Magnitude of Equilibrium Constant

8 Key excerpts on "Magnitude of Equilibrium Constant"

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  eBook - PDF

  Chemistry

  An Industry-Based Introduction with CD-ROM

  • John Kenkel, Paul B. Kelter, David S. Hage(Authors)
  • 2000(Publication Date)
  • CRC Press

    (Publisher)

  Because there is no change in these counts, we can divide the number of students on one side by the number of students on the other side and always obtain the same number. This same concept applied to a chemical equilibrium system results in a number called the equilibrium constant . In a chemical equilibrium system, the “count” is the molar concentration of the chemical species involved. For the purpose of symbolizing this molar concentration (and the equilibrium constant), we now introduce the symbolism of the brackets, “[].” The molar concentration (molarity) of a chemical species is symbolized by enclosing the formula for this species within brackets . For example, [H ] refers to the molar concentration of the hydrogen ion, [NH 3 ] refers to the molar concentration of ammonia, and [Cl ] refers to the molar concentration of the chloride ion. The equilibrium constant for a chemical equilibrium is defined as the molar concentrations of the products of the reaction, raised to the power of their respective balancing coefficients and multiplied together, divided by the molar concentrations of the reactants of the reaction, raised to the power of their balancing coefficients and multiplied together. Thus, for the general reaction (11.11) the equilibrium constant, symbolized as K eq , is defined as in Equation (11.12). (11.12) Knowing the molar concentrations of all the chemicals involved in the equilibrium, we can calculate the number that is given by the equilibrium constant. For Eq. (11.7), K eq is as shown in Equation (11.13). (11.13) and for Eq. (11.8), K eq is shown below, (11.14) and for Eq. (11.9) it is as follows. (11.15) Equations (11.8) and (11.9) represent “ionization” equilibria in which an uncharged chemical species (molecule or formula unit) splits apart into ions. Equation (11.8) represents the ionization of a weak acid, acetic acid, and Eq. (11.9) represents the ionization of a weak base, NH 4 OH.

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  eBook - ePub

  Chemistry

  Concepts and Problems, A Self-Teaching Guide

  • Richard Post, Chad Snyder, Clifford C. Houk(Authors)
  • 2020(Publication Date)
  • Jossey-Bass

    (Publisher)

  equilibrium constant is the ratio of the concentration of the products divided by the concentration of the reactants at equilibrium and at a specified temperature. The equilibrium constant (product concentrations divided by reactant concentrations) is valid only at a specified temperature after the reaction has gone to (completion, equilibrium) __________

  Answer: equilibrium

  Below is a reversible reaction and the expression for the equilibrium constant for this reversible reaction.

  The symbol K

  eq

  represents the equilibrium constant and the brackets [] represent the concentration (usually in moles per liter) of each product and reactant. Look at the placement of each reactant and product in the equilibrium constant expression. In the equilibrium constant expression for a reversible reaction, the (products, reactants) ____________ are located in the numerator or upper part of the fraction and the (products, reactants) ________________ are located in the denominator or lower part of the fraction.

  Answer: products; reactants

  The standard equation, then, for K

  eq

  is as follows.

  Write the equilibrium constant expression for the following reversible reaction.

  K

  eq

   = ___________________

  Answer:

  (Since there are two products, they should be placed in the upper part of the fraction. The one reactant belongs in the lower part of the fraction.)

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  Introductory Chemistry

  An Active Learning Approach

  • Mark Cracolice, Edward Peters, Mark Cracolice(Authors)
  • 2020(Publication Date)
  • Cengage Learning EMEA

    (Publisher)

  720 Chapter 18 Chemical Equilibrium 18.9 The Significance of the Value of K Goal 12 Given an equilibrium equation and the value of the equilibrium constant, identify the direction in which the equilibrium is favored. By definition, an equilibrium constant is a ratio—a fraction. The numerical value of an equilibrium constant may be very large, very small, or anyplace in between. Even though there is no defined intermediate range, equilibria with constants between 0.01 and 100 (10 22 to 10 2 ) will have appreciable quantities of all species present at equilibrium. To see what is meant by “very large” or “very small” K values, consider an equi- librium similar to the hydrogen iodide system studied in Section 18.8. If we substi- tute chlorine for iodine, the equilibrium equation is H 2 sgd 1 Cl 2 sgd (Figure 18.19) m 2 HCl(g). At 25°C, K 5 fHClg 2 fH 2 g fCl 2 g 5 2.4 3 10 33 This is a very large number—10 billion times larger than the number of particles in a mole! The only way an equilibrium constant ratio can become so huge is for the concentration of one or more reacting species to be very close to zero. If the denom- inator of a ratio is nearly zero, the value of the ratio will be very large. A near-zero denominator and large K mean the equilibrium is favored overwhelmingly in the forward direction. By contrast, if the equilibrium constant is very small, it means the concentra- tion of one or more of the species on the right-hand side of the equation is nearly zero. This puts a near-zero number in the numerator of K, and the equilibrium is strongly favored in the reverse direction. You improved your skill at writing equilibrium constant expressions. What did you learn by solving this Active Example? Practice Exercise 18.9 Write the equilibrium constant expressions for the following: a) 2 H 2 O(O) m 2 H 2 (g) 1 O 2 (g) b) CoCl 2 (s) 1 6 H 2 O(g) m CoCl 2 ? 6 H 2 O(s) Figure 18.19 Chlorine gas has a greenish-yellow color.

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  Chemistry

  The Molecular Nature of Matter

  • Neil D. Jespersen, Alison Hyslop(Authors)
  • 2014(Publication Date)
  • Wiley

    (Publisher)

  For a given overall chemical composition, the amounts of reactants and products that are present at equilibrium are the same regardless of whether the equilibrium is approached from the direction of pure “reactants,” pure “products,” or any mixture of them. Explain the basics of equilibrium laws The mass action expression is a fraction. The concentrations of the products, raised to powers equal to their coefficients in the chemical equation for a homogeneous equilibrium, are multi- plied together in the numerator. The denominator is con- structed in the same way from the concentrations of the reactants raised to powers equal to their coefficients. The numerical value of the mass action expression is the reaction quotient, Q. At equilibrium, the reaction quotient is equal to the equilibrium constant, K c . If partial pressures of gases are used in the mass action expression, is represented as K P . The magnitude of the equilibrium constant is roughly proportional to the extent to which the reaction proceeds to completion when equilibrium is reached. Equilibrium equations can be manipulated by multiplying the coefficients by a common fac- tor, changing the direction of the reaction, and by adding two or more equilibria. The rules given in the description of the Tools for Problem Solving below apply. Write and convert between equilibrium laws based on molar concentration and gas pressures The values of K P and K c are only equal if the same number of moles of gas are represented on both sides of the chemical equa- tion. When the numbers of moles of gas are different, K P is related to K c by the equation K P = K c (RT) n g . Remember to use R = 0.0821 L atm mol -1 K -1 and T = absolute temperature. Also, be careful to calculate ∆n g as the difference between the number of moles of gaseous products and the number of moles of gaseous reactants in the balanced equation.

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  eBook - ePub

  Rapid Review of Chemistry for the Life Sciences and Engineering

  With Select Applications

  • Armen S. Casparian, Gergely Sirokman, Ann Omollo(Authors)
  • 2021(Publication Date)
  • CRC Press

    (Publisher)

  4 Chemical Equilibrium

  DOI: 10.1201/9781003092759-4

  4.1 Basic Concept

  Reaction equations describe substances, called reactants, which when put together react and produce other different substances, called products. It may appear as if only products remain after the reaction is finished. In reality, many reactions do not go to completion, even if the reactants are present in stoichiometric ratios or amounts. Rather, they reach a condition known as equilibrium, denoted by double, reversible arrows in the reaction equation. Equilibrium means that there is a balance between the reactant side and the product side, or simply between the reactants and the products, and that the reaction is reversible. The chemistry of many air pollutants falls and many bodily functions under the heading of equilibrium reactions. The equilibrium condition is dynamic, not static, allowing microscopic changes in reactant and product concentrations to take place, such that no net change in reactant or product concentrations occurs, provided that no external stresses are applied. At any given time, all species in the reaction equation—reactants and products—are present at equilibrium in varying amounts. The relationship among these varying amounts can be described by a mathematical formula known as the equilibrium constant expression or simply the equilibrium expression. The equilibrium expression is set equal to an equilibrium constant symbolized by Kc .

  An equilibrium reaction can be generally represented as follows:

  a A + b B ⇋ g G   + h H

  (4.1)

  The Kc expression can then be expressed as follows:

  K c

  =

  [ G ]

  g

  [ H ]

  h

  [ A ]

  a

  [ B ]

  b

  (4.2)

  where a, b, g, and h represent the stoichiometric coefficients in the balanced reaction, and the brackets [ ] indicate molar concentrations. The simplest interpretation of Kc is that it is a measure of the extent to which a reaction goes toward completion, i.e., a reaction where the product side is favored. The meaning of Kc

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  eBook - ePub

  Survival Guide to General Chemistry

  • Patrick E. McMahon, Rosemary McMahon, Bohdan Khomtchouk(Authors)
  • 2019(Publication Date)
  • CRC Press

    (Publisher)

  constant, K (or K (subscript) to indicate a specific type of reaction). One conceptual view of equilibrium is described through the general rate expressions for the forward and reverse reactions (a more exact derivation can be developed using the techniques described in Chapter 24): k (forward) [A] x [B] y = k (reverse) [C] x [D] y ; this equation can be rewritten as: k (forward) k (reverse) = [C] x [D] y [A] x [B] y where k (forward) k (reverse) is related to the equilibrium constant K. An equation that expresses the correct equilibrium concentration ratio equal to the equilibrium constant (either the symbol or its actual numerical value) is termed the equilibrium expression: K (forward reaction) = [C] c [D ] d / [A] a [B] b The equilibrium constant, K, has a specific numerical value determined by the concentrations of each molecule in the balanced equation under specific. conditions. Example: Use the general definitions to write the complete equilibrium expression for the following reversible reaction; the symbol, K, is used since no numerical value is given. CH 4 + 2 Cl 2 → CH 2 Cl 2 + 2 HCl ← K = [C H 2 C l 2 ]  [HCl ] 2 [C H 4 ]  [C l 2 ] 2 Example: Assume that under certain conditions, the concentrations at equilibrium of each species in the previous equation are: [CH 2 Cl 2 ] = 0.850 M; [HCl] = 0.145 M [CH 4 ] = 0.0522 M; [Cl 2 ] = 0.166 M. Calculate the numerical value of K. K= [CH 2 Cl 2 ] [HCl] 2 [CH 4 ] [Cl 2 ] 2 = (0.850 M) (0.145 M) 2 (0.0522 M) (0.166 M) 2 K = 1 2. 4 The expression for the reverse reaction could be stated as: K (r e v e r s e r e a c t i o n) = [A] a [B ] b [C] c [D ] d The symmetry of the expressions for the forward and reverse reactions shows

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  eBook - ePub

  General Chemistry for Engineers

  • Jeffrey Gaffney, Nancy Marley(Authors)
  • 2017(Publication Date)
  • Elsevier

    (Publisher)

  For the equilibrium constants of reactions in aqueous solution, the concentration units are molar and the unit for the equilibrium constant in Eq. (4) is; K eq solution = M c M d M a M b = M c + d − a + b (5) The exponent, (c + d) − (a + b), represents the change in the number of moles when going from reactants to products. For cases where the number of moles of products equal the number of moles of reactants, (a + b) = (c + d), the exponent is zero and K eq is unitless. Example 7.1: Determining the Equilibrium Constant From Known Equilibrium Concentration Values Calculate the value of the equilibrium constant, K eq, for the reaction of 0.4 mol of sulfur dioxide with 1.0 mol of oxygen to form 1.4 mol of sulfur trioxide in a 2 L vessel at equilibrium. 1. Write the balanced chemical equation. 2SO 2 g + O 2 g ⇄ 2SO 3 2. Write the equilibrium constant expression for the reaction. K eq = SO 3 2 SO 2 2 O 2 3. Convert all concentrations to. molar. SO 2 = 0.4 mol 2 L = 0.2 M O 2 = 1.0 mol 2 L = 0.5 M SO 3 = 1.4 mol 2 L = 0.7 M 4. Solve for K eq. K eq = SO 3 2 SO 2 2 O 2 = 0.7 M 2 0.2 M 2 0.5 M = 24.5 M − 1 Example 7.2: Determining the Equilibrium Concentrations From Initial Concentrations of Reactants and the Equilibrium Constant What are the equilibrium concentrations for the decomposition of 0.100 M phosphorous pentachloride to phosphorous trichloride and chlorine gas (K eq = 0.030 M at 250°C)? 1. Write the balanced. chemical equation. PCl 5 g ⇄ PCl 3 g + Cl 2 g 2. Write the equilibrium constant expression for the reaction. K eq = PCl 3 Cl 2 PCl 5 = 0.030 M 3. Derive expressions for the equilibrium concentrations. At equilibrium, an unknown amount (x) of PCl 5 will be decomposed to PCl 3 and Cl 2 PCl 5 = 0.100 − x M PCl 3 = x M Cl 2 = x M 4. Insert concentration values into the equilibrium constant expression and solve

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  eBook - ePub

  Handbook of Biochemistry

  Section D Physical Chemical Data, Volume I

  • Gerald D Fasman(Author)
  • 2018(Publication Date)
  • CRC Press

    (Publisher)

  We offer in this report several recommendations with the aim of increasing the usefulness of biochemical equilibrium data and coordinating the results of different investigators. These recommendations include a set of standard conditions which would facilitate the attainment of a common body of knowledge of a wide range of biochemical equilibria. This does not preclude the choice of special experimental conditions that may be appropriate for certain reactions; but whenever possible these reactions should also be studied under the recommended standard conditions. To avoid confusion in interpretation we also recommend standardization of terminology, symbols, and units in the presentation of such data.

  For other discussions of the presentation of numerical data and of thermodynamic data derived from experiments, we call the attention of the reader to guides prepared by CODATA1 and IUPAC.2

  PART I. STANDARD CONDITIONS FOR EQUILIBRIUM MEASUREMENTS

  True thermodynamic equilibrium constants are defined in terms of activities of the reactants and products. In many systems of biochemical interest it is not possible to evaluate the activities of all components. It is, therefore, frequently necessary to calculate equilibrium constants in terms of concentrations. The proper quotient of equilibrium concentrations is acceptably constant for many purposes, and will be referred to in this document as the concentration equilibrium constant, with the symbol Kc . However, it should be recognized that values for such equilibrium constants, Kc , and corresponding Gibbs energy changes,

  Δ

  G c o

  , may not be truly constant as the composition of the system is changed.*

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