CHEMICAL EQUILIBRIUM Chapter 7. Chemical equilibrium Chemical reactions tend to move towards a dynamic equilibrium in which both reactants and products.

CHEMICAL EQUILIBRIUM Chapter 7

Chemical equilibrium Chemical reactions tend to move towards a dynamic equilibrium in which both reactants and products are present but have no further tendency to undergo net change. Chemical reactions tend to move towards a dynamic equilibrium in which both reactants and products are present but have no further tendency to undergo net change.

Spontaneous chemical reactions The direction of spontaneous change at constant temperature and pressure is towards lower values of Gibbs energy. The direction of spontaneous change at constant temperature and pressure is towards lower values of Gibbs energy. This idea also applies to chemical reactions. This idea also applies to chemical reactions. If we can calculate the minimum value of the Gibbs energy for a particular reaction mixture, this corresponds to the location of the equilibrium composition. If we can calculate the minimum value of the Gibbs energy for a particular reaction mixture, this corresponds to the location of the equilibrium composition.

Spontaneous chemical reactions The quantity  (xi) is called the extent of the reaction and has units of moles. The quantity  (xi) is called the extent of the reaction and has units of moles.

Spontaneous chemical reactions The reaction Gibbs energy  r G is defined as the slope of the Gibbs energy plotted against the extent of reaction The reaction Gibbs energy  r G is defined as the slope of the Gibbs energy plotted against the extent of reaction

Spontaneous chemical reactions

Exergonic and endergonic reactions We can express the spontaneity of a reaction at constant temperature and pressure in terms of the reaction Gibbs energy. We can express the spontaneity of a reaction at constant temperature and pressure in terms of the reaction Gibbs energy. If  r G < 0, the forward reaction is spontaneous If  r G < 0, the forward reaction is spontaneous If  r G > 0, the reverse reaction is spontaneous If  r G > 0, the reverse reaction is spontaneous If  r G = 0, the reaction is at equilibrium If  r G = 0, the reaction is at equilibrium

Exergonic and endergonic reactions If a reaction for which  r G < 0 is called exergonic. If a reaction for which  r G < 0 is called exergonic. Because the process is spontaneous it can be used to drive another process, such as another reaction, or used to do non-expansion work. Because the process is spontaneous it can be used to drive another process, such as another reaction, or used to do non-expansion work.

Exergonic and endergonic reactions In biological cells, the oxidation of carbohydrates acts as the heavy weight that drives other reactions such as formation of proteins from amino acids, muscle contractions and brain activity. In biological cells, the oxidation of carbohydrates acts as the heavy weight that drives other reactions such as formation of proteins from amino acids, muscle contractions and brain activity.

Exergonic and endergonic reactions If a reaction for which  r G > 0 is called endergonic. If a reaction for which  r G > 0 is called endergonic. The reaction is not spontaneous and can only proceed by doing work on it, such as electrolyzing water to reverse its spontaneous formation reaction. The reaction is not spontaneous and can only proceed by doing work on it, such as electrolyzing water to reverse its spontaneous formation reaction.

Equilibrium

Equilibrium A stoichiometric number is positive for products and negative for reactants A stoichiometric number is positive for products and negative for reactants

Equilibrium If  changes by , then the change in the amount of of any species J is J  If  changes by , then the change in the amount of of any species J is J 

Equilibrium If initially there is 10 mol of N 2 present, when the extent of reaction changes from x = 0 to x = 1 (so  = +1 mol), the amount of N 2 changes from 10 mol to 9 mol. If initially there is 10 mol of N 2 present, when the extent of reaction changes from x = 0 to x = 1 (so  = +1 mol), the amount of N 2 changes from 10 mol to 9 mol.

Equilibrium When  = +1 mol, the amount of NH 3 changes by +2 mol and the amount of H 2 changes by -3 mol. When  = +1 mol, the amount of NH 3 changes by +2 mol and the amount of H 2 changes by -3 mol.

Equilibrium When  = +10 mol, all the N 2 is consumed. When  = +10 mol, all the N 2 is consumed.

Equilibrium

Equilibrium An equilibrium constant K expressed in terms of activities is called a thermodynamic equilibrium constant. An equilibrium constant K expressed in terms of activities is called a thermodynamic equilibrium constant. Activities are dimensionless numbers so the thermodynamic equilibrium constant is also dimensionless. Activities are dimensionless numbers so the thermodynamic equilibrium constant is also dimensionless.

Equilibrium In elementary applications, activities can be replaced by numerical values of molalities, molarities or partial pressures. In elementary applications, activities can be replaced by numerical values of molalities, molarities or partial pressures. The resulting expressions are only approximations. The resulting expressions are only approximations.

Equilibrium In elementary applications, K  = 1 so K ≈ K b In elementary applications, K  = 1 so K ≈ K b

How equilibria respond to pressure The equilibrium constant depends on the value of  r G θ, which is defined at a single, standard pressure. Hence K is independent of the pressure. The equilibrium constant depends on the value of  r G θ, which is defined at a single, standard pressure. Hence K is independent of the pressure.

How equilibria respond to pressure The conclusion that K is independent of pressure does not necessarily mean that the equilibrium composition is independent of the pressure. The conclusion that K is independent of pressure does not necessarily mean that the equilibrium composition is independent of the pressure. It depends on how pressure is applied. It depends on how pressure is applied.

How equilibria respond to pressure Consider a reaction vessel in which the pressure in the vessel is increased by injecting an inert gas. Consider a reaction vessel in which the pressure in the vessel is increased by injecting an inert gas. The presence of another gas does not alter the equilibrium composition because the partial pressure of each reacting gas molecules does not changed upon addition of the inert gas. The presence of another gas does not alter the equilibrium composition because the partial pressure of each reacting gas molecules does not changed upon addition of the inert gas.

How equilibria respond to pressure If however, the pressure is increased by confining the gases to a smaller volume. If however, the pressure is increased by confining the gases to a smaller volume. Consider the reaction A  2B. Consider the reaction A  2B.

How equilibria respond to pressure Consider the reaction A  2B. Consider the reaction A  2B. For the right hand side of the equation to remain constant, p A must increase sufficiently to cancel out the increase in the square of p B. For the right hand side of the equation to remain constant, p A must increase sufficiently to cancel out the increase in the square of p B.

How equilibria respond to pressure Consider the reaction A  2B. Consider the reaction A  2B. In order for p A to increase sufficiently, the equilibrium composition must shift in favor of A at the expense of B. The number of A molecules will increase as the volume is decreased. In order for p A to increase sufficiently, the equilibrium composition must shift in favor of A at the expense of B. The number of A molecules will increase as the volume is decreased.

How equilibria respond to pressure The increase in the number of A molecules and the corresponding number B molecules in the equilibrium A  2B is a special case of a Le Chatelier’s principle that states: The increase in the number of A molecules and the corresponding number B molecules in the equilibrium A  2B is a special case of a Le Chatelier’s principle that states: “A system at equilibrium, when subject to a disturbance, responds in a way that tends to minimize the effect of the disturbance”.

How equilibria respond to pressure The principle implies that, if a system at equilibrium is compressed, then the reaction will adjust to minimize the pressure. It does this by reducing the number of particles in the gas phase. The principle implies that, if a system at equilibrium is compressed, then the reaction will adjust to minimize the pressure. It does this by reducing the number of particles in the gas phase.

How equilibria respond to pressure Suppose that there is an amount n of A present initially (no B). At equilibrium the amount of A is (1-  )n and the amount of B is 2  n, where  is the extent of dissociation of A into 2B. Suppose that there is an amount n of A present initially (no B). At equilibrium the amount of A is (1-  )n and the amount of B is 2  n, where  is the extent of dissociation of A into 2B.

How equilibria respond to pressure So even though K is independent of pressure, the amounts of A and B do depend on pressure. So even though K is independent of pressure, the amounts of A and B do depend on pressure.

How equilibria respond to temperature Le Chatelier’s principle predicts that a system at equilibrium will tend to shift in the endothermic direction if the temperature is raised. Le Chatelier’s principle predicts that a system at equilibrium will tend to shift in the endothermic direction if the temperature is raised. Conversely, an equilibrium can be expected to shift in the exothermic direction if the temperature is lowered. Conversely, an equilibrium can be expected to shift in the exothermic direction if the temperature is lowered.

How equilibria respond to temperature Exothermic reactions: increased temperature favors the reactants. Exothermic reactions: increased temperature favors the reactants. Endothermic reactions increased temperature favors the products. Endothermic reactions increased temperature favors the products.

How equilibria respond to temperature The van’t Hoff equation (Justification 7.2), is an expression for the slope of a plot of the equilibrium constant as a function of temperature. The van’t Hoff equation (Justification 7.2), is an expression for the slope of a plot of the equilibrium constant as a function of temperature.

How equilibria respond to temperature For an exothermic reaction, dlnK/dT < 0. The negative slope means that ln K, and therefore K itself, decreases as the temperature rises. For an exothermic reaction, dlnK/dT < 0. The negative slope means that ln K, and therefore K itself, decreases as the temperature rises. If K decreases, then equilibrium shifts away from products. If K decreases, then equilibrium shifts away from products.

How equilibria respond to temperature For an exothermic reaction,  r H θ /T is negative and corresponds to the increase of entropy in the surroundings. For an exothermic reaction,  r H θ /T is negative and corresponds to the increase of entropy in the surroundings. Increasing entropy drives a spontaneous change. Increasing entropy drives a spontaneous change.

How equilibria respond to temperature When the temperature is increased,  r H θ /T decreases and so the decreasing entropy of the surroundings has less importance, so there is less driving force for the forward reaction and reactants are favored. When the temperature is increased,  r H θ /T decreases and so the decreasing entropy of the surroundings has less importance, so there is less driving force for the forward reaction and reactants are favored.

How equilibria respond to temperature For an endothermic reaction,  r H θ /T is positive and corresponds to the decrease of entropy in the surroundings. For an endothermic reaction,  r H θ /T is positive and corresponds to the decrease of entropy in the surroundings. Driving force is the increase of entropy in the system. Driving force is the increase of entropy in the system.

How equilibria respond to temperature When the temperature is increased,  r H θ /T gets smaller. This corresponds to less loss of entropy in the surroundings. When the temperature is increased,  r H θ /T gets smaller. This corresponds to less loss of entropy in the surroundings. This favors a shift towards reaction products. This favors a shift towards reaction products.

How equilibria respond to temperature If we assume  r H θ varies little with temperature over the temperature range of interest, then we can take it outside the integral. If we assume  r H θ varies little with temperature over the temperature range of interest, then we can take it outside the integral.

Calculating an equilibrium constant Calculate the equilibrium constant for the reaction N 2 + 3H 2  2NH 3 at 298 K. Calculate the equilibrium constant for the reaction N 2 + 3H 2  2NH 3 at 298 K.

Calculating degree of dissociation The standard Gibbs energy of reaction for the decomposition H 2 O(g)  H 2 (g)+ ½ O 2 (g) is +118.08 kJ mol -1 at 2300 K. What is the degree of dissociation of H 2 O at 2300 K and 1.00 bar? The standard Gibbs energy of reaction for the decomposition H 2 O(g)  H 2 (g)+ ½ O 2 (g) is +118.08 kJ mol -1 at 2300 K. What is the degree of dissociation of H 2 O at 2300 K and 1.00 bar?

H2OH2OH2H2 O2O2 Initial amountn00 Change at equilibrium -n-n+n+n+1/2  n Amount at equilibrium (1-  )n nn½(  n) Mole fraction (1-  )/(1+½  )  /(1+½  )½  /(1+½  ) Partial Pressure (1-  )p/(1+½  )  p/(1+½  )½  p/(1+½  )

H2OH2OH2H2 O2O2 Initial amount n00 Change at equilibrium -n-n+n+n+1/2  n Amount at equilibrium (1-  )n nn½(  n) Mole fraction (1-  )/(1+½  )  /(1+½  )½  /(1+½  ) Partial Pressure (1-  )p/(1+½  )  p/(1+½  )½  p/(1+½  )

Equilibrium electrochemistry An electrochemical cell consists of two electrodes, in contact with an electrolyte. An electrochemical cell consists of two electrodes, in contact with an electrolyte. An electrolyte is a material that allows the transport of charged species or an ionic conductor. This may be a solution, a liquid, or a solid. An electrolyte is a material that allows the transport of charged species or an ionic conductor. This may be a solution, a liquid, or a solid. An electrode and its electrolyte comprise an electrode compartment. An electrode and its electrolyte comprise an electrode compartment.

Equilibrium electrochemistry There are a number of electrode configurations. There are a number of electrode configurations. A common electrode configuration consists of a metal that participates in the electrochemical reaction i.e. M(s)|M + (aq) – metal/metal ion electrode type. A common electrode configuration consists of a metal that participates in the electrochemical reaction i.e. M(s)|M + (aq) – metal/metal ion electrode type. An ‘inert’ metal may make up one of the electrodes but is only present as a source or sink of electrons. It takes no other part in the reaction other than acting as a catalyst for it i.e. Pt(s)|X 2 (g)|X + (aq) or Pt(s)|X 2 (g)|X + (aq) – gas electrode. An ‘inert’ metal may make up one of the electrodes but is only present as a source or sink of electrons. It takes no other part in the reaction other than acting as a catalyst for it i.e. Pt(s)|X 2 (g)|X + (aq) or Pt(s)|X 2 (g)|X + (aq) – gas electrode.

Equilibrium electrochemistry M(s)|MX(s)|X - (aq) – Metal/insoluble salt M(s)|MX(s)|X - (aq) – Metal/insoluble salt Pt(s)|M + (aq)|M 2+ (aq) - redox electrode. Pt(s)|M + (aq)|M 2+ (aq) - redox electrode. Redox – Reduction – Oxidation Redox – Reduction – Oxidation OIL RIG OIL RIG A redox reaction implies the transfer of electrons. A redox reaction implies the transfer of electrons. Oxidizing agent (or oxidant) is the electron acceptor. Oxidizing agent (or oxidant) is the electron acceptor. Reducing agent (or reductant) is the electron donor. Reducing agent (or reductant) is the electron donor. A redox equation may be expressed in terms of two half reactions. One oxidation reaction and one reduction equation. A redox equation may be expressed in terms of two half reactions. One oxidation reaction and one reduction equation.

A galvanic cell is an electrochemical cell that produces electricity as a result of a spontaneous reaction. A galvanic cell is an electrochemical cell that produces electricity as a result of a spontaneous reaction. An electrolytic cell is an electrochemical cell in which a non-spontaneous reaction is driven by an external source of current. An electrolytic cell is an electrochemical cell in which a non-spontaneous reaction is driven by an external source of current. Potential difference Potential difference

Varieties of cells The simplest type of cell has a single electrolyte common to both electrodes. The simplest type of cell has a single electrolyte common to both electrodes. In some cases it is necessary to immerse the electrodes in different electrolytes as in the Daniell cell in which the redox couple at one electrode is Cu 2+ /Cu and at the other is Zn 2+ /Zn. In some cases it is necessary to immerse the electrodes in different electrolytes as in the Daniell cell in which the redox couple at one electrode is Cu 2+ /Cu and at the other is Zn 2+ /Zn.

Zn(s)  Zn 2+ (aq) + 2e - Zn(s)  Zn 2+ (aq) + 2e - Cu 2+ (aq) + 2e -  Cu(s) Cu 2+ (aq) + 2e -  Cu(s) Copper is the cathode Copper is the cathode Zinc is the anode Zinc is the anode

Liquid junction potentials In a cell with two different electrolyte solutions, as in the Daniell cell, there is an additional source of potential difference across the interface of the two electrolytes. In a cell with two different electrolyte solutions, as in the Daniell cell, there is an additional source of potential difference across the interface of the two electrolytes. This potential is called the liquid junction potential, E lj. This potential is called the liquid junction potential, E lj. A way to reduce this potential is to use a salt bridge to join the electrolyte compartments. A way to reduce this potential is to use a salt bridge to join the electrolyte compartments.

Notation Phase boundaries are represented by vertical bars | Phase boundaries are represented by vertical bars | CuSO 4 (aq)|Cu(s) CuSO 4 (aq)|Cu(s) A liquid junction is represented by 3 vertical dots A liquid junction is represented by 3 vertical dots A double vertical line || denotes an interface in which it is assumed the junction potential has been eliminated. A double vertical line || denotes an interface in which it is assumed the junction potential has been eliminated. Zn(s)|ZnSO 4 (aq)||CuSO 4 (aq)|Cu(s) Zn(s)|ZnSO 4 (aq)||CuSO 4 (aq)|Cu(s) Convention is to write the anode half cell first and the cathode half cell second. Convention is to write the anode half cell first and the cathode half cell second.

The electromotive force The electric current produced by a galvanic cell arises from a spontaneous chemical reaction taking place inside it. The electric current produced by a galvanic cell arises from a spontaneous chemical reaction taking place inside it. Zn(s)|ZnSO 4 (aq)||CuSO 4 (aq)|Cu(s) Zn(s)|ZnSO 4 (aq)||CuSO 4 (aq)|Cu(s) The cathode is where reduction takes place and the anode is where oxidation takes place: The cathode is where reduction takes place and the anode is where oxidation takes place: Right hand electrode: Cu 2+ (aq) + 2e -  Cu(s) Left hand electrode: Zn(s)  Zn 2+ (aq) + 2e -

The Nernst equation A cell in which the overall cell reaction has not reached chemical equilibrium can do electrical work as the reaction drives electrons through an external circuit. A cell in which the overall cell reaction has not reached chemical equilibrium can do electrical work as the reaction drives electrons through an external circuit. The work that a given transfer of electrons can depends on the potential difference between the two electrodes. The work that a given transfer of electrons can depends on the potential difference between the two electrodes. The cell potential is measured in volts, V. The cell potential is measured in volts, V. - FE =  r G (Justification 7.3) - FE =  r G (Justification 7.3)  is the stoichiometric coefficient of the electrons in the half reactions, F is Faraday’s constant, and E is the emf.  is the stoichiometric coefficient of the electrons in the half reactions, F is Faraday’s constant, and E is the emf.

The Nernst equation E θ - standard EMF of a cell. E θ - standard EMF of a cell.

The Nernst equation

Cells at equilibrium

For a Daniell cell: Cu 2+ (aq) + Zn(s)  Cu(s) + Zn 2+ (aq) For a Daniell cell: Cu 2+ (aq) + Zn(s)  Cu(s) + Zn 2+ (aq) = 2 and the standard emf is +1.10 V = 2 and the standard emf is +1.10 V

Cells at equilibrium For a Daniell cell: Cu 2+ (aq) + Zn(s)  Cu(s) + Zn 2+ (aq) For a Daniell cell: Cu 2+ (aq) + Zn(s)  Cu(s) + Zn 2+ (aq) = 2 and the standard emf is +1.10 V = 2 and the standard emf is +1.10 V

Standard Potentials A galvanic cell is a combination of two electrodes and each one can be considered as making a characteristic contribution to the overall cell potential. A galvanic cell is a combination of two electrodes and each one can be considered as making a characteristic contribution to the overall cell potential. It is not possible to measure the contribution of a single electrode, so we measure the potential of electrodes by defining the standard hydrogen electrode (SHE) to be zero and then measure the electrode of interest in combination with the SHE. It is not possible to measure the contribution of a single electrode, so we measure the potential of electrodes by defining the standard hydrogen electrode (SHE) to be zero and then measure the electrode of interest in combination with the SHE. Pt(s)|H 2 (g)|H + (aq)E θ = 0 V Pt(s)|H 2 (g)|H + (aq)E θ = 0 V

Standard Potentials For two redox couples Ox 1 /Red 1 and Ox 2 /Red 2 For two redox couples Ox 1 /Red 1 and Ox 2 /Red 2 Red 1 |Ox 1 ||Red 2 |Ox 2 E θ = E θ 2 – E θ 1 Red 1 |Ox 1 ||Red 2 |Ox 2 E θ = E θ 2 – E θ 1 Red 1 + Ox 1  Ox 2 + Red 2 is spontaneous if E θ > 0 Red 1 + Ox 1  Ox 2 + Red 2 is spontaneous if E θ > 0 If E θ < 0 then work has to be done on the system for the reaction occur as written. If E θ < 0 then work has to be done on the system for the reaction occur as written.

Standard Potentials Pt(s)|H 2 (g)|H + (aq)||Cu 2+ (aq)|Cu(s) E θ = +0.34 V Pt(s)|H 2 (g)|H + (aq)||Cu 2+ (aq)|Cu(s) E θ = +0.34 V Pt(s)|H 2 (g)|H + (aq)||Zn 2+ (aq)|Zn(s) E θ = -0.76 V Pt(s)|H 2 (g)|H + (aq)||Zn 2+ (aq)|Zn(s) E θ = -0.76 V

Determining other thermodynamic functions

CHEMICAL EQUILIBRIUM Chapter 7. Chemical equilibrium Chemical reactions tend to move towards a dynamic equilibrium in which both reactants and products.

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CHEMICAL EQUILIBRIUM Chapter 7. Chemical equilibrium Chemical reactions tend to move towards a dynamic equilibrium in which both reactants and products.

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Presentation on theme: "CHEMICAL EQUILIBRIUM Chapter 7. Chemical equilibrium Chemical reactions tend to move towards a dynamic equilibrium in which both reactants and products."— Presentation transcript:

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