Chemical Equilibrium Free Energy and Equilibrium By Engr

Chemical Equilibrium, Free Energy and Equilibrium By Engr. Asadullah Memon B. E (Petroleum & Natural Gas)

The Concept of Equilibrium Chemical equilibrium occurs when a reaction and its reverse reaction proceed at the same rate.

The Concept of Equilibrium • As a system approaches equilibrium, both the forward and reverse reactions are occurring. • At equilibrium, the forward and reverse reactions are proceeding at the same rate.

A System at Equilibrium Once equilibrium is achieved, the amount of each reactant and product remains constant.

Depicting Equilibrium In a system at equilibrium, both the forward and reverse reactions are being carried out; as a result, we write its equation with a double arrow N 2 O 4 (g) 2 NO 2 (g)

The Equilibrium Constant • Forward reaction: N 2 O 4 (g) 2 NO 2 (g) • Rate law: Rate = kf [N 2 O 4]

The Equilibrium Constant • Reverse reaction: 2 NO 2 (g) N 2 O 4 (g) • Rate law: Rate = kr [NO 2]2

The Equilibrium Constant • Therefore, at equilibrium Ratef = Rater kf [N 2 O 4] = kr [NO 2]2 • Rewriting this, it becomes kf kr [NO 2]2 = [N 2 O 4]

The Equilibrium Constant The ratio of the rate constants is a constant at that temperature, and the expression becomes Keq = kf kr [NO 2]2 = [N 2 O 4]

The Equilibrium Constant • To generalize this expression, consider the reaction a. A + b. B c. C + d. D • The equilibrium expression for this reaction would be [C]c[D]d Kc = [A]a[B]b Equilibrium Constants 2 A + 3 B C + 4 D Ke = [C][D]4/[A]2[B]3

The Equilibrium Constant Because pressure is proportional to molar concentration (n/V) for gases in a closed system, the equilibrium expression can also be written (PC)c (PD)d Kp = (PA)a (PB)b

Chemical Equilibrium The state of a reversible reaction when the two opposing reaction occur at the same rate and the concentrations of reactants and products do not change with time.

The rate of the forward reaction diminishes with time, while that of the backward reaction increases, until they are equal. A large K means the reaction lies far to the right at equilibrium. Fig. Progress of a chemical reaction. ©Gary Christian, Analytical Chemistry, 6 th Ed. (Wiley)

Chemical Equilibrium • Review of Principles. • Chemical reactions are never “complete” • Chemical reactions proceed to a state where ratio of products to reactants is constant • NH 3 + HOH NH 4+ + OH • [NH 4+][OH-]/[NH 3][HOH] = Kb • If Kb << 1 (little ionization) • H 2 SO 4 + HOH H 3 O+ + HSO 4 • [H 3 O+][HSO 4 -] / [H 2 SO 4][HOH] = Ka • If Ka >> 1 (mostly ionized)

Chemical Equilibrium • Equilibrium – is not reached instantaneously – can be approached from either direction – is a dynamic state – amounts of reactants/products can be changed by “mass action” – (adding/ deleting products/reactants) – HCO 3 - + H+ CO 2(g) + HOH – Ke = [CO 2][HOH]/[HCO 3 -][H+]

Relationship between Kc and Kp • From the ideal gas law we know that PV = n. RT • Rearranging it, we get n P= RT V

Relationship between Kc and Kp Plugging this into the expression for Kp for each substance, the relationship between Kc and Kp becomes Kp = Kc (RT) n Where n = (moles of gaseous product) − (moles of gaseous reactant)

Equilibrium Can Be Reached from Either Direction As you can see, the ratio of [NO 2]2 to [N 2 O 4] remains constant at this temperature no matter what the initial concentrations of NO 2 and N 2 O 4 are.

Equilibrium Can Be Reached from Either Direction This is the data from the last two trials from the table on the previous slide.

Equilibrium Can Be Reached from Either Direction It does not matter whether we start with N 2 and H 2 or whether we start with NH 3. We will have the same proportions of all three substances at equilibrium.

What Does the Value of K Mean? • If K >> 1, the reaction is product-favored; product predominates at equilibrium.

What Does the Value of K Mean? • If K >> 1, the reaction is product-favored; product predominates at equilibrium. • If K << 1, the reaction is reactant-favored; reactant predominates at equilibrium.

Manipulating Equilibrium Constants The equilibrium constant of a reaction in the reverse reaction is the reciprocal of the equilibrium constant of the forward reaction. N 2 O 4 (g) 2 NO 2 (g) [NO 2]2 2 NO 2 (g) Kc = [N O ] = 0. 212 at 100 C 2 4 [N 2 O 4] 1 K = N 2 O 4 (g) = c [NO 2]2 0. 212 = 4. 72 at 100 C

Heterogeneous Equilibrium The Concentrations of Solids and Liquids Are Essentially Constant Both can be obtained by dividing the density of the substance by its molar mass— and both of these are constants at constant temperature.

The Concentrations of Solids and Liquids Are Essentially Constant Therefore, the concentrations of solids and liquids do not appear in the equilibrium expression Pb. Cl 2 (s) Pb 2+ (aq) + 2 Cl−(aq) Kc = [Pb 2+] [Cl−]2

Le Châtelier’s Principle It Stated that “When a stress is applied on a system in equilibrium, the system tends to adjust itself so as to reduce the stress” “If a system at equilibrium is disturbed by a change in temperature, pressure, or the concentration of one of the components, the system will shift its equilibrium position so as to counteract the effect of the disturbance or minimize the stress. ”

Le Châtelier’s Principle There are three ways in which the stress can be caused on a chemical equilibrium: (a) Changing the concentration of a reactant or product. (b) Changing the pressure (or volume) of the system. (c) Changing the temperature. Thus, this principal stated that, “if a change in concentration, pressure, or temperature is caused to a chemical reaction in equilibrium, the equilibrium will shift to the right ot the left so as minimize the change”

Gibbs Free Energy & Equilibrium Constant • G = H – TS but H = E + PV – G = Gibbs Free Energy H = Enthalpy – T = Temperature S = Entropy – E = Internal Energy P = Pressure V = Volume • G = E + PV – TS but E = q – w G = q – w + PV - TS Derivative d. G = dq - dw + (Pd. V + Vd. P) – (Td. S – Sd. T)

d. G = dq - dw + (Pd. V + Vd. P) – (Td. S – Sd. T) Let’s Simplify by imposing some conditions on the reaction. a) b) c) Constant Temperature: d. T = 0 Sd. T = 0 Reversible Reaction: dq = Td. S Expansion work only: dw = Pd. V Then all terms except one cancel d. G = Vd. P Now consider 1 mole of an ideal gas V = RT/P d. G = RTd. P/P

Now lets integrate: d. G = RTd. P/P Result: G 2 -G 1 = RTln(P 2/P 1) Make state 1 = standard state G – Go = RTln(P/Po) but Po = 1 atm Activity is defined: a = P/Po G = Go + RTln(a) This equation is called Van’t Hoff reaction Isotherm.

General Expressions: r. R + s. S t. T + u. U Each Free Energy Term Expressed in Terms of Activity Ø Ø t. GT = t. GTo + RT ln a. T u. GU= u. GUo + RT ln a. U r. GR = r. GRo + RT ln a. R s. GS = s. GSo + RT ln a. S G = Go + RT ln (a. Tt a. Uua. Rr a. Ss)

G = Go + RT ln (a. Tt a. Uu/a. Rr a. Ss) At Equilibrium: G = 0 Reaction quotient Q = (a. Tt a. Uu/a. Rr a. Ss) = Ko Where Ko is thermodynamic equilibrium constant 0 = Go + RT ln Ko Go = - RT ln Ko Where Go is indicate whether forward or reverse is spontaneous. ln Ko = - Go/RT Ko = e(- DG /RT) o

CASES Case 1: If Go is negative, Log k must be positive and reaction proceeds spontaneous in the forward reaction. Case 2: If Go is Positive, Log k must be negative and reaction proceeds spontaneous in the Reverse reaction. Case 3: If Go is Zero, Log k must be unity and reaction is at equilibrium.

Ionic Equilibria The Ostwald’s Dilution Law: Wilhelm Ostwald’s dilution law is a relationship between the dissociation constant (Kp/Kc) and the degree of dissociation of a weak electrolyte (acids, bases). The fraction of the amount of the electrolyte in solution present as free ions is called the Degree of Dissociation. Where, Kp is dissociation constant, α is degree of dissociation, c(A-) is concentrations of anions, c(K+) concentration of cations, c 0 is overall concentration, c(KA) is concentration of associated electrolyte.

According to the Arrhenius Theory of Dissociation, An electrolyte dissociates into ions in the water solutions These ions are in a state of equilibrium with the undissociated molecules. These equilibrium is called Ionic equilibrium Or The molecules of an electrolyte in solution are constantly splitting up into ions and the ions are constantly reuniting to form unionized molecules. Therefore, a dynamic equilibrium exists between ions and unionized molecules of the electrolyte in solution.

If one mole of electrolyte be dissolved in V litre of the solution then C = 1/V Where V is known as the Dilution For the solution. Therefore, Kc = α 2 / (1 - α )V For weak electrolytes, Put (1 - α ) = 1, Therefore α = √ Kc. V Or α = K’√V It implies that, the degree of dissociation is proportional to the square root of the dilution. For Strong electrolytes, α 2+ αKc-Kc. V=0

Limitations of Ostwald's dilution law v The law holds good only for weak electrolytes and fails completely in the case of strong electrolytes. v The value of 'α' is determined by conductivity measurements by applying the formula Λ/Λ∞. v The cause of failure of Ostwald's dilution law in the case of strong electrolytes is due to the following factors" (i) The law is based on the fact that only a portion of the electrolyte is dissociated into ions at ordinary dilution and completely at infinite dilution. Strong electrolytes are almost completely ionized at all dilutions and Λ/Λ∞ does not give accurate value of 'α'. (ii) When concentration of the ions is very high, the presence of charges on the ions appreciably effects the equilibrium. Hence, law of mass action its simple form cannot be strictly applied in the case of string electrolytes.

Theory of Strong Electrolytes (Debye-Huckel Theory) The Debye–Hückel theory was proposed by Peter Debye and Erich Hückel as a theoretical explanation for departures from ideality in solutions of electrolytes. The main ideas of theory are given below: 1. The strong electrolyte is completely ionized at all dilutions. 2. Since oppositely charged ions attract each other 3. It suggests that anions and cations are not uniformly distributed in the solution of an electrolyte but that the cation tend to be found in the vicinity of anions and vice-versa. 4. Degree in equivalent conductance with increase in concentration is due to fall in mobilities of the ions to greater inter-ionic effect and vice-versa.

Buffer Solution v Necessary to main the certain p. H of a solution in lab: or Industrial Processes. v Defined as “A buffer solution is one which maintain its p. H fairly constant even upon the addition of small amounts of acid or base”. v How to buffer operates. v Two Types of buffer solution 1. A weak acid together with a salt of the same acid with the strong base. These are called Acid Buffers e. g. CH 3 COOH + CH 3 COONA. 2. A weak base and its salt with a strong acid. These are called Basic Buffers e. g. NH 4 OH + NH 4 CL

Acid-Base Indicators v In a acid base titration the base solution can be added gradually from a burette into an acid solution contained in a receiver flask. When the amount of the base added equals the amount of the acid in the flask, the equivalence point ot the end point is reached. v The end point of the titration is shown by the colour change of an indicator previously added to the acid solution in the receiver flask. v An acid base indicator is an organic dye that signals the end point by a visual change colour. v Examples: Phenolpathalein and methyl orange v Phenolphythalein (Pink in base solution and colourless in acid solution) v Methyl orange (Colour change from red (in acid) to yellow (in base)).

Acid-Base Indicators p. H range of Indicator Colour Change (Acid- Base) p. H range Methyl orange Red – Orange 3. 1 - 4. 4 Methyl red Red – yellow 4. 4 - 6. 0 Litmus Red – Blue 5. 0 - 8. 0 Bromothymol blue Yellow – Blue 6. 0 - 7. 6 phenolpathalein Colourless – Pink 8. 3 - 10. 0

Catalysis v A substance which alters the rate of a chemical reaction, itself remaining chemically unchanged at the end of the reaction. v Catalyst may increase or decrease the arte of the reaction. v Positive catalyst and Positive catalysis. v Negative catalyst and Negative catalysis. v Two types of catalysis: 1. Homogenous catalysis: The catalyst is in the same phase as the reactants and is evenly distributed throughout. 2. Heterogeneous catalysis: The catalyst is in the different physical phase as the reactants.