Doc Brown's Chemistry Advanced A Level Notes - Theoretical–Physical Advanced Level Chemistry – Equilibria – Chemical Equilibrium Revision Notes PART 2

2a. Chemical equilibrium expressions, equilibrium constant and the effect of temperature on the equilibrium constant K

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Introduction

How do we write out chemical equilibrium expressions. What is the equilibrium constant? How do you do equilibrium calculations?

All is explained with examples including the units for concentrations (mol dm^–3) or partial pressures (e.g. atm, Pa or kPa) and how to solve equilibrium problems using concentration or partial pressure units.

The equilibrium constant K_c is deduced from the equation for a reversible reaction, NOT experimental data as for rate expressions in kinetics. The concentration, in mol dm^-3, of a species X involved in the expression for K_c is represented by in square brackets i.e. [X]

The value of the equilibrium constant is not affected either by changes in concentration or addition of a catalyst.

You need to be able to construct an expression for K_c for a homogeneous system in equilibrium, calculate a value for K_c from the equilibrium concentrations for a homogeneous system at constant temperature, perform calculations involving K_c and predict the qualitative effects of changes of temperature on the value of K_c.

IT IS IMPORTANT and ESSENTIAL that Equilibria Part 1 is studied before working through this page

2.a Molar concentration expressions

• K_c concentration equilibrium expression INTRODUCTION

  • It is found experimentally that the concentrations at the equilibrium point are related by a simple mathematical equation known as an equilibrium expression which is governed by an equilibrium constant K, at constant temperature.

    • K only varies with temperature, and nothing else!

    • These equilibrium expressions (many on this page) were originally derived from experimental analysis of mixtures at equilibrium.

    • Patterns in these equilibrium concentrations were 'spotted' and the resulting mathematical expression of these concentrations were considered to conform to what was called the 'law of mass action' ( a term not really used these days!).

    • A classic study of the ester formation equilibrium is often described in textbooks.

      • ALCOHOL + ACID ESTER + WATER

      • Knowing the initial amounts of alcohol and acid, it was easy to titrate the remaining free carboxylic acid and then logically work out the amounts of the water, alcohol and ester left in the equilibrium mixture.

      • They would also have found out that it took some time to reach equilibrium, but eventually all the concentrations remained constant i.e. in the mixture, the point of equilibrium was reached.

        • Later studies were producing graphs of concentration versus time, and these showed that eventually all the component concentrations levelled out i.e. became constant at the first point in time that a true equilibrium was established.

      • See example 2.2a.1 ester equilibrium calculation and 2.a.5 too.

    • The theoretical justification for K expressions came later in chemical history and this need not concern us at this level because it involves some pretty advanced thermodynamics theory!

    • From a student's point of view, here at this level, you are using K in terms of concentrations or partial pressures only and therefore all other equilibrium terms, apart from K itself, should be quoted in either ...

      • ... for liquid mixtures or solutions

        • [x] = concentration of x in mol dm^–3 in a K_c equilibrium expression

      • ... or for gaseous mixtures

        • p_x = partial pressure of x in eg. Pa or atm. in a K_p equilibrium expression

        • Note

        • (i) Partial pressure is effectively a concentration term e.g. double a partial pressure and you effectively double the concentration of the gaseous component.

        • (ii) The subscript c in K_c means a concentration equilibrium expression using mol dm^–3 and the subscript p in K_p means a partial pressure equilibrium using partial pressures.

        • (iii) The units of K depend on which units for concentration or partial pressure you have used for the quantities inserted in the equilibrium expression.

          • This means that sometimes the concentration or partial pressure units cancel each other out, hence K can be dimensionless!

  • For any reaction in solution or a gaseous mixture:

    • aA + bB + cC etc. tT + uU + wW etc.

    • in terms of concentrations ...

    • Kc =	[T]t [U]u [V]v etc.
      	–––––––––––––––––
      	[A]a [B]b [C]c etc.

    • [x_(?)] square brackets indicates concentration of x e.g. in mol dm^–3 and the state_(?) should be quoted too.
    • Note that all the equilibrium expressions you will deal with at this level only involve concentrations or partial pressures.

  • By convention, the arithmetical product of the product concentrations^* of the forward reaction (RHS) are on the top line and the arithmetical product of the reactant concentrations^* from the backward reaction (LHS) are on the bottom line.

    • ^* In all cases the product concentrations are raised to the appropriate power (a, b, c, .. t, u, w, ..) given by the stoichiometric mole ratios of the balanced equation.

    • AND again note that K_c (like K_p) is only constant for a specific constant temperature at which the concentrations of the equilibrium components might vary from one dynamic equilibrium situation to another (e.g. in reacting liquid mixtures or in solutions).

  • For heterogeneous equilibria, K expressions do not normally include values for solid phases, since their chemical potential cannot change since the concentration of a solid cannot change.

• The effect of temperature on the equilibrium constant (Kc or Kp)

  • Please remember, only temperature changes K, because only changing temperature can change the energy of the molecules.

  • First consider the simple equilibrium: aA + bB   cC + dD   {(i) ΔH -ve, (ii) ΔH +ve}

  • Using the convention described above, writing out the concentration equilibrium expression gives ...

  • Kc =	[C]c [D]d
    	–––––––––
    	[A]a [B]b

• The equilibrium constant, K_c (or K_p later), is governed by temperature, which is the only factor that can alter the internal potential energy of the reactants or products. The 'rule' for the trend in K value change is provided by Le Chatelier's Principle.

  • (i) If the forward reaction is exothermic, K_c (or K_p later) will decrease in value with increase in temperature.

    • From Le Chatelier's Principle, the equilibrium position will shift more to the left in the endothermic direction to minimise the temperature increase due to the effect of increased heat input.

    • So, mathematically, by convention, the top line concentrations of the forward products, [C] & [D], will numerically decrease and the bottom line concentrations [A] & [B] must therefore numerically increase, since some of the C & D are converted to A & B.

    • Hence the equilibrium constant K must decrease for the new equilibrium position.

  • (ii) If the forward reaction is endothermic, K_c (or K_p) will increase in value with increase in temperature.

    • From Le Chatelier's Principle, the equilibrium position will shift more to the right in the endothermic direction to minimise the temperature increase due to the effect of increased heat input.

    • So, mathematically, by convention, the top line concentrations of the forward products, [C] & [D], must numerically increase and the bottom line concentrations of [A] & [B] must therefore numerically decrease, since some of A & B are converted to C & D.

    • Hence the equilibrium constant K must increase for the new equilibrium position.

  • Changes in pressure or concentration have no effect on a K value for ideal mixtures of gases/liquids or solutions.

  • Application of a catalyst to a reaction also has no effect on a K value.

  • Why are the values of equilibrium constants affected by temperature?

    • As we have noted, it is very important to quote the specific constant temperature that applies to any K_c or K_p value BECAUSE equilibrium constants vary with temperature AND ONLY temperature.

    • This is because changes in concentration, partial pressure or employing a catalyst do NOT affect the energy content of the molecules themselves (referred to in thermodynamics as the internal energy of the molecule).

      • internal energy (symbol U) = chemical energy + thermal energy

    • However, if you change the temperature, you also change the fundamental energy content of a molecule, and we are now talking about the thermodynamic property values of the equilibrium components.

    • Electronic energy is stored in the chemical bonds of the molecules (chemical potential energy) plus their thermal energies of translation (kinetic energy of movement), rotation (of the whole or parts of a molecule) and vibration (of bonded atoms).

      • internal energy  = chemical potential energy + thermal energy

    • If you change the temperature, all the internal energy contents of the molecules are also changed, but they don't change to the same amount for each molecule for the same rise in temperature.

    • If you think of the internal energy as a sort of chemical potential to effect a chemical change, the formation of 'reactants' or 'products' may be favoured one way or the other (l to r or r to l as you write the equilibrium equation).

    • Hence the equilibrium constant not only changes, but may increase or decrease depending on whether the reaction is endothermic or exothermic (as argued above).

      • The enthalpy content of a molecule (H) is related to its internal energy (U), but that's as far as we need to go here!

    • Therefore the change in the internal energy (caused by change in temperature), a fundamental thermodynamic property of a molecule, explains why equilibrium constants are ONLY affected by temperature and NOT by concentration, pressure or indeed, the presence of a catalyst.

    • You can calculate equilibrium constant from thermodynamic Gibbs free energy change data for the reaction, but this may not be part of your course and certainly not appropriate to study here.

• See later specific examples for the units of K_c (or K_p later) and if K has no units you should state so.

• Some 'VERY rough rules of thumb' for an equilibrium K value and 'position' of the equilibrium in terms of LHS (e.g. original reactants of he forward reaction and the RHS (products of the forward reaction)

  • For: LHS RHS

  • (for A + B C + D the rules below work ok BUT once the ratios of reactants or products are not 1:1, things are not so simple)

  • If K is >> 1 the equilibrium is mainly on the RHS, maybe virtually 100% completion of the forward reaction i.e. a very large RHS yield i.e. and likely to be very thermodynamically feasible.

  • If K is approx. 1 the equilibrium is more evenly distributed between the RHS and LHS.

  • If K_c (or K_p) is << 1 the equilibrium is mainly on the LHS, maybe virtually 0% of products of the forward reaction i.e. a very low RHS yield i.e. likely to be less thermodynamically feasible.

  • BUT remember K changes with temperature considerably changing the position of an equilibrium, AND, at constant temperature, and therefore constant K, the position of an equilibrium can change significantly depending on relative concentrations/pressures of 'reactants' and 'products'.

  • Finally a catalyst may speed up getting to the equilibrium but a catalyst cannot affect the position of the equilibrium constant or the value of the equilibrium constant K (K_c or K_p).

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WHAT NEXT?

Advanced Equilibrium Chemistry Notes Part 1. Equilibrium, Le Chatelier's Principle–rules * Part 2. K_c and K_p equilibrium expressions and calculations * Part 3. Equilibria and industrial processes * Part 4 Partition between two phases, solubility product K_sp, common ion effect, ion–exchange systems * Part 5. pH, weak–strong acid–base theory and calculations * Part 6. Salt hydrolysis, acid–base titrations–indicators, pH curves and buffers * Part 7. Redox equilibria, half–cell electrode potentials, electrolysis and electrochemical series * Part 8. Phase equilibria–vapour pressure, boiling point and intermolecular forces watch out for sub-indexes to multiple sections or pages

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