concentration and pressure values are dimensionless (they have no units); consequently, so are the reaction quotients. For purposes of this introductory text, it will suffice to use the simplified equations and to disregard units when computing Q. In most cases, this will

PDF page 735: The status of a reversible reaction is conveniently assessed by evaluating its reaction quotient (Q). For a reversible reaction described by mA + nB + ⇌ xC + yD the reaction quotient is derived directly from the stoichiometry of the balanced equation as x y [C] [D] Qc = m n [A] [B] where the subscript c denotes the use of molar concentrations in the expression. If the reactants and products are gaseous, a reaction quotient may be similarly derived using partial pressures: x y P P C D Q p = m n P P A B Note that the reaction quotient equations above are a simplification of more rigorous expressions that use relative values for concentrations and pressures rather than absolute values. These relative concentration and pressure values are dimensionless (they have no units); consequently, so are the reaction quotients. For purposes of this introductory text, it will suffice to use the simplified equations and to disregard units when computing Q. In most cases, this will

PDF page 737: The numerical value of Q varies as a reaction proceeds towards equilibrium; therefore, it can serve as a useful indicator of the reaction’s status. To illustrate this point, consider the oxidation of sulfur dioxide: 2SO (g) + O (g) ⇌ 2SO (g) 2 2 3 Two different experimental scenarios are depicted in Figure 13.5, one in which this reaction is initiated with a mixture of reactants only, SO2 and O2, and another that begins with only product, SO3. For the reaction that begins with a mixture of reactants only, Q is initially equal to zero: 2 2 [SO ] 0 3 = = 0 Qc = 2 2 [SO ] [O ] [SO ] [O ] 2 2 2 2 As the reaction proceeds toward equilibrium in the forward direction, reactant concentrations decrease (as does the denominator of Qc), product concentration increases (as does the numerator of Qc), and the reaction quotient consequently increases. When equilibrium is achieved, the concentrations of reactants and product remain constant, as does the value of Qc. If the reaction begins with only product present, the value of Qc is initially undefined (immeasurably large, or

PDF page 738: infinite): 2 2 [SO ] [SO ] 3 3 = Qc = 2 0 → ∞ [SO ] [O ] 2 2 In this case, the reaction proceeds toward equilibrium in the reverse direction. The product concentration and the numerator of Qc decrease with time, the reactant concentrations and the denominator of Qc increase, and the reaction quotient consequently decreases until it becomes constant at equilibrium. The constant value of Q exhibited by a system at equilibrium is called the equilibrium constant, K: K ≡ Q at equilibrium Comparison of the data plots in Figure 13.5 shows that both experimental scenarios resulted in the same value for the equilibrium constant. This is a general observation for all equilibrium systems, known as the law of mass action: At a given temperature, the reaction quotient for a system at equilibrium is constant.

PDF page 738: infinite): 2 2 [SO ] [SO ] 3 3 = Qc = 2 0 → ∞ [SO ] [O ] 2 2 In this case, the reaction proceeds toward equilibrium in the reverse direction. The product concentration and the numerator of Qc decrease with time, the reactant concentrations and the denominator of Qc increase, and the reaction quotient consequently decreases until it becomes constant at equilibrium. The constant value of Q exhibited by a system at equilibrium is called the equilibrium constant, K: K ≡ Q at equilibrium Comparison of the data plots in Figure 13.5 shows that both experimental scenarios resulted in the same value for the equilibrium constant. This is a general observation for all equilibrium systems, known as the law of mass action: At a given temperature, the reaction quotient for a system at equilibrium is constant.

PDF page 738: By its definition, the magnitude of an equilibrium constant explicitly reflects the composition of a reaction mixture at equilibrium, and it may be interpreted with regard to the extent of the forward reaction. A reaction exhibiting a large K will reach equilibrium when most of the reactant has been converted to product, whereas a small K indicates the reaction achieves equilibrium after very little reactant has been converted. It’s important to keep in mind that the magnitude of K does not indicate how rapidly or slowly equilibrium will be reached. Some equilibria are established so quickly as to be nearly instantaneous, and others so slowly that no perceptible change is observed over the course of days, years, or longer. The equilibrium constant for a reaction can be used to predict the behavior of mixtures containing its reactants and/or

PDF page 738: By its definition, the magnitude of an equilibrium constant explicitly reflects the composition of a reaction mixture at equilibrium, and it may be interpreted with regard to the extent of the forward reaction. A reaction exhibiting a large K will reach equilibrium when most of the reactant has been converted to product, whereas a small K indicates the reaction achieves equilibrium after very little reactant has been converted. It’s important to keep in mind that the magnitude of K does not indicate how rapidly or slowly equilibrium will be reached. Some equilibria are established so quickly as to be nearly instantaneous, and others so slowly that no perceptible change is observed over the course of days, years, or longer. The equilibrium constant for a reaction can be used to predict the behavior of mixtures containing its reactants and/or

PDF page 740: Qc < Kc (0.040 < 0.64) The reaction will proceed in the forward direction.

PDF page 739: products. As demonstrated by the sulfur dioxide oxidation process described above, a chemical reaction will proceed in whatever direction is necessary to achieve equilibrium. Comparing Q to K for an equilibrium system of interest allows prediction of what reaction (forward or reverse), if any, will occur. To further illustrate this important point, consider the reversible reaction shown below: CO(g) + H O(g) ⇌ CO (g) + H (g) T = 800 °C Kc = 0.640 2 2 2 The bar charts in Figure 13.6 represent changes in reactant and product concentrations for three different reaction mixtures. The reaction quotients for mixtures 1 and 3 are initially lesser than the reaction’s equilibrium constant, so each of these mixtures will experience a net forward reaction to achieve equilibrium. The reaction quotient for mixture 2 is initially greater than the equilibrium constant, so this mixture will proceed in the reverse direction until equilibrium is established.

PDF page 741: A homogeneous equilibrium is one in which all reactants and products (and any catalysts, if applicable) are present in the same phase. By this definition, homogeneous equilibria take place in solutions. These solutions are most commonly either liquid or gaseous phases, as shown by the examples below:

PDF page 741: 3 2 4 ⎣NH ⎦ 3 These examples all involve aqueous solutions, those in which water functions as the solvent. In the last two examples, water also functions as a reactant, but its concentration is not included in the reaction quotient. The reason for this omission is related to the more rigorous form of the Q (or K) expression mentioned previously in this chapter, in which relative concentrations for liquids and solids are equal to 1 and needn’t be included. Consequently, reaction quotients include concentration or pressure terms only for gaseous and solute species. The equilibria below all involve gas-phase solutions:

PDF page 742: For gas-phase solutions, the equilibrium constant may be expressed in terms of either the molar concentrations (Kc) or partial pressures (Kp) of the reactants and products. A relation between these two K values may be simply derived from the ideal gas equation and the definition of molarity: PV = nRT ⎛n ⎞ P = RT ⎝V ⎠ = MRT where P is partial pressure, V is volume, n is molar amount, R is the gas constant, T is temperature, and M is molar concentration. For the gas-phase reaction mA + nB ⇌ xC + yD: