When a reactant is added to a system in equilibrium more product is produced but the value of the equilibrium constant K remains unaltered?

3) Reactants A and B are placed in a 2.00 L sealed reaction vessel and allowed to reach equilibrium. The reaction is given below.
A2(g) + 2B2(g)

a) Calculate the equilibrium constant at the :

- 4 minute mark
Solution

- 10 minute mark
Solution

b) What happened at the 6 minute mark? Solution

c) At the 11 minute mark substance X is added to the system. Substance X reacts with AB2 to form a solid compound. Draw, on the graph on the right, how the system will react. Solution

4) What are the advantages and disadvantages of increasing the temperature of an equilibrium system involving an exothermic reaction? Solution

5) How can the disadvantages be overcome in question 4) above? Solution

Page 2

Draw how the system will respond by completing the graphs shown on the right when at :

t1 - the concentration of nitrogen gas is increased to 9.0 M

t2 - the volume of the reaction vessel is decreased

t3 - the temperature of the reaction vessel is cooled.

Solution

You have studied several topics in Year 11 which will help form the basics and understandings of The Chemical Equilibrium. The following topics will be studied:

• Exothermic and Endothermic reactions
• Rates of reaction
• Entropy and free energy

Section 1: Exothermic and Endothermic Reactions.

• During a chemical reaction, substances (ie reactants, products and catalysts) can be thought of as they are present in a
• The matter/ molecules present around this chemical system are known as the

During a chemical reaction, energy can either be conserved, gained or lost to the surroundings. The total energy stored within the reactant bonds and the bonds within the products can greatly differ, and thus allowing chemical reactions can either be exothermic or endothermic relative to the total bond energy of the substances present within the system.
Exothermic Reaction– Heat is given off to the surroundings (the energy required to break the bonds within the reactants is greater than the energy required to form the bonds of the products and thus an excess of energy is released).
Endothermic Reaction- Heat (energy) is absorbed from the surroundings (the energy required to break the reactant bonds is less than the energy required to form product bonds, thus an excess of heat is absorbed)
Both of these types of reactions can be presented on energy profile diagrams:

Diagram (Left)- Exothermic Reaction
Diagram (Right)- Endothermic Reaction

Activation Energy (RED LINE ON DIAGRAMS)- Minimum amount of energy required to before a chemical reaction can proceed (can be thought of as the amount of effort exerted to push a ball up a hill that effort is known as the activation energy).

Both exothermic and endothermic reactions have particular activation energies depending on the type of reactants and products present (relative to bond energies). A low activation energy (the length of the red line is shorter ie exothermic reaction diagram- the quicker the chemical reaction can be initiated (easier for reactant collisions to readily occur). A higher activation energy correlates to a greater energy input required in order for the desired reactant collisions to occur.

Enthalpy and Thermochemical Equations

Another component presented on the above diagrams is the green line (Enthalpy Change) Denoted as DeltaH.

Enthalpy Change – The amount (quantitative) of energy released or absorbed during the chemical reaction.

Thermochemical Equations: Show enthalpy change in a reaction by writing the delta H value on the right-hand side of a given chemical reaction. This energy can be denoted either in Joules per mole (Jmol) or kilojoules per mole (kJmol).
Hence the delta H correlates directly to specific molear amounts relative to the coefficients of both reactants and products (Molears ratios).

• A change in coefficients- delta H value changes by same factor
• When a chemical reaction is reversed, the sign of delta H is also reversed
• States of matter in a chemical reaction should be shown in all equations, as changes of state, can change the value and sign of delta H.

Example Reaction: (Respiration = Exothermic, since delta H is less than 0)

Rates of Reaction:
The rate of reaction of a given chemical reaction can be calculated by observing the changes in the relative concentrations of reactants and products changing over time as the reaction proceeds. This rate of reaction can be increased by:

• Increasing the concentration or pressure of solutions and gases respectively.
• Increased surface area of solid reactant (ie powdered form)
• Increased temperature (faster collisions within reactants)
• Using a catalyst (to lower the activation energy, thus reaction proceeds quicker).

This leads onto the collision theory to further our understanding of how the above 4 factors can increase the rate of reaction.

Collision theory- Relies on the rate and frequency of reactant collisions having an impact on the rate of reaction. As noted above, for a chemical reaction to occur, collisions must occur: although it must be noted that not all collisions lead to successful reactions.  A chemical reaction occurs when the following are addressed:

• Frequency of collisions
• Orientation of particles upon collision
• Energy of particles upon colliding (relative to activation energy).

Our understanding of the collision theory can be applied to further our knowledge and conceptual understanding of why concentration, surface area, temperature and catalysts directly affect the rate of a chemical reaction.

Entropy and Free Energy

Entropy (symbol S)- Measure of the number of possible arrangements of a system, can also be denoted as the degree of disorder within a given chemical system. For the purposes of the HSC Chemistry syllabus: the following rule can be followed- Entropy increases (Delta S) as:

• The volume occupied by particles in a system increases (or a decrease in pressure)
• Increase in the number of particles
• Increase in the temperature of the system
• Change in state of matter of a substance (from solid to liquid or liquid to gas)

This leads us onto the second law of thermodynamics: Overall entropy of the entire universe is increasing according to the formula:

Depending on the particular type of chemical reaction, the entropy either increases or decreases. A chemical reaction which involves a decrease in entropy occurs directly when there is an increase in the entropy of the surroundings, in which case the sum of the two entropies (System and surroundings) produces an increase in entropy for the universe, according to the formula above.
(note: system and surrounding entropy are inversely proportional).

Spontaneous Reaction- Defined as a reaction which occurs without the input of any form of energy or heat (occurs of its own accord). Gibbs free energy is used to quantitively measure if a given reaction is spontaneous. The formula to calculate the change in Gibbs free energy (denoted as delta G)- (written the same way in standard stable conditions- 298K, 1 bar).

Note: In the above formula- Delta H = Enthalpy.
TdeltaS- Total ENTROPY FROM ABOVE (UNIVERSE)
The 3 scenarios to determine the state of a given reaction are noted below:

• Reactions which are exothermic (delta H is less than 0), with delta S positive are always spontaneous, in accordance with above formula.
• Reactions with delta H greater than 0 (endothermic) with Delta S (less than 0) will never be spontaneous), that is non-spontaneous reactions occur, when the above second law of thermodynamics is followed.
• If in a given case the magnitude of delta H and delta S is equivalent, then delta G will = 0, thus the reaction will be at equilibrium.

Open and Closed Systems

Open System- An environment where matter and energy can be easily exchanged with the surroundings. E.g. Bush Fire, River water. In these examples, carbon dioxide and water vapour are omitted into the atmosphere.

Closed System- Only energy can be exchanged with the surroundings. E.g. submarine travelling in a streamlined fashion underwater (matter does not get transferred or moved).

Irreversible and Reversible Reactions

• In junior school, we learnt that in a chemical reaction, the reactant is completely converted into a product- this can be denoted as an irreversible reaction. These reactions only occur in one direction and are sometimes also called non-reversible.
  Examples of irreversible reactions can include:
  • Frying an egg (the chemical and physical structure of a cooked egg, cannot be converted back into initial state- thus irreversible)
  • Combustion reactions involving the reaction of a fuel with sufficient oxygen to produce C02 and water. Once the fuel has burnt, the products cannot react with each other to re-form initial reactants, thus irreversible.

• Reactions in which the products formed, can react together to re-form the reactant are known as reversible reactions. This reversibility can be observed physically (changing state) or chemically, and in most cases, both can be observed. Examples of reversible reactions include:
  • Evaporation or condensation of water– This is an example of a physical change. Water can cycle between the 3 states of matter, with each process being reversible. This is presented within the equations below:

The above beakers showcase a diagram of a reversible (two- way reaction) involving the evaporation and condensation of water occurring. In chemistry, for ease of denotation and presentation, a reversible reaction is showcased with a double arrow , allowing both equations listed above to be expressed within a singular equation as follows;

The above changes in state can either occur in open or closed systems. In an open system, the water vapour can easily escape (via evaporation) and can increase through condensation, thus unequal rates of forward and reverse reactions. Hence open systems cannot be in equilibrium. Within a closed system water vapour cannot escape, and thus reversible reactions within a closed system eventually reach a point of chemical equilibria (moment in time when rate of forward and reverse reactions are equal- whereby no physical change can be observed).

Saturated sugar solution– A saturated solution contains the maximal amount of solute in the given amount of solvent. Thus, when we consider a saturated sugar solution in contact with undissolved crystallised sugar molecules to view the concept of equilibrium:

The sugar molecules being added to the saturated solution above are dissolving at an equivalent rate at which they are crystallising (the constant saturation point is maintained). Although there is no lid for the beaker, the system involves solid and aqueous sugar (regarded as a closed system in this case, for the purposes of the HSC syllabus).

This process can be represented in a single chemical equilibrium equation format in the following way:

NOTE: ALWAYS REMEMBER STATES AND DOUBLE HEADED ARROW IN EQIULBRIUM SYMBOL IN ALL EQUATIONS.

Explaining Reversibility: In a chemical reaction, when particles collide energy stored within reactant bonds, is released and rearranged to aid in the formation of new products. As mentioned above, the energy required for a successful reaction to proceed is known as the activation energy. Recall to our prior knowledge of energy profile diagrams to present why reversible reactions can also occur:

In the above diagram, after the products are formed the product particles can also collide at an energy equal to or greater than the magnitude of activation energy for the reverse reaction allows reverse reactions to proceed (see diagram).

IMPORTANT NOTE: In the above diagram, the forward reaction is endothermic (delta H is greater than 0), thus reverse reaction will be exothermic and vice versa.

Dynamic Equilibrium

In the previous section we studied the concept behind chemical equilibrium, and section 2.2 of the syllabus involves further investigation into the concepts behind stoppage of macroscopic changes in a closed system, whilst microscopic changes still occur.

Equilibrium and Collision Theory
In a reversible reaction, once the forward reaction has been initiated, collisions between product particles results in reactants being reformed.

Consider an example of a system at equilibrium, The Haber Process (involving the production of ammonia from constituent hydrogen and nitrogen gas):

A typical exam diagram to represent this system is presented below:

The above diagram also indicates the respective ratios of reactants and products; thus, it is also vital to notice molar ratios within the chemical equation of the HABER PROCESS.

• It is important to notice that initially, collisions between nitrogen and hydrogen molecules according to the collision theory, form ammonia (the product), as the concentration of reactant molecules decreases, the forward reaction (rate of ammonia production) is also decreased.
• These formed ammonia molecules also collide under standard industrial conditions, and in turn favour the reverse reaction (to reform constituent gases).
• Initially, there is only reactants present in the system, as the reaction proceeds, concentration of ammonia (red) increases, until point of constant equilibrium is reached (at TIME B). When this occurs, the rate of forward and reverse reaction is equal but it is vital to note that the CONCENTRATION OF REACTANTS AND PRODUCTS IS NOT NECESSARILY EQUAL AT EQIULLBRIUM).

Extent of Reaction

Extent of Reaction- Amount of product formed when the system reaches equilibrium

Rate of Reaction- Measure of the relative amount of reactant and product present as a function of time.

The degree of ionisation of independent acids and bases along with their relative ability and extent to which they donate/ receive charged carriers can be measured. Although some reactions are reversible, they do not all reach a state of dynamic equilibrium to the same extent.

We conduct an experiment to verify this:

• Hydrogen Chloride (HCL) and ethanoic acid (CH3COOH) react with water in the following way:

• From the above chemical reactions: it is evident that both acid molecules produce mobile charge carries upon reaction with water (charged ions) capable of conducting electricity. By measuring the relative amount of electrical conductance of each reaction: the extend of dissociation/ reaction can be determined.

Observed Results:

• When HCL dissociates in water, the resulting solution is a much better conductor of electricity than ethanoic acid, considering the amount of acid molecules and volume of water used were kept constant (ensures validity of the experiment).

Equilibrium Scenarios in Comparison:

Combustion Reactions
Combustion reactions are irreversible exothermic reactions (release heat). The combustion reaction involving octane can be represented in the following way:

The products (water and carbon dioxide) are stable and thus do not react with each other. This reaction is deemed irreversible, and hence cannot reach equilibrium in a closed system (combustion reactions are non-equilibrium systems). Following the above sub-section information, this reaction involves:

• Increase in entropy (number of gas molecules in vessel increases as 13.5 reactant molecules convert into 17 produced gas particles)
• Using the Gibbs free energy formula, whether the combustion of octane at 100 degrees is spontaneous can be determined. The final calculated value is -5257kJ/mol. Since delta G is negative, this is a spontaneous reaction and no input of

energy is required. Thus, this reaction continues, and the products do not recombine to form an equilibrium reaction.

NOTE: Photosynthesis is another example of a non-equilibrium system which can also be used as an example if studied in depth.

Calculating an Equilibrium Constant

Reaction Quotient:
Reconsider the Haber process chemical equation:

This is just one of many possible equilibrium reactions which can be asked in exam questions. The fraction

From the above table, the reaction quotient has an almost constant value, regardless of the concentrations of each component. Hence when a system is at equilibrium, the value of the reaction quotient (Q) is equal to the equilibrium constant (K).

• Each differing equilibrium reaction has a different K value.
• Since K and Q are ratios of products over reactants, the value of K indicates the relative proportions of reactant and product in a given chemical system
• K for a given system, is only changed upon a change in temperature (K remains the same when the pressure, concentrations or relative volumes are changed).

Equilibrium Law

• K is the concentrations of products divided by the concentrations of reactants (usually given in exam style questions)
• Index of each component in the formula, directly correlates to the coefficient for the particular substance in the chemical equation

Consider the general equation:

Then the equilibrium expression can be written as:

A more general expression is the following:

NOTE: if there if more than one product or reactant, you must multiply the different respective products and reactants.

The relationship between reaction quotient and the equilibrium constant:

Hence, it is important to note that the formula for K and Q remains the same:

• K is calculated when the system is at equilibrium
• Q is calculated when the system is not at equilibrium, in order to determine the direction in which the system can shift to attain equilibrium.

General deductions and rules can be made in order to determine the direction in which the system should shift:

• If Q> K, then the concentration of products is too great, hence the system should shift to the “right” in order to decrease the concentration of products, and hence make Q=K.
• If Q=K, system is at equilibrium
• If Q<K then the reactant concentration is too great, hence the system will have to shift to the “left” to increase the product concentration, to reach the K value.

NOTE: Questions involving calculation of writing correct expressions for equilibrium constant should be attempted at this stage.

Homogenous and Heterogenous Equilibria:

In the previous Haber process example, the reactants and products were both in gaseous phases (homogenous equilibrium system). Heterogenous equilibrium also exist- when reactants and products are present in different states/phases, and its direct impact on equilibrium constant calculation.

Consider the following chemical equation:

Conditions whilst calculating K:

• In calculation of equilibrium constants, since the concentration of solids is considered to be constant, it is removed from the equilibrium expression.
• If water is acting as a solvent (in liquid form), then it can also be removed from the calculation. If present in aqueous form (acting as a reactant or product) then it should be included

Thus, K in this case would be equal to the concentration of carbon dioxide gas.

Working with Equilibrium Constants

Various equilibrium reactions can be represented in different ways, having a direct effect on the value and formula of the equilibrium constant:

• If a given chemical reaction is reversed, the equilibrium constant is reciprocated.
• Doubling the molar ratios throughout a chemical reaction (coefficients of reactants and products), then the value of K is squared.
• Halving coefficients, means the value of K will be square rooted.

HENCE it is vital to correctly write chemical equilibria reactions

Meaning of the value of equilibrium constant

Equilibrium constant is calculated by dividing the relative concentration of products involved within the reaction, by the concentration of reactants. Hence the K value indicates the extent of the reaction at equilibrium, and the equilibrium yield.

The following guidelines can be followed to determine the relative side which the chemical reaction lies towards using the K value:

• If K is >104–: Almost a complete reaction: the concentration of products is much higher than the concentration of reactants, hence the forward reaction is being preferably favoured.
• If 10-4 <K<104: Reaction lies midway- nearly the same concentration of reactants and products are present.
• If K<10-4: The concentration of reactants is much higher than the relative concentration of products, hence the reaction lies to the left (reverse reaction is being favoured).

Effect of Temperature on an Equilibrium Constant
From above, we have briefly discussed that the K value is only affected by a change in temperature. The value of K is not affected by addition of reactants or products, changes in volumes or the addition of catalysts. The relative change in the K value depends on whether the reaction is exothermic or endothermic:

• If the reaction is exothermic and the temperature is decreased, the system will shift right to favour the forward exothermic side, hence increasing the K value (due to an increase in products).
• If the reaction is endothermic and the temperature is decreased, the system will shift to the left, to favour the reverse exothermic direction, and thus the value of K will decrease (as there will be a great increase in the concentration of reactants).

Calculations involving Equilibrium

K as stated above, can be written as a ratio of the molar concentration of products, over the molar concentration of reactants. It is vital to practice and formulate personal methods to correctly solve questions involving K.

NOTE: Ensure a basic understanding of significant figures to score full marks in such calculations.

An equilibrium constant can be calculated using the molar concentration of products over that of the reactants.

In harder HSC style questions, you can use the given value of the equilibrium constant of a reaction to determine the unknown concentration of either a reactant or a product.

Calculating an equilibrium constant using stoichiometry
For a few given questions, stoichiometry is used to calculate molar equilibrium concentrations of the reactants and products. Once these are known, the K value can be calculated. The general method used to calculate K values is using the ICE table (with a layout of initial concentration, change in concentration and concentration at equilibrium) of each of the reactant and products.

Factors that affect equilibrium

Changes to an Equilibrium System
The relative amounts of reactants and products in a given closed system is called the position of equilibrium, which is directly dependant on the reaction conditions. Position of equilibrium can be changed by:

• Addition or removal of reactant or product
• Change in volume or pressure (inversely proportional) concerned with equilibrium involving gases
• Change in temperature
• Diluting

Controlling of reaction conditions can maximise yield and rates of reaction on an industrial scale through correct application of equilibria knowledge and Le Chatliers Principle.

Le Chatliers Principle
“A system at equilibrium will remain at equilibrium by counteracting any changes that occur”

Adding extra reactant or product
Consider the following chemical equilibrium reaction:

At chemical equilibrium, rates of forward and reverse reactions are equal. When an excess of nitrogen gas is added to the system:

CLASSIC EXAM STYLE ANSWER:

An excess of nitrogen gas is added to the system. Le Chatliers Principle states that “a system at equilibrium will remain at equilibrium by counteracting any change that occurs. Thus, upon the addition of nitrogen gas, the system will shift to decrease the concentration of nitrogen gas, and thus the forward reaction will be favoured. Hence the concentration of nitrogen gas will be reduced and equilibrium will be regained. Note: if a reactant or product is removed, system will shift to increase it and regain equilibrium.

Further Applications of Le Chatliers Principle

Le Chatliers Principle is used to understand how natural equibria shift to mitigate changes, as well as to optimise yield of industrially important products and/or reactants. Hence, in this section we will study in depth about links of the collision theory, rates of reaction and effects of adding a catalyst or changing any conditions on yield of product and reactant.

Changing Pressure by Changing Volume
Pressure is inversely proportional to changing volume. (an increase in pressure means decrease in volume and vice versa). Pressure and volume are only concerned with gaseous molecules within an equilibrium system (given the temperature remains constant).

In the following reaction, the left-hand side has more gaseous molecules than the right-hand side (3:2). Hence when the pressure of a system is increased (or the volume is decreased), the c=gaseous molecules are forced into a more confined place, more collisions are possible. To regain equilibrium, for an increase in pressure, the system shifts to the side with least gaseous molecules (which in this case will be to favour the forward reaction).

In the case of a decrease in pressure (or increase in volume), the net number of gaseous molecules relative to the area available have been decreased (reduced amount of collisions can occur). Thus, in the case of a decrease in pressure, the system will shift to the side with more gaseous molecules, which in this case will be the reverse reaction, to regain equilibrium.

NOTE: Despite a change in the concentration of reactants and products (initial too final from above) when this change occurs, the K constant value (ratio of products to reactants) still remains the exact same, hence K is unchanged.

• Pressure does not affect the position of the system for reactants or products that are in liquid or solid phase. These particles are too tightly packed for an increase or decrease in pressure (hence negligible change for solids or liquids- no effect of changing pressure).
• When equal ratios of gaseous molecules are present on both sides of the reaction, no change will occur when the pressure of the system is changed.

Changing pressure by adding inert gas
Although the total pressure of a system will be increased by the addition of an inert gas, there is no effect on the concentrations of reactants or products, hence no effect on the position of the system at equilibrium.

Dilution
This is the process of adding water or some other form of solvent to the system, to lower the concentration of reactants/products relative to solvent volume. Hence the focus is on the number of particles per volume of solution.

Diluting by water reduces relative number of particles in solution, thus system will shift to the side with more/greater particles in solution to regain equilibrium.

• An addition of water to the system above, will shift the system to the reverse left side, to re-increase number of particles in solution. (side with more particles in solution).
• Removal of water from the system, will leave a greater relative number of particles in solution than is required in equilibrium state, hence system will shift to favour the forward reaction (side with least particles in solution).

The diagram above, showcases a sudden decrease in the concentration of all reactants and products when the dilution occurs. This is caused by a sudden decrease in relative concentration of reactants and products within the system as water is added. Following the sudden drop, the shift of the equilibrium system according to Le Chatliers principle can be followed. Note: no change in K constant occurs due to dilutions.

Changing Temperature The overall net effect of changing temperature can be explained using Le Chatliers Principle, can be linked to rates of reaction and the collision theory and the effect on K can be investigated.

Consider the following system: