Titrations, Indicators and Titration Curves

The technique of titration is used to find out accurately how much of a chemical substance is dissolved in a given volume of a solution, that is, the concentration of the solution.
The technique uses a set of apparatus with which volumes of solutions can be measured to an accuracy of greater than 0.1 cm³. Three important pieces of apparatus are:

Burette                  Measures accurately the volume of a solution added. Readings can be taken to an accuracy of half a division, that is ±0.05 cm³.

Pipette                         Delivers an accurate volume of a solution. Often this is 25 cm³.

Volumetric flask     Used to make up an accurate volume of a solution, for example, 250 cm³. This could be a standard solution (of exactly known concentration and known solute).


An indicator is a substance that undergoes a change in colour when the end-point of a titration is reached. Acid-base indicators are used to signal the end of acid-base titrations.

An acid-base indicator is itself a weak acid (or its conjugate base).

An acid-base indicator is a weak acid having a different colour in aqueous solution from its conjugate base.

 

Consider methyl orange, if the acid form of the indicator is represented by HIn and its conjugate base form by In^-, the following equilibrium exists in aqueous solution:

 

According to LeChatelier's Principle, the addition of an acid shifts the equilibrium to the left and the solution turns red. The addition of base removes H⁺, shifting the equilibrium to the right and the solution turns yellow.
The equilibrium condition for the reaction is:

 

Rearranging this expression:

 

Therefore, the ratio [HIn] / [In^-] depends on the pH, and determines the colour of the solution. With methyl orange, the solution is red if [HIn]>> [In^-], yellow if [In^-]>>[HIn], and varying shades of orange when [HIn] and [In^-] are about the same.
Therefore, at the end-point of the titration [HIn(aq)] / [In^-(aq)] » 1, and

K_a = [H₃O⁺(aq)]_eqm    or    pK_a = pH

pK_a for an indicator is (about) equal to the pH of the solution at the end-point.

Methyl orange as an indicator in strong acid-weak base titrations. It changes from red (at pH 3.1) to orange-yellow (at pH 4.4).

We can see the colour changes of methyl orange because it absorbs light in the visible part of the electromagnetic spectrum. Its molecule contains an extended system of delocalised electrons called a chromophore. The differences in energy between the quantised electronic energy levels correspond to the energies of photons of visible light. Electrons are promoted when these photons are absorbed, removing their frequencies from those that enter the eye. In methyl orange, when the molecule becomes protonated in acidic solution, the differences in energy between the electron energy levels change slightly from the unprotonated form. This results in the absorption of different frequencies of visble light and so a change in colour of the indicator. Methyl orange in acidic solution absorbs blue-green light, which makes its solution appear red. In alkaline solution it absorbs blue-green and red light making it appear yellow.

 

Titration curves

Acid-base indicators take advantage of the rapid change in pH of the solution being titrated as the equivalence point is reached. When an acid and base have been mixed in equivalent amounts (according to the chemical equation for the reaction) they are said to have neutralised each other. However, this term is somewhat misleading because the pH of the solution depends on the salt formed, and may not be pH 7.

The choice of an indicator is determined by the pH of the solution at the equivalence point.

For example, at the equivalence point of a titration involving ethanoic acid and sodium hydroxide, the only product is an aqueous solution of the ionic compound sodium ethanoate. It is the ethanoate ions behaving as a base that cause the solution at the end-point to have an alkaline pH.

CH₃COOH(aq) + OH^-(aq)     H₂O(l) + CH₃COO^-(aq)

Indeed, the pH of a solution formed at the equivalence point is important because it influences the choice of acid-base indicator for the titration. This is because...

acid-base indicators change colour within characteristic pH ranges.

Two familiar acid-base indicators are methyl orange and phenolphthalein.

Indicator                    Acid                 Base                  pH range

Methyl Orange             Red                 Yellow                 3.1 - 4.4

Phenolphthalein            Colourless         Pink                    8.3 - 10.0

 

 

Introducing Acid and Base Concepts

Very sensitive instrumentation can be used to show that even the purest water has some ability to conduct an electric current. This is due to the presence of ions, formed as a result of water undergoing an acid-base reaction with itself. Here, water is behaving as both an acid (proton donor) and a base (proton acceptor), according to Brönsted-Lowry definitions.

H₂O(l) + H₂O(l)      H₃O⁺(aq) + OH^-(aq)

H₂O(l)      H⁺(aq) + OH^-(aq)

At a temperature of 298 K, the concentration of H⁺(aq) is found to be 1 x 10^-7 mol dm^-3. The [OH^-(aq)] is also 1 x 10^-7 mol dm^-3.  

The pH Scale

pH was introduced as an abbreviation for 'power of Hydrogen'. The pH scale is used to measure how acidic (or alkaline) a solution is. It is often shown ranging from pH 1 to pH 14.

pH is related to the [H⁺(aq)].

pH = -log₁₀ [H⁺(aq)]       or       pH = log₁₀ (1/[H⁺(aq)])

A ten times increase in [H⁺(aq)] results in a decrease in pH of one unit.

Universal Indicator is a mixture of different indicators giving a series of colours across the pH range. The illustration below shows the colours of Universal Indicator.      

  

Universal Indicator
pH	1	2	3	4	5	6	7	8	9	10	11	12	13	14
	increasing acidity           neutral                      increasing alkalinity

 
Bronsted-Lowry definitions

An acid is a proton donor.
A base is a proton acceptor.

An acid is a substance that contains hydrogen which it can give up as H⁺ ions. The Bronsted-Lowry definition of an acid is that it is a proton donor. A base is the opposite of an acid; it is a proton acceptor.

The concentration and strength of an acid or base are different.

By the strength of an acid we mean how readily it will give up its hydrogen as H⁺ ions. By the strength of a base we mean how readily it will accept H⁺ ions. The stronger an acid the greater is its tendency to donate H⁺ ions; the stronger a base the greater is its tendency to accepts H⁺ ions. Concentration refers to the amount of a substance that is dissolved in unit volume of a solution. An acid, may be concentrated but nonetheless weak, or in dilute solution but still a strong acid. The same is the case for bases.

A strong acid is fully ionised in aqueous solution.

When a strong acid, for example hydrochloric acid, is added to water it becomes completely ionised.

HCl(aq) + H₂O(l)    H₃O⁺(aq) + Cl^-(aq)

The [H⁺(aq)] is considered to be due entirely to the ionisation of strong acid since the ionisation of water contributes only negligibly.

A weak acid is only partially ionised in aqueous solution.

A weak acid, for example ethanoic acid, becomes only partially ionised in water. In this case a chemical equilibrium is established in aqueous solution. That is, at any instant of time only a small proportion of the original number of acid molecules have become ionised.

CH₃COOH(aq) + H₂O(l)      H₃O⁺(aq) + CH₃COO^-(aq)

HCl(aq) and Cl^-(aq), and CH₃COOH(aq) and CH₃COO^-(aq), form what is called a conjugate acid-base pair. It follows that a strong acid has a weak conjugate base, and a weak acid has a strong conjugate base.

An equilibrium expression, equal to K_a, can be written for the equilibrium established by the acid in aqueous solution. K_a is called the acid dissociation constant (or acid ionisation constant). Notice that water (H₂O) is not included in this expression since it is present in vast excess and its concentration changes negligibly on equilibrium being reached.

Comparing the strengths of acids

We now want to compare the strengths of different acids, say ethanoic acid and benzoic acid. We allow each acid separately to react with the same base. The base chosen is water. Each acid is allowed to establish equilibrium in aqueous solution, and the equilibrium concentrations of the acid, H⁺(aq) ions, and conjugate base are measured. K_a for each acid can now be calculated. The more readily the acid donates H⁺ ions to water molecules, the more the equilibrium position will favour the products. The stronger the acid, the bigger the value of K_a.

CH₃COOH(aq) + H₂O(l)      H₃O⁺(aq) + CH₃COO^-(aq)
K_a = 1.75 x 10^-5 mol dm^-3

C₆H₅COOH(aq) + H₂O(l)      H₃O⁺(aq) + C₆H₅COO^-(aq)
K_a = 6.46 x 10^-5 mol dm^-3

 pK_a = -log₁₀ K_a.
The smaller the value of pK_a the stronger the acid.

NUCLEAR CHEMISTRY

Rate of Radioactive Decay

Radioactivity is the spontaneous disintegration of atoms of certain elements into atoms of other elements with the emission of smaller particles.
Elements, such as uranium, which spontaneously emit energy without the absorption of energy are said to be naturally radioactive.
Imagine having a very small sample of ²³⁸U, say 1 mg. This small mass contains many trillions of atoms. Now consider just one of these atoms. When will this particular atom undergo radioactive decay? The answer is that it is impossible to predict when, if ever, an atom will decay. Fortunately, the chemist is rarely concerned with the behaviour of a single particle. 1 mg of ²³⁸U contains 2.5 x 10¹⁸ atoms. With such large numbers of atoms it is possible to make precise predictions about rates of decay.
Experiments show that radioactive decay rates are directly proportional to the number of atoms present:

rate = k x N

where N = the number of atoms.
Different radioisotopes decay at different rates, so how can we compare their decay rates?

• The above expression tells us that for a radioactive isotope, the time taken for a fixed proportion of the original number of atoms to decay is constant.
• The proportion scientists have taken is 'one-half' of the original number of atoms, and the time taken for these to decay is called the half-life, denoted as t_½.
• In this way, the decay rates of different radioisotopes can be compared. The half-life is a direct measure of the stability of an isotope: the shorter the half-life, the faster is the rate of decay.
• The half-life is a characteristic of each radioisotope, but it is independent of the number of atoms.

⁹⁰Sr undergoes beta decay and has a half-life of 28 years. Given 8 g of this isotope, 4 g would remain after 28 years, 2 g would remain after 56 years, and 1 g after 84 years.

The table below gives the half-lives of some radioisotopes, all of which undergo beta decay:

Isotope Half-Life 3H 12.3 years 14C 5.73 x 103 years 32P 14.3 days 59Fe 45.1 days 60Co 5.27 years 90Sr 28 years 131I 8.04 days

the time required for one-half of a given quantity of a reactant to react. Half-life is commonly used as a measure of the rate of first-order reactions. It indicates the kinetic stability of a reactant: the longer the half-life, the greater the stability. The decomposition of dinitrogen pentoxide in tetrachloromethane is a typical first-order reaction: N2O5(sol) ® 2NO2(sol) + ½O2(g) Its rate equation is: rate = k[N2O5(sol)] where k is a constant called the rate constant. It can be deduced that: k = 0.693/t½ The half-life may be evaluated from the rate constant or vice versa. The shorter the half-life, the faster the reaction. The half-life for the decomposition of N2O5 in tetrachloromethane at 30 ºC is 2.4 hours. If we start with 10.0 g of N2O5 at t = 0 (q0), then, after a period of 2.4 hours, 5.0 g will remain. After a second period of 2.4 hours (4.8 hours in total), 2.5 g remain. After a total of 7.2 hours, 1.25 g remain, and so on. For 3 half-lives, the amount of N2O5 remaining at time t (qt) is: qt = 10 g x (0.5)3 = 1.25 g Generalising, we have qt = q0(0.5)t/t½ in which t/t½ gives the number of half-lives. XD

Le Chatelier's Principle

It seems that by raising the pressure of the system and at the same time reducing its temperature we can maximise the yield of ammonia at equilibrium. This is not without its problems. Maintaining a higher pressure is expensive; more robust plant (thicker pipes and stronger joints, for example) is required, and more electricity would have to be used to drive pumps to maintain this pressure. Lowering the temperature slows the rate at which chemical reactions take place resulting in a longer wait for equilibrium to be achieved. A 'compromise' has to be settled upon. The conditions selected approximate to those given above.

Does a catalyst affect the equilibrium position?

No. The addition or removal of a catalyst does not cause a shift in equilibrium. A catalyst is a substance that affects the rate of a reaction, but is not consumed in the reaction. It does this by providing an alternative mechanism for the reaction but of lower activation enthalpy. It therefore changes the rate of approach of equilibrium and so affects the forward and reverse reaction rates in the same way. The composition of the equilibrium mixture is unchanged. 

Heterogeous Equilibrium


An equilibrium involving more than one phase - gas and solid, for example, or liquid and solid - is said to be heterogeneous. For example:

H₂(g) + I₂(s)        2HI(g)

In the above example, the equilibrium expressions for this reaction are:
Notice that I₂ is missing from the equilibrium expressions. This is because, at room temperature, iodine is a solid. The composition of the equilibrium mixture of H₂(g) and HI(g) is independent of the amount of solid iodine present, as long as some of it is always present. [The partial pressure of I₂(g) (which is its vapour pressure) in equilibrium with I₂(s) is constant at a constant temperature, and is independent of the volume of the container and of the quantity of solid.] 

Equilibrium in Solution

Here we will consider homogeneous and heterogeneous chemical equilibria in which the solvent is much more abundant than all the other components put together. The solvent may also be a reactant or product itself.
First of all, let's look at an equilibrium that is not in solution: 
 

CH₃COOH(l) + CH₃CH₂OH(l)        CH₃COOCH₂CH₃(l) + H₂O(l)

 In this case, water is not a solvent but a product only.
Now consider the same equilibrium in very dilute aqueous solution. The chemical equation is: 

CH₃COOH(aq) + CH₃CH₂OH(aq)        CH₃COOCH₂CH₃(aq) + H₂O(l)

And the equilibrium expression is:
Water is now both a product and a solvent. In reaching a state of equilibrium the concentration of the water changes so little that it is effectively constant. For this reason its value is taken along with the equilibrium constant, K_c.

Here are some more examples of chemical equilibria in aqueous solution:

CH₃COOH_(aq) + H₂O_(l)        CH₃COO^-_(aq) + H₃O⁺_(aq)

K_a is called the acid dissociation constant. Again, the concentration of water changes negligibly on reaching equilibrium and so its value is taken along with the equilibrium constant (K_c) to form the 'modified' equilibrium constant, K_a.

NH_3(aq) + H₂O_(l)        NH₄⁺_(aq) + OH^-_(aq)

K_b is called the base dissociation constant. Again, the concentration of water changes negligibly on reaching equilibrium and so its value is taken along with the equilibrium constant (K_c) to form the 'modified' equilibrium constant, K_b.

AgCl_(s)        Ag⁺_(aq) + Cl^-_(aq)

K_s is the Solubility Product. It is the equilibrium constant for the equilibrium that exists between a slightly soluble salt and its ions in saturated solution. The solid, AgCl, is omitted from the equilibrium expression. As long as there is some solid present the concentration of the saturated solution of ions remains constant at a given temperature. 

XD

THE EQUILIBRIUM CONSTANT

Now consider we have a mixture of reactants and products that is not yet at equilibrium, or one that is at equilibrium. 

 

Which way will the reaction go in order to reach equilibrium?

How far will the reaction go, that is, what will be the amounts of reactants and products at equilibrium?

If we make changes to the system, such as to its volume, or add more of a reactant, how will the equilibrium composition be affected? 

To be able to answer these questions we have to know about the Equilibrium Constant. Now back to the equilibrium involving H₂(g), I₂(g) and HI(g) at 720K.

H₂(g) + I₂(g)        2HI(g)

In four separate experiments at 720 K, chemical equilibrium was allowed to establish. Two were started with different concentrations of H₂(g) and I₂(g) only in each, and two with differing initial concentrations of HI(g) only. In each of the four experiments, the equilibrium concentration of H₂(g), I₂(g) and HI(g) were measured. These are given in the table below:

Equilibrium concentrations (mol dm-3)
[H2(g)]eqm	[I2(g)]eqm	[HI(g)]eqm
1.14 x 10-2	0.12 x 10-2	2.52 x 10-2
0.92 x 10-2	0.20 x 10-2	2.96 x 10-2
0.34 x 10-2	0.34 x 10-2	2.35 x 10-2
0.86 x 10-2	0.86 x 10-2	5.86 x 10-2

If we substitute these equilbrium concentrations into the expression below:

then a constant value, within experimental error, is obtained. The square brackets represent concentrations in mol dm^-3.

The value of this ratio of equilibrium concentrations (in mol dm^-3) is known as the equilibrium constant, represented by the symbol K_c.

Many other chemical equilibrium reactions have been studied and in each case an equilibrium constant relating to the stoichiometric chemical equation has been calculated. This observation can be universally applied, in what is sometimes called the Law of Chemical Equilibrium, as illustrated by the general chemical equilibrium:

aA_(g) + bB_(g)        cC_(g) + dD_(g)

Can the equilbrium constant be expressed in other terms?

The Ideal Gas Equation shows that the pressure of a gas is proprtional to its concentration.

pV = nRT

where p is pressure of a particular gas (its partial pressure) in an equilibrium mixture, V is the total volume, n is the number of moles of the particular gas, R is the general gas constant, and T is the absolute temperature.

In the above equation where the temperature is also constant,

P a n / V

The equilibrium constant can therefore also be expressed in terms of partial pressures, and is denoted as K_p:

Does the equilbrium constant have units?

The equilibrium constant (K_c or K_p) may or may not have units; this depends precisely upon the equilibrium expression. 

Does the equilibrium constant depend on temperature?

Yes. An equilibrium constant is constant only at a constant temperature. Changing the temperature of a chemical system at equilibrium will change the value of the equilibrium constant, and also the position of the equilibrium. 

Are K_c and K_p related?

Yes. The relationship depends on the reaction and how it is written. Specifically, it depends on the number of moles of gaseous reactants and products.

The equation is:

K_p = K_c(RT)^Dn

where Dn is the number of moles of gaseous products minus the number of moles of gaseous reactants, R is the gas constant, and T is the absolute temperature at which the equilibrium exists.

Which way will the reaction go in order to reach equilibrium?

We have a mixture of SO₂(g), O₂(g), and SO₃(g) at 1000K which has still to reach equilibrium. The partial pressures are p_SO2 = 0.48 atm, p_O2 = 0.18 atm, and p_SO3 = 0.72 atm. K_p = 3.40 atm^-1. The reaction is:

2SO₂(g) + O₂(g)      2SO₃(g)

Which way must the reaction go to reach equiilibrium? 

Answer:

                    Calculate a value (Q) for the reaction which can be compared with the equilibrium constant, K_p. This is given by the expression:

                                                                       

     The value of Q calculated is 12.50 atm^-1. Since Q is greater than K_p, to reach equilibrium, the equilibrium must go from right to left.

     If we make changes to the system, such as to its volume, or add more of a reactant, how will the equilibrium composition be affected?


     This question is really an extension of the first, except that a reactant or product may be added or removed, the volume or pressure changed, or the temperature of the system increased or decreased. We consider that these changes are made to a chemical system already at equilibrium.

     At the instant when such a change is made, we consider that the system is no longer at equilibrium. We are going to consider, in qualitative terms, what the new equilibrium composition will be. Calculating the new amounts of reactants and products at equilibrium might be possible but the working is often tricky, so we'll give this a miss. We will discuss an approach in the next section with reference to Le Chatelier's Principle.

CHEMICAL CHANGE AND EQUILIBRIUM

Chemical change is one of the two central concepts of chemical science, the other being structure. The very origins of Chemistry itself are rooted in the observations of transformations such as the combustion of wood, the freezing of water, and the winning of metals from their ores that have always been a part of human experience. It was, after all, the quest for some kind of constancy underlying change that led the Greek thinkers of around 200 BCE to the idea of elements and later to that of the atom.

Chemical change occurs when the atoms that make up one or more substances rearrange themselves in such a way that new substances are formed. These substances are the components of the chemical reaction system; those components which decrease in quantity are called reactants, while those that increase are products.
A given chemical reaction system is defined by a balanced net chemical equation which is conventionally written as

reactants → products

The first thing we need to know about a chemical reaction represented by a balanced equation is whether it can actually take place. If the reactants and products are all substances capable of an independent existence, then in principle, the answer is always "yes". 

WHAT IS EQUILIBRIUM


Basically, the term refers to what we might call a "balance of forces". In the case of mechanical equilibrium, this is its literal definition. A book sitting on a table top remains at rest because the downward force exerted by the earth's gravity acting on the book's mass (this is what is meant by the "weight" of the book) is exactly balanced by the repulsive force between atoms that prevents two objects from simultaneously occupying the same space, acting in this case between the table surface and the book. If you pick up the book and raise it above the table top, the additional upward force exerted by your arm destroys the state of equilibrium as the book moves upward. If you wish to hold the book at rest above the table, you adjust the upward force to exactly balance the weight of the book, thus restoring equilibrium.

An object is in a state of mechanical equilibrium when it is either static (motionless) or in a state of unchanging motion. From the relation f = ma , it is apparent that if the net force on the object is zero, its acceleration must also be zero, so if we can see that an object is not undergoing a change in its motion, we know that it is in mechanical equilibrium.

Thermal equilibrium

Another kind of equilibrium we all experience is thermal equilibrium. When two objects are brought into contact, heat will flow from the warmer object to the cooler one until their temperatures become identical. Thermal equilibrium arises from the tendency of thermal energy to become as dispersed or "diluted" as possible.

A metallic object at room temperature will feel cool to your hand when you first pick it up because the thermal sensors in your skin detect a flow of heat from your hand into the metal, but as the metal approaches the temperature of your hand, this sensation diminishes. The time it takes to achieve thermal equilibrium depends on how readily heat is conducted within and between the objects; thus a wooden object will feel warmer than a metallic object even if both are at room temperature because wood is a relatively poor thermal conductor and will therefore remove heat from your hand more slowly.

Thermal equilibrium is something we often want to avoid, or at least postpone; this is why we insulate buildings, perspire in the summer and wear heavier clothing in the winter.

Chemical equilibrium

When a chemical reaction takes place in a container which prevents the entry or escape of any of the substances involved in the reaction, the quantities of these components change as some are consumed and others are formed. Eventually this change will come to an end, after which the composition will remain unchanged as long as the system remains undisturbed. The system is then said to be in its equilibrium state, or more simply, "at equilibrium".

Why reactions go toward equilibrium

What is the nature of the "balance of forces" that drives a reaction toward chemical equilibrium? It is essentially the balance struck between the tendency of energy to reside within the chemical bonds of stable molecules, and its tendency to become dispersed and diluted. Exothermic reactions are particularly effective in this, because the heat released gets dispersed in the infinitely wider world of the surroundings.
In the reaction represented here, this balance point occurs when about 60% of the reactants have been converted to products. Once this equilibrium state has been reached, no further net change will occur. (The only spontaneous changes that are allowed follow the arrows pointing toward maximum dispersal of energy.) 


It's very important that you know this definition: 


 "A chemical reaction is in equilibrium when there is no tendency for the quantities of reactants and products to change."


WHAT IS A REVERSIBLE REACTION? 

A chemical equation of the form A → B represents the transformation of A into B, but it does not imply that all of the reactants will be converted into products, or that the reverse reaction B → A cannot also occur.


If the equilibrium state is one in which significant quantities of both reactants and products are present (as in the hydrogen iodide example given above), then the reaction is said to incompletereversible. or

The latter term is preferable because it avoids confusion with "complete" in its other sense of being completed or finished, implying that the reaction has run its course and is now at equilibrium.

• If it is desired to emphasize the reversibility of a reaction, the single arrow in the equation is replaced with a pair of hooked lines pointing in opposite directions, as in A B.
Note that there is no fundamental difference between the meanings of A → B and A B. Some older textbooks just use A = B.
• A reaction is said to be complete or quantitative when the equilibrium composition contains no significant amount of the reactants. However, a reaction that is complete when written in one direction is said "not to occur" when written in the reverse direction.

In principle, all chemical reactions are reversible, but this reversibility may not be observable if the fraction of products in the equilibrium mixture is very small, or if the reverse reaction is very slow (the chemist's term is "kinetically inhibited")

WHAT IS THE LAW OF MASS ACTION?\


 Berthollet's ideas about reversible reactions were finally vindicated by experiments carried out by others, most notably the Norwegian chemists (and brothers-in-law) Cato Guldberg and Peter Waage. During the period 1864-1879 they showed that an equilibrium can be approached from either direction (see the hydrogen iodide illustration above), implying that any reaction
aA + bB → cC + dD is really a competition between a "forward" and a "reverse" reaction. When a reaction is at equilibrium, the rates of these two reactions are identical, so no net (macroscopic) change is observed, although individual components are actively being transformed at the microscopic level.

Guldberg and Waage showed that for a reaction aA + bB → cC + dD,
the rate (speed) of the reaction in either direction is proportional to what they called the "active masses" of the various components:

rate of forward reaction = k_f [A]^a [B]^b

rate of reverse reaction = k_r [C]^c [D]^d

in which the proportionality constants k are called rate constants and the quantities in square brackets represent concentrations. If we combine the two reactants A and B, the forward reaction starts immediately; then, as the products C and D begin to build up, the reverse process gets underway. As the reaction proceeds, the rate of the forward reaction diminishes while that of the reverse reaction increases. Eventually the two processes are proceeding at the same rate, and the reaction is at equilibrium:

rate of forward reaction = rate of reverse reaction

k_f [A]^a [B]^b = k_r [C]^c [D]^d

The composition of the equilibrium state depends on the ratio of the forward- and reverse rate constants.

Be sure you understand the difference between the rate of a reaction and a rate constant. The latter, usually designated by k, relates the reaction rate to the concentration of one or more of the reaction components — for example, rate = k [A].

At equilibrium the rates of the forward and reverse processes are identical, but the rate constants are generally different. To see how this works, consider the simplified reaction A → B in the following three scenarios.

k_f >> k_r

If the rate constants are greatly different (by many orders of magnitude), then this requires that the equilibrium concentrations of products exceed those of the reactants by the same ratio. Thus the equilibrium composition will lie strongly on the "right"; the reaction can be said to be "complete" or "quantitative".

k_f << k_r

The rates can only be identical (equilibrium achieved) if the concentrations of the products are very small. We describe the resulting equilibrium as strongly favoring the left; very little product is formed. In the most extreme cases, we might even say that "the reaction does not take place".

k_f ≈ k_r

If k_f and k_r have comparable values (within, say, several orders of magnitude), then signficant concentrations of products and reactants are present at equilibrium; we say the the reaction is "incomplete" and "reversible".

 

HOW DO WE KNOW WHEN A REACTION IS AT EQUILIBRIUM


Clearly, if we observe some change taking place— a change in color, the release of gas bubbles, the appearance of a precipitate, or the release of heat, we know the reaction is not yet at equilibrium.
But the absence of any apparent change does not by itself establish that the reaction is at equilibrium. The equilibrium state is one in which not only no change in composition take place, but also one in which no energetic tendency for further change is present. Unfortunately, "tendency" is not a property that is directly observable! Consider, for example, the reaction representing the synthesis of water from its elements:

2 H₂(g) + O₂(g) → 2 H₂O(g)

You can store the two gaseous reactants in the same container indefinitely without any observable change occurring. But if you create an electrical spark in the container or introduce a flame, bang! After you pick yourself up off the floor and remove the shrapnel from what's left of your body, you will know very well that the system was not initially at equilibrium! It happens that this particular reaction has a tremendous tendency to take place, but for reasons that we will discuss in a later chapter, nothing can happen until we "set it off" in some way— in this case by exposing the mixture to a flame or spark, or (in a more gentle way) by introducing a platinum wire, which acts as a catalyst.

A reaction of this kind is said to be highly favored thermodynamically, but inhibited kinetically. The similar reaction of hydrogen and iodine

H₂(g) + I₂(g) → 2 HI(g)

by contrast is only moderately favored thermodynamically (and is thus incomplete), but its kinetics are both unspectacular and reasonably facile.