How far - the extent of chemical reactions

The Characteristics of Dynamic Equilibrium

What are reversible reactions?

• Some reactions go to completion where the reactants are used up to form the products and the reaction stops when all of the reactants are used up

• In reversible reactions, the products can react to reform the original reactants

• To show a reversible reaction, two half arrows are used: ⇌

A reversible reaction

The diagram shows an example of a forward and backward reaction that can be written as one equation using two half arrows

What is dynamic equilibrium?

• In a dynamic equilibrium the reactants and products are dynamic (they are constantly moving)

• In a dynamic equilibrium:

  • The rate of the forward reaction is the same as the rate of the backward reaction in a closed system

  • The concentrations of the reactants and products are constant

• There is no change in macroscopic properties such as colour and density as they depend on the concentration

Dynamic equilibrium between hydrogen, iodine and hydrogen iodide

The diagram shows a snapshot of a dynamic equilibrium in which molecules of hydrogen iodide are breaking down to hydrogen and iodine at the same rate as hydrogen and iodine molecules are reacting together to form hydrogen iodide

Graph of concentration against time

The diagram shows that the concentration of the reactants and products does not change anymore once equilibrium has been reached (equilibrium was approached using reactants)

Graph of concentration against time

The same equilibrium can be approached starting with the products

Examiner Tip

• Dynamic equilibrium can also be established in physical systems, for example, in a bottle of ethanol

  • Some liquid ethanol will evaporate and some ethanol vapour will condense

  • An equilibrium exists between the two phases as the rate of evaporation = the rate of condensation.

C₂H₅OH (l) ⇌ C₂H₅OH (g)

What is a closed system?

• A closed system is one in which none of the reactants or products escape from the reaction mixture

• In an open system some matter is lost to the surroundings

• When a reaction takes place entirely in solution, equilibrium can be reached in open flasks

• If the reaction involves gas, equilibrium can only be reached in a closed system

A closed system

The diagram shows a closed system in which no carbon dioxide gas can escape and the calcium carbonate is in equilibrium with the calcium oxide and carbon dioxide

An open system

The diagram shows an open system in which the calcium carbonate is continually decomposing as the carbon dioxide is lost causing the reaction to eventually go to completion

Examiner Tip

• A common misconception is to think that the concentrations of the reactants and products are equal, however,  they are not equal but constant (the concentrations are not changing)

  • Stating that the concentrations are equal will lose a mark in an exam

• The dynamic equilibrium can be reached by starting either with the reactants or products

  • In both cases, the concentrations of the reactants and products remain constant once dynamic equilibrium has been reached

The Equilibrium Law

• Equilibrium law explains how the equilibrium constant, K, can be found from the stoichiometry of the reaction

The equilibrium constant equation

• The equilibrium constant expression is an expression that links the equilibrium constant, K, to the concentrations of reactants and products at equilibrium taking the stoichiometry of the equation into account

• So, for a given reaction:

aA + bB ⇌ cC + dD

• The corresponding equilibrium constant expression is written as:

K = [C]c[D]d[A]a[B]b{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" height="47" width="116" alt="bold italic K bold space bold equals bold space fraction numerator stretchy left square bracket C stretchy right square bracket to the power of bold c stretchy left square bracket D stretchy right square bracket to the power of bold d over denominator stretchy left square bracket A stretchy right square bracket to the power of bold a stretchy left square bracket B stretchy right square bracket to the power of bold b end fraction" loading="lazy" style="box-sizing: border-box; vertical-align: -18px; max-inline-size: 100%; block-size: auto; object-fit: contain;">

• Where:

  • [A] and [B] = equilibrium reactant concentrations (mol dm^-3)

  • [C] and [D] = equilibrium product concentrations (mol dm^-3)

  • a, b, c and d = number of moles of corresponding reactants and products

• Solids are ignored in equilibrium constant expressions

• The equilibrium constant, K, of a reaction is specific to a given equation

• Examiner Tip

• You must use square brackets in equilibrium constant expressions as they have a specific meaning, representing concentrations

• In an exam answer, you would lose the mark if you used round brackets.

The Equilibrium Constant

The equilibirium constant, K

• The size of the equilibrium constant, K, tells us how the equilibrium mixture is made up with respect to reactants and products

K = [products]eqm[reactants]eqm{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" height="51" width="163" alt="bold italic K bold space bold equals bold space stretchy left square bracket products stretchy right square bracket subscript bold eqm over stretchy left square bracket reactants stretchy right square bracket subscript bold eqm" style="box-sizing: border-box; vertical-align: -20px; max-inline-size: 100%; block-size: auto; object-fit: contain;">

• If K > 1, the concentration of products is greater than the concentration of reactants and we say that the equilibrium lies to the right hand side

  • When K >> 1, equilibrium lies far over to the right hand side and the reaction almost goes to completion

• If K < 1, then the concentration of reactants is greater than the concentration of products and we say that the equilibrium lies to the left hand side

  • When K << 1, equilibrium lies far over to the left hand side and the reaction hardly proceeds

• When K = 1, at equilibrium, there are significant amounts of both reactants and products and equilibrium does not lie in favour of either the reactants or products

• K is a constant at a specified temperature

• Since temperature can affect the position of equilibrium, it follows that K is dependent on temperature

• Stronger acids dissociate more than weaker acids in solution, meaning that equilibrium lies towards the products

• So, stronger acids will have a higher value of K than weaker acids.

The relationship between K values for reactions that are the reverse of each other

• The equilibrium constant expression is dependent on a specific reaction

• For example, take the reaction between nitrogen and hydrogen to make ammonia:

N_2(g)    +    3H_2(g)  ⇌     2NH_3(g)

• The equilibrium constant expression for this reaction is:

K&#160;=NH32N2H23{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" height="57" width="111" alt="K space equals fraction numerator open square brackets NH subscript 3 close square brackets squared over denominator open square brackets straight N subscript 2 close square brackets open square brackets straight H subscript 2 close square brackets cubed end fraction" loading="lazy" style="box-sizing: border-box; vertical-align: -23px; max-inline-size: 100%; block-size: auto; object-fit: contain;">

• If we reverse the equation:

2NH_3(g) ⇌ N_2(g)    +    3H_2(g)

• The equilibrium constant expression for the reverse of this reaction, K', is:

K'&#160;=[N2]H23[NH3]2{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" height="57" width="116" alt="K apostrophe space equals fraction numerator stretchy left square bracket straight N subscript 2 stretchy right square bracket open square brackets straight H subscript 2 close square brackets cubed over denominator stretchy left square bracket NH subscript 3 stretchy right square bracket squared end fraction" loading="lazy" style="box-sizing: border-box; vertical-align: -22px; max-inline-size: 100%; block-size: auto; object-fit: contain;">

• What is the relationship between these two K values? At the same temperature, K'  becomes the reciprocal of the original K value:

Position of equilibrium

• The position of the equilibrium refers to the relative amounts of products and reactants in an equilibrium mixture.

• When the position of equilibrium shifts to the left, it means the concentration of reactants increases

• When the position of equilibrium shifts to the right, it means the concentration of products increases

Le Chatelier’s principle

• Le Chatelier’s principle says that if a change is made to a system at dynamic equilibrium, the position of the equilibrium moves to minimise this change

• The principle is used to predict changes to the position of equilibrium when there are changes in temperature, pressure or concentration

Effects of concentration on the position of equilibrium

• When the concentration of a reactant increases, the rate of the forward reaction increases and the system is no longer in equilibrium

• When a new equilibrium is established, there will be more product and less reactant within the reaction mixture, so the equilibrium has shifted to the right

• This shift has reduced the effect of the increase by removing some of the reactant

Effects of Concentration Table

Effects of concentration of the value of K

• If all other conditions stay the same, the equilibrium constant K is not affected by any changes in concentration of the reactants or products

• For example, the decomposition of hydrogen iodide:

2HI ⇌ H₂ + I₂

• The equilibrium expression is:

K&#160;=&#160;H2I2HI2&#160;=&#160;6.25&#160;&#215;&#160;10-3{"language":"en","fontFamily":"Times New Roman","fontSize":"18","autoformat":true}" class="Wirisformula" role="math" height="53" width="245" alt="K space equals space fraction numerator open square brackets H subscript 2 close square brackets open square brackets I subscript 2 close square brackets over denominator open square brackets H I close square brackets squared end fraction space equals space 6.25 space cross times space 10 to the power of negative 3 end exponent" loading="lazy" style="box-sizing: border-box; vertical-align: -19px; max-inline-size: 100%; block-size: auto; object-fit: contain;">

• Adding more HI makes the ratio of [ products ] to [ reactants ] smaller

• To restore equilibrium, [H₂] and [I₂] increases and [HI] decreases

• Equilibrium is restored when the ratio is 6.25 x 10^-3 again

Effects of pressure on the position of equilibrium

• Changes in pressure only affect reactions where the reactants or products are gases

• The pressure of a gas in a fixed volume increases as the number of gas molecules increases

• Changes in pressure will cause the equilibrium to shift to reduce the effect of this change

Effects of Pressure Table

Effects of pressure on the value of K

• If all other conditions stay the same, the equilibrium constant K is not affected by any changes in pressure of the reactants and products

Effects of temperature on the position of equilibrium

• When the temperature changes, the equilibrium will respond by moving in the direction which will absorb or release energy

Effects of Temperature Table

Effects of temperature on the value of K

• Changes in temperature change the equilibrium constant K

• For an endothermic reaction such as:

• An increase in temperature:

  • [H₂] and [I₂] increases

  • [HI] decreases

• Because [H₂] and [I₂] are increasing and [HI] is decreasing, the equilibrium constant K increases

• For an exothermic reaction such as:

• An increase in temperature:

  • [SO₃] decreases

  • [SO₂] and [O₂] increases

• Because [SO₃] decreases and [SO₂] and [O₂] increases the equilibrium constant K decreases

Effects of catalysts

• A catalyst is a substance that increases the rate of a chemical reaction (they increase the rate of the forward and reverse reaction equally)

• Catalysts only cause a reaction to reach its equilibrium faster

• Catalysts therefore have no effect on the position of the equilibrium or on the value of K

• Examiner Tip

  • When conditions of industrial processes are chosen, Le Chatelier's principle can be used to predict the conditions that would cause the equilibrium to lie towards the products, giving a high equilibrium yield

  • However, the kinetics of the reaction must also be considered as the rate of reaction needs to be sufficiently fast.

  • For example, consider a reversible reaction whose forward reaction is exothermic

    • According to Le Chatelier's principle, lower temperatures would produce a higher equilibrium yield

    • However, higher temperatures will give a faster rate of reaction

    • A compromise temperature is used which gives a lower yield of product but is made more quickly

  Heterogeneous equilibria

  • Le Chatelier's principle can also be applied to heterogeneous equilibria

  • For example, in a fizzy drink bottle, an equilibrium exists between the dissolved CO₂ and gaseous CO₂:

  CO₂ (g) ⇌ CO₂ (aq)

  • When the bottle is opened, some CO₂ (g) escapes, the equilibrium shifts to the left to reduce the effect of this change and bubbles of CO₂ (g) are observed