Chem Ch. 14
Le Chatelier's Principle: How a System at Equilibrium Responds to Disturbances
A chemical system not in equilibrium tends to progress toward equilibrium. Relative concentrations of the reactants and products at equilibrium are characterized by the equilibrium constant, K. Le Chatelier's principle: When a chemical system at equilibrium is disturbed, the system shifts in a direction that minimizes disturbance. In other words, a system at equilibrium tend to main that equilibrium. We can disturb a system in chemical equilibrium in several different ways, including chaining the concentration of a reactant or product, icing the volume or pressure, and changing the temperature.
The Significance of the Equilibrium Constant
A large equilibrium constant (K > 1) indicates that the numerator (which specifies the amounts of products at equilibrium) is larger than the denominator (which specifies the amounts of reactants at equilibrium). Therefore, when the equilibrium constant is large, the forward reaction is favored (i.e. the equilibrium point for the reaction lies to the right). A large equilibrium constant means that there is a high concentration of products and a low concentration of reactants. A small equilibrium constant (K < 1) indicates that the reverse reaction is favored and that there will be more reactants than products when equilibrium is reached (i.e. the equilibrium point for the reaction lies far to the left). A small equilibrium constant means that there is a high concentration of reactants and a low concentration of products. K > 1 = Forward reaction is favored; forward reaction proceeds essentially to completion. K < 1 = Reverse reaction is favored; forward reaction doesn't proceed very far. K = 1 = Neither direction is favored; forward reaction doesn't proceed very far. Remember, an equilibrium constant says nothing about how fast a reaction reaches equilibrium, only how far the reaction has proceeded once equilibrium is reached.
Heterogeneous Equilibria: Reactions Involving Solids and Liquids
A solids concentration remains constant in a chemic reaction (e.g. if you double the amount of carbon, its concentration remains the same). The concentration of a solid doesn't change because a solid doesn't expand to fill its container. Its concentration, therefore, depends only on its density, which is constant as long as some solid is present. For this reason, pure solids aren't included in the equilibrium expression (because their constant value is incorporated into the value of K). Similarly, the concentration of a pure liquid doesn't change. So, pure liquids are also excluded form the equilibrium expression. Note, aqueous solutions are STILL included. Only those expression labeled with "l" are excluded.
The Effect of Temperature Change on Equilibrium
An exothermic reaction (-∆H) emits heat. Heat is a product of an exothermic reaction. An endothermic reaction absorbs heat. Heat is a reactant in an endothermic reaction. Changing the temperature DOES change the value of the equilibrium constant. Increasing the temperature causes an exothermic reaction to shift left (in the direction of the reactants); the value of the equilibrium constant decreases. Decreasing the temperature causes an exothermic reaction to shift right (in the direction of the products); the value of the equilibrium constant increases. Increasing the temperature causes an endothermic reaction to shift right (in the direction of the products); the value of the equilibrium constant increases. Decreasing the temperature causes an endothermic reaction to shift left (in the direction of the reactants); the value of the equilibrium constant decreases.
The Effect of Volume (or Pressure) Change on Equilibrium
Changing the volume of a gas results in a change in pressure. Pressure and volume are inversely related: a decrease in volume cause and increase in pressure, and an increase in volume causes a decrease in pressure. If the volume of a reaction mixture at chemical equilibrium is changed, the pressure changes and the system shifts in a direction to minimize that change. Decreasing the volume cause the reaction to shift in the direction that has the fewer moles of gas particles. Increasing the volume causes the reaction to shift in the direction that has the greater number of moles of gas particles. If a reaction has an equal number of moles of gas on both sides of the chemical equation, then a change in volume produces no effect on the equilibrium. Adding an inert gas to the mixture at a fixed volume has no effect on the equilibrium because although the overall pressure of the mixture increase, the partial pressures of the reactants and products don't change.
Finding Equilibrium Concentrations from the Equilibrium Constant and Initial Concentrations or Pressures
Example: A(g) ⇌ 2B(g) I: [A] = 1.0, [B] = 0.0 C: [A] = -x, [B] = +2x E: [A] = 1.0 - x, [B] = 2x
Expressing the Equilibrium Constant in Terms of Pressure
For gaseous reactions, the partial pressure of a particular gas is proportional to its concentration. Therefore, we can also express the equilibrium constant in terms of the parietal pressures of the reactants and products. From this point on, we designate "Kc" as the equilibrium constant with respect to concentration in molarity. We now designate "Kp" as the equilibrium constant with respect to partial pressures in atmospheres (atm). The expression for Kp takes the form of the expression Kc, except that we use the partial pressure of each gas in place of its concentration: Kp = [Pproduct(s)]ⁿ/[Preactant(s)]ⁿ The value of Kp for a reaction isn't necessarily equal to the value of Kc because the partial pressure of a gas in atmospheres is not the same as its concentration. However, as long as the gases are behaving ideally, we can derive a relationship between the two constants. We get: Kp = Kc(RT)^Δn Δn is the difference between the number of moles of gaseous products and gaseous reactants. R is 0.08206 (L∙atm/mol∙K). T is the temperature in kelvins. If you are not given a temperature, go with room temperature (298 K). Notice that if the total moles of gas is the same after the reaction as before (Δn = 0), then Kp is equal to Kc.
Mastering Chemistry
For the decomposition of A to B and C, A(s) ⇌ B(g)+C(g) how will the reaction respond to each of the following changes at equilibrium? - Leftward shift: Double the concentrations of both products. - No shift: Add more A. Double the concentrations of both products then double the container volume. Double the concentration of B and halve the concentration of C. - Rightward shift: Double the container volume. Double the concentrations of both products and then quadruple the container volume. For the reaction of A and B forming C, A(g)+B(s) ⇌ 2C(g) how will the reaction respond to each of the following changes at equilibrium? - Leftward shift: Halve the concentration of A. Double the concentrations of A and C. - No shift: Quadruple the number of moles of B. - Rightward shift: Halve the concentration of C. Double the concentration of A. 1. If you reverse the equation, invert the equilibrium constant. 2. If you multiply the coefficients in the equation by a factor, raise the equilibrium constant to the same factor. 3. If you add two or more individual chemical equations to obtain an overall equation, multiply the corresponding equilibrium constants by each other to obtain the overall equilibrium constant. The concentration of a solid or a pure liquid is constant as long as some of the pure substance is present since concentration depends only on density. Changing the volume of the container does not affect a reaction when the number of moles of gaseous product is the same as the number of moles of gaseous reactants. True statements: Increasing the temperature causes an exothermic reaction to produce more reactants. Decreasing the temperature causes an exothermic reaction to produce more products. Increasing the temperature of an endothermic reaction increases the equilibrium constant.
Relationships between the Equilibrium Constant and the Chemical Equation
If a chemical equation is modified in some way, then the equilibrium constant for the equation changes because of the modification. (1) If you reverse the equation, invert the equilibrium constant (i.e. flip the equation over). Kforward = [C]/[A][B] Kreverse = [A][B]/[C] K reverse = 1 / Kforward (2) If you multiply the coefficients in the equation by a factor, raise the equilibrium constant the the same factor. nA + 2nB ⇌ 3nC K' = ([C]^3n) / ([A]^n ∙ [B]^2n) = ([C]³/[A]∙[B]²)^n = K^n (3) If you add 2 or more individual chemical equations to obtain an overall equation, multiply the corresponding equilibrium constants by each other to obtain the overall equilibrium constant. A ⇌ 2B, K1 = [B]²/[A] 2B ⇌ 3C, K2 = [C]³/[B]² A ⇌ 3C, Koverall = [C]³/[A]
The Effect of a Concentration Change on Equilibrium
Increasing the concentration of one or more of the reactants (which makes Q < K) causes the reaction to shift to the right (in the direction of the products). Increasing the concentration of one or more of the products (which makes Q > K) causes the reaction to shift to the left (in the direction of the reactants). Decreasing the concentration of one or more of the reactants (which makes Q > K) causes the reaction to shift to the left (in the direction of the reactants). Decreasing the concentration of one or more of the products (which makes Q < K) causes the reaction to shift to the right (in the direction of the products).
The Concept of Dynamic Equilibrium
Reaction rates generally increase with increasing concentration of the reactants (unless there reaction order is zero) and decrease with decreasing concentration of the reactants. A reaction that can proceed in both the forward and reverse directions is said to be reversible. Nearly are chemical reactions are at least theoretically reversible. In many cases, however, the reversibility is so small that it can be ignored. As the concentrations of reactants decrease, the rate of the forward reaction also decreases. At the same time, the concentration of the product begins to increase, so the reverse reaction starts to occur at a faster and faster rate. Eventually the rate of the reverse reaction (which has been increasing) equal the rate of the forward reaction (which has been decreasing). At that point, dynamic equilibrium is reached. Dynamic equilibrium for a chemical reaction is the condition in which the rate of the forward reaction is equal to the rate of the reverse reaction. Dynamic equilibrium is called "dynamic" because the forward and reverse relations are still occurring; however, they are occurring at the same rate. When dynamic equilibrium is reached, the concentrations of the reactants and products no longer change; they remain constant because they're forming at the same rate that they are depleted. Note that the this does not mean that the concentrations of reactants and products are equal to one another at equilibrium. Rather, the concentrations of reactants(s) and product(s), whatever ratio that may be, no longer changes.
Calculating the Equilibrium Constant from Measured Equilibrium Concentrations
The most direct way to obtain an experimental value for the equilibrium constant of a reaction is to measure the concentrations of the reactants and products in a reaction mixture at equilibrium. The concentrations within Kc should always be written in moles per liter (M). However, we don't normally include the units when expressing the value of the equilibrium constant, so Kc is unitless. For any reaction, the equilibrium concentrations of the reactants and products depend on the initial concentrations (and in general vary from one set of initial concentrations to another). However, the equilibrium constant (i.e. the formula and value of Kc) is always the same at a given temperature, regardless of the initial concentrations. Whether you start with only reactants or only products, the reaction reaches equilibrium concentrations at which the equilibrium constant is the same. No matter what the initial concentrations are, the reaction always goes in a direction that ensures that the equilibrium concentrations, when substituted into the equilibrium expression, give the same constant, K. Note that since equilibrium constants depend on temperature, many equilibrium problems state the temperature even though it has no formal part in the calculation. *See pages 663-664 for helpful examples*
Introduction
The speed of a reaction is determined by kinetics. The extent of a chemical reaction is determined by thermodynamics. We can describe and quantify how far a chemical reaction goes based on an experimentally measurable quantity called the equilibrium constant. A reaction with a large equilibrium constant proceeds nearly to completion. A reaction with a small equilibrium constant barely proceeds at all: nearly all the reactants remain as reactants, hardly forming any products. Double arrows in a reaction indicate that the reaction can occur in both the forward and reverse directions and can reach chemical equilibrium. The concentrations of the reactants and products in a reaction at equilibrium are described by the equilibrium constant, K. A large value of K means that the reaction lies to far to the right at equilibrium: a high concentration of products and low concentration of reactants. A small value of K means that the reaction lies far to the left at equilibrium: a high concentration of reactants and a low concentration of products. The value of K is a measure of how far a reaction proceeds, i.e. the large the value of K, the more the reaction proceeds towards the products. Any system at equilibrium responds to changes in ways that maintain equilibrium. If any of the concentrations of the reactants or products change, the reaction shifts to counteract that change.
Units of K
We express concentrations and partial pressures within the equilibrium constant expression in units of molarity and atmospheres, respectively. The values of concentration or partial pressure that we substitute into the equilibrium constant expression are ratios of the concentration or pressure to a reference concentration (exactly 1 M) or a reference pressure (exactly 1 atm). As long as concentration units are expressed in molarity for Kc and pressure units are expressed in atmospheres for Kp, we can skip this formality and enter the units directly into the equilibrium expression, dropping their corresponding units.
The Equilibrium Constant (K)
We know that the concentrations of reactants and products are not equal at equilibrium: rather, the rates of forward and reverse reactions are equal. the equilibrium constant is a way to quantify the concentrations of the reactants and products at equilibrium. aA + bB ⇌ cC + dD, where A and B are reactants, C and D are products, and a, b, c, and d are the respective stoichiometric coefficients in the equation. The equilibrium constant (K) for the reaction is defined as the ratio, at equilibrium, of the concentrations the products raised to their stoichiometric coefficients divided by the concentrations of the reactants raised to their stoichiometric coefficients: K = ([C]^c ∙ [D]^d) / ([A]^a ∙ [B]^b) [A] represents the molar concentration of A. This relationship between the balanced chemical equation and the expression of the equilibrium constant is known as the law of mass action.
Simplifying Approximations in Working Equilibrium Problems
When K is small, x is also small. The "x is small" approximation only works when: the initial concentration of the reactant is relatively large and the equilibrium constant is small. The x is small approximation does not mean that x is zero. If that were the case, the reactant and product concentrations wouldn't change from their initial values. The x is small approximation just means that when x is added or subtracted to another number, it doesnt' change that number by very much. The x is small approximation must satisfy the <5% rule, whereby the x approximation divided by the number it was subtracted from is is less than 5% (or 0.05). The method of successive approximation is solving for x as if it were small, and then substituting the value obtained back into the equation (where x was initially neglected) to solve for x again. This can be repeated until the calculated value of x stops changing with each iteration, an indication that we have arrived at an acceptable value for x.
The Reaction Quotient: Predicting the Direction of Change
When the reactants of a chemical reaction mix, they generally react to form products: we say that the reaction proceeds to the right (toward the products). the amount of products formed when equilibrium is reached depends on the magnitude of the equilibrium constant, as we have seen. However, what if a reaction mixture not a equilibrium contains both reactants and products? To gauge the progress of a reaction relative to equilibrium, we use a quantity called the reaction quotient. We define the reaction quotient (Qc) as the ratio, at any point in the reaction, of the concentrations of the products raised to their stoichiometric coefficients divided by the concentrations of reactants raised to their stoichiometric coefficients: Qc = ([C]^c ∙ [D]^d)/([A]^a ∙ [B]^b) Qp = (PC^c ∙ PD^d)/(PA^a ∙ PB^b) At a given temperature, the equilibrium constant has only one value and it specifies the relative amounts of reactants and products at equilibrium. The reaction quotient, by contrast, depends on the current state of the reaction and has many different values as the reaction proceeds. In a mixture containing only reactants, the reaction quotient is 0: Qc = [0]^c[0]^d/[A]^a[B]^b = 0 In a mixture containing only products, the reaction quotient is infinite: Qc = [C]^c[D]^d/[0]^a[0]^b = ∞ In a reaction mixture containing both reactants and products, each at a concentration of 1 M, the reaction quotient is 1: Qc = [1]^c[1]^d/[1]^a[1]^b = 1 The value of Q relative to K is a measure of the progress of the reaction toward equilibrium. At equilibrium, the reaction quotient is equal to the equilibrium constant. Q < K Reaction goes to the right (towards products). Q gets smaller as the reactant concentration increases and the product concentration decreases. Q > K Reaction goes to the left (towards reactants). Q gets bigger as the reaction concentration decreases and the product concentration increases. Q = K Reaction is at equilibrium. The reaction will not proceed in either direction.
