2 LABORATORY PRACTICUM: EQUILIBRIUM OF HOMOGENEOUS CHEMICAL SYSTEMS

2.1 THEORETICAL INTRODUCTION

Definition of Chemical Equilibrium

Knowledge of laws of chemical thermodynamics allows predicting a possibility of a spontaneous reaction and determining its limit – the equilibrium state. Thermodynamic calculations help determining concentrations of reactants in an equilibrium reaction mixture and how external conditions influence the state of equilibrium and output of reaction products that is of great practical importance.

Let’s provide the determination for the term “chemical equilibrium”. Chemical equilibrium is the thermodynamic equilibrium in a system

with chemical reaction occurring between its components. When chemical equilibrium is achieved, concentrations of reactants and other system parameters do not change with time.

Chemical reactions are reversible in most cases. A reaction between initial compounds (direct reaction) is always accompanied by the reverse reaction between products. The rate of a direct reaction decreases with time, while the rate of the reverse reaction grows. When these rates become equal, chemical equilibrium is achieved and the number of molecules in a system is unchanged.

Chemical equilibrium is a state of a system with equal rates of direct and reverse reactions.

Chemical equilibrium is characterized by constant macroscopic characteristics of a system: concentrations of all the reactants, system volume and temperature, density and viscosity. No release of gas, precipitation color change or turbidity is observed. This may be, however, an insufficient indication as some processes can be extremely slow. A reliable confirmation of equilibrium in a system is the following:

a)Changes were observed in a system, then the reaction slowed down and finally a system reached equilibrium;

b)A system was moved from the equilibrium state by a certain impact, but when it stopped, this system returned to the equilibrium state spontaneously.

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Chemical Equilibrium Characteristics

1.Equilibrium is a dynamic state. It means that chemical processes do not stop at equilibrium. Both direct and reverse reactions continue to occur. They have the same rates. Initial reactants transform into products and the same amount of these reactants from products at the same time in the reverse process.

2.Equilibrium can be achieved by two pathways. It is well illustrated by hydrogen iodide synthesis reaction studied by Bodenstein:

H2 + I2 → 2HI.

When the pressure is 1 atm and the temperature is 445 оС, the system reaches equilibrium in approximately 20 hours (Fig. 2.1, Curve 1). The equilibrium mixture contains 78% of HI. The same equilibrium state is

reached by the system, where thermal dissociation of HI occurs: 2HI → H2

+I2, (Fig. 2.1, Curve 2).

3.The concentration of substances at the state of equilibrium are equilibrium concentrations. Equilibrium concentrations are interrelated

and if we change one of concentration, other concentrations change immediately.

4.If external conditions are constant, the state of equilibrium is endless.

5.Equilibrium is mobile and its displacement occurs when external conditions change.

6.Chemical equilibrium is stable. If an external factor disappears, the

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system returns to its previous state. That is why these systems can be roughly considered as thermodynamically reversible.

7. Chemical equilibrium in a closed system is characterized by minimal values of the Gibbs Function G (when Р and Т = const) and the Helmholtz Function A (when Р and V = const) (Fig. 2.2.). The equilibrium criteria:

(dA)V,T = 0;

An isolated system in its equilibrium state has maximum entropy.

Mass Action Law and Equilibrium Constant

Let’s consider the transition from the conditions of equilibrium, determined by the equation (1) to the numerical definition of constants.

Let’s assume that the following reaction occurs at constant Р and Т: mM + dD ↔ xX +yY,

all the reactants are ideal gases. The full differential of the Gibbs function has the following form:

dG = VdP – SdT + ∑µidni;

in an isobaric-isothermic system: dG = ∑µidni,

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where ∑µidni is the sum of chemical potentials of reactants with the respective sign (plus for products and minus for initial reactants) and with the consideration of stoichiometric coefficients.

Chemical potential of a gas mixture component is expressed by the equation

where µоi is the chemical potential of a pure substance, Pi is the relative partial pressure of the ith component equal to the ratio of the partial pressure to the standard value Ро = 1 atm = 1,01325∙105 Pa.

A combination of chemical potentials of all the reaction participants (equation 2.2) is the following sum:

Equilibrium is characterized by drG = ∑µidni = 0 (r is for a reaction), thus:

xµоX + yµоY - mµоM - dµоD = - RT(xlnPX + ylnPY - mlnPM – nlnPD). (2.5)

As chemical potential of a pure substance at standard conditions is equal to the standard Gibbs function of this substance, the left part of the equation (2.5) is the change of the Gibbs function during a reaction:

rGo = xµоX + yµоY - mµоM - dµоD, therefore

rGo = -RT(xlnPX + ylnPY - mlnPM – dlnPD).

His is chemical equilibrium constant КP.

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We should emphasize that we considered equilibrium conditions, therefore Рi are the relative partial pressures of reaction participants at the moment of equilibrium.

Equation (2.6) is the mathematical interpretation of the mass action law. Its definition: the rate of any chemical reaction is proportional to the product of the masses of the reacting substances, with each mass raised to a power equal to the coefficient that occurs in the chemical equation. This law was formulated over the period 1864–79 by the Norwegian scientists Cato M. Guldberg and Peter Waage, while its thermodynamic interpretation was provided by Van’t Hoff (1885).

Thermodynamic equilibrium constants are dimensionless values, because dimensionless relative partial pressure is used in the equation (2.3) for the mass action law.

Expression of Equilibrium Constants

Equilibrium constants are usually expressed through equilibrium partial pressures (КP), equilibrium concentrations (КC), and equilibrium molar parts (КN) of reaction participants. If a reaction occurs in a real system, then we cannot avoid consideration of sizes of molecules and their interactions. Constants are expressed in this case through fugitivity (Кf) or equilibrium activities (Ка). The concentration of the ith gas Сi is the ratio of the moles of this gas ni to a volume V of the system.

Сi = ni/V.

For an ideal gas mixture, Сi can be found from the MendeleevClapeyron equation РiV = niRT:

Сi = Рi/RT,

Therefore: Рi = СiRT.

By expressing partial pressures of all the reaction participants (equation 6) in this way, we will get the following equation:

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or

where ∆n = y + x − d − m is the change of the number of moles during

a reaction.

To express the constant through molar parts, let’s use the Dalton law:

Рi = NiP,

where Р is the general pressure of the gas mixture, Рi is the partial pressure of the ith component with the respective molar part Ni.

Having expressed partial pressures of all the reaction participants in the equation (2.6) in this way, we will get the following equation:

Equations (2.8) and (2.9) stipulate that the constants КP, КC and КN are equal for the reaction with the number of moles unchanged and ∆n = 0 .

Equilibrium Constant of a Heterogeneous Reaction

Chemical reactions with reactants in different phases are heterogeneous reactions.

We assumed that all the substances in the equations (2.6) and (2.7) are ideal gases. Their chemical potential is expressed through their partial pressure (2.3). If a pure substance participates in a reaction, in a condensed state (liquid or solid), its partial pressure is equal to the pressure of its saturated vapor P*i at a given temperature. Therefore, chemical potential

of a pure substance in a condensed phase µ*i is constant at Т = const and the equilibrium state will depend only on partial pressures of gases participating in the reaction.

For example, let’s consider the following reaction

where substances М and Х are ideal gases, while substances D and Y are pure substances in a condensed state. At the equilibrium state:

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Thus, the equilibrium constant for a heterogeneous reaction (2.10) has the following form:

The Use of the Mass Action Law for the Calculation of an Equilibrium Mixture Composition

If we know concentrations of reaction participants at an initial moment of time and the value of equilibrium constant, we can calculate the content of products and initial reactants in an equilibrium mixture. Let’s analyze the HI synthesis reaction occurring at 1 atm and 298 К:

H2 + I2 ↔ 2HI.

Let’s consider that this reaction occurs in an ideal gas system. The КP equilibrium constant is calculated by the following equation:

КP at given conditions can be calculated by the equation (7), which stipulates the following:

An equilibrium composition can be expressed through molar parts by the transition from КP to КN using equation (2.9). Let’s determine ∆n for the reaction we discuss:

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∆n = 2 – (1 + 1) = 0. Therefore:

Let’s take X moles of hydrogen and Y moles of iodine. Assume Z is the number of HI moles formed at the equilibrium point and determine the composition of the equilibrium mixture respectively. Each elementary act of reaction is the interaction of a molecule of hydrogen with a molecule of iodine. Two HI molecules form as the result. Therefore, we need ½Z moles of hydrogen and ½Z moles iodine to form Z moles of HI.

Molar parts of the equilibrium mixture components are calculated by the following equation:

Ni = ni/∑ni,

where ∑ni is the total number of moles in an equilibrium mixture.

∑ni = nH2 + nI2 + nHI = X - ½Z + Y - ½Z + Z = X + Y.

The calculation process is summarized below (Table 1):

If we know the values of КP, Х, and Y, we can calculate Z and determine the composition of the equilibrium mixture.

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Displacement of Equilibrium. Le Chatelier's Principle.

Factors Influencing Equilibrium Constants

External influence, resulting in displacement of equilibrium, can be different. Displacement of equilibrium can occur through change of temperature, pressure or concentration of a reactant or through introduction of additives. The Le Chatelier's principle predicts the direction of equilibrium displacement.

Le Chatelier's principle: When any system at equilibrium is subjected to change in concentration, temperature, volume, or pressure, then the system readjusts itself to counteract the effect of the applied change and a new equilibrium is established.

According to Le Chatelier's principle, increase of temperature leads to displacement of equilibrium to the endothermic process. Increase of pressure results in displacement to the reduction of gas release. Increase of concentration a reactant displaces the system to a process where this reactant is an initial compound.

The system readjusts itself after the applied change and new equilibrium is achieved.

Displacement of equilibrium does not always lead to the change of КP value. In ideal systems, pressure change does not change КP; concentration change does not change КС. An illustration of this is a heterogeneous reaction:

Са(СО)3(solid) = СаО(solid) + СО2,

Where equilibrium constant depends on СО2 pressure only, as it was stated in Section 5:

K p = PCO2 .

At 298 К, the constant K p can be calculated by the reference data using equation (12):

rGo = fGо СО2 + fGоСаО - fGоСа(СО)3 =

= -394.37 + (-603.46) – (-1,128.35) = 130.52 kilojoules.

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Therefore, the equilibrium pressure of СО2 is equal to РСО2 = 0.005 atm.

The reaction occurs with gas release, ∆n = 1. If we increase pressure, equilibrium displaces to the reverse process, direct process rate will drop. At the same time, the rate of the following reaction will increase:

СаО(solid) + СО2 → Са(СО)3(solid).

This reaction result in pressure drop until a new equilibrium is established with the pressure of 0.005 atm.

For ideal systems, the influence of pressure change on equilibrium is characterized by КN.

In real systems pressure exerts influence on КP; in other words, КP is not a thermodynamic constant in real systems. A constant is expressed through fugacities in such cases. Кf is a true thermodynamic constant, which does not depend on pressure in real systems.

All the equilibrium constants change with temperature.

The numerical value of equilibrium constants depends on the way we represent the reaction equation. For example, there are two ways two represent the reaction of hydrogen iodide synthesis:

1)H2 + I2 ↔ 2HI;

2)1/2H2 + 1/2I2 ↔ HI;

Equilibrium constants can be expressed by the following equations:

Therefore, when we analyze reaction equilibrium, we use the same way to represent it.

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Equilibrium of a Chemical Reaction Isotherm

In the Section “Mass Action Law and Equilibrium Constant” we discussed equilibrium conditions for the reaction:

mM + dD ↔ xX +yY.

What will happen when partial pressures of components differ from equilibrium ones? For example, let’s take a mixture of components M, D, X, and Y with the respective partial pressures Р/M, Р/D, Р/X, and Р/Y (the symbol «/» indicates non-equilibrium pressures). What in the reaction direction in this case?

In non-equilibrium conditions: drG = ∑µidni ≠ 0. By analogy with (2.4):

∑µidni = x(µоX + RTlnP/X) + y(µоY + RTlnP/Y) - - m(µоM + RTlnP/M) - d(µоD+ RTlnP/D) ≠ 0.

As

rGo = xµоX + yµоY - mµоM - dµоD, and

rGo = - RTlnКP, then

rG = ∑µidni = - RTlnКP + RT(xlnPX + ylnPY - mlnPM – dlnPD);

where ПP is the ratio of multiplied non-equilibrium partial pressures of reaction products with the respective degrees corresponding to their stoichiometric coefficients, to multiplied non-equilibrium partial pressures of initial compounds.

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In other words, ПP and КP are calculated using similar equations but non-equilibrium (initial) values of partial pressures are used for ПP.

Equation (2.13) is called equation of chemical reaction isotherm. If we know equilibrium constant value, we can use this equation to determine the sign of rG, and, therefore, process direction.

The analysis of the equation (2.13) reveals that if КP > ПP, than rG < 0

Equation (2.13) is the mathematic interpretation of the Le Chatelier principle. For example, if we increase the concentration of reaction products in an equilibrium system, than this system leaves its equilibrium state and the ПP value increases: the numerator in the fraction (2.14) will increase. The rG value will be above zero and equilibrium will displace to the reverse reaction (according to the Le Chatelier Principle).

Temperature Dependence of a Chemical Reaction. Isobaric and

Isochoric Equations

differentiate isotherm equation (2.13) with respect to T and P = const. Consider that КP is a function of temperature, while ПP does not depend on temperature.

Let’s transform this equation. A partial derivative of the Gibbs function with respect to temperature and Р = const is the reverse entropy:

Equation (2.13) demonstrates that

∆Tr G = −R ln KP + R ln ПР .

Therefore, equation (2.15) will take the following form:

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Equation (2.16) is the Van’t Hoff Isobar equation.

The right part of the equation (2.16) predicts how КP changes with

therefore, only numerator affects the equilibrium constant, which is the sign and the value of a reaction heat effect ∆r H . If heat absorbs during a

reaction (it is endothermic, ∆r H > 0 ), than d ln KP > 0 , and equilibrium dT

constant will increase with temperature. If heat releases during a reaction

decreases with temperature growth. Thus, the isobar equation (2.16) is another mathematic interpretation of the Le Chatelier Principle with respect to temperature.

If we want to use the isobar equation for calculation of equilibrium constant at the temperature Т, we need to derive the variables:

d ln KP = ∆RTr H2 dT

and then integrate: the result:

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If the temperature interval is narrow and we can neglect the temperature factor in the calculation of the reaction thermal effect ( ∆r H = const), than

Equations (2.17) and (2.18) are used for approximate calculations. For more accurate calculations, we need to know the dependence of reaction thermal effect on temperature.

Similarly to the equation (2.16), we can derive isochoric equation (2.19), for a system at a constant volume:

LABORATORY EXERCISE 5.

CHEMICAL EQUILIBRIUM OF HOMOGENEOUS CHEMICAL

SYSTEMS

Experiment Procedure

Work objective: studying the main rules of the reversible reactions on the example of interaction between potassium iodide KI and ferric chloride

FeCl3. To calculate the equilibrium constant КС and ∆r G of the reaction.

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The reversible reaction between potassium iodide KI and ferric chloride FeCl3 proceeds in aqueous solution at room temperature. The reaction equation looks as follows

2KI + 2FeCl3 ↔ 2 KCl + 2FeCl2 + I2,

Or in ionic form

2I- + 2Fe+3 ↔ 2Fe+2 + I2,

Equilibrium constant КС of the reaction is expressed as follows:

The reaction behavior is observed by the released iodine concentration change. Iodine concentration is found by means of titration with sodium hyposulphite solution Na2S2O3; starch is used as an indicator. The same quantity of sodium thiosulfate, which is used for titration in two sequential samples, shows that the reaction has achieved its equilibrium.

Tasks:

1.Draw the kinetic curve of the reverse reaction that shows how the iodine concentration changes with time. Determine the moment when chemical equilibrium is achieved.

2.Calculate the equilibrium concentrations of initial substances and

reaction products. Calculate the equilibrium concentration КС and ∆r G .

3. Evaluate the influence of temperature and concentration on the equilibrium state.

Equipment and materials:

1.Solutions: KI 0.03 М; FeCl3 0.03 М; sodium hyposulphite Na2S2O3 0.015 М; starch.

2.Graduated cylinders, 25 ml; 5 ml glass dropper; burette, 50 ml flask with stopper, 50 ml Erlenmeyer flask for titration, Bunsen beakers, hot plate, ice water.

Work procedure.

1. Prepare a burette (Fig. 2.4.) for titration: a) Pour water from the burette;

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b)Fill the burette with sodium hyposulphite Na2S2O3 using a funnel 2;

c)Let the air out of burette tip 6;

d)Set the liquid level in the burette at 0 (count from the lower edge of the liquid meniscus) (Fig. 2.4a.).

2. Measure out VКI ml of potassium iodide and VFeCl3 ml of ferric

3.Pour the solutions into a dry clean flask with stopper. Register the mixing time (time when the reaction begins).

4.Determine the concentration of released iodine in the reaction mixture at specified time interval after beginning of the reaction (upon the instruction of a faculty member). Follow the procedure:

a) Pour 20 ml of chilled water into Erlenmeyer flask for titration (in order to slow down the reaction).

b) Using a glass dropper sample out 5 ml of the reaction mixture. Transfer the sample into the Erlenmeyer flask for titration. Fix the sampling time with accuracy of 1 minute (the moment of pouring the sample into the titration flask is to be considered as the sampling time).

c) Right after pouring the sample, titrate the released iodine with

sodium hyposulphite solution Na2S2O3. Add the sodium hyposulphite solution until the color is changed from red-brown to maize yellow.

d) Add several drops of amylum and titrate with hyposulphite until the blue coloring disappears. (Do not consider the light blue coloring that appears in several minutes after titration).

g) Fill the table 3 with the findings.

Table 2.3

Time after beginning of the reaction t, min

Hyposulphite volume used for titration, Vtitr ml

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where СKI and СFeCl3 are the concentrations of the initial solutions of

potassium iodide and ferric chloride, mol/L.

2. Draw the kinetic curve of the reaction Vtitr = f(t) (Fig. 2.5.) according to the experimental data. Determine the hyposulphite volume to be used for titration at the moment of equilibrium V∞.

Fig. 2.5. Kinetic curve of the reaction

3. Calculate the equilibrium concentrations of the reactants:

a) The equilibrium concentration of iodine is calculated on the basis of the chemical equation of the reaction between iodine and sodium hyposulphite:

I2 + 2Na2S2O3 → 2NaI + Na2S4O6.

Considering that the two Na2S2O3 molecules participate in the reaction with iodine molecule

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where СNa2S2O3 is the concentration of hyposulphite, mol/l; Vtitr –

volume of the sample for titration; V∞ - volume of hyposulphite for titration at equilibrium.

b) Considering that the reaction in question results in two Fe+2 ions per one iodine molecule, the equilibrium concentration of iron (II) ions is two times higher than the equilibrium concentration of iodine ions:

СFe+2 = 2 CI2 , mol/L,

c) In order to determine the equilibrium concentration of I- and Fe+3 ions, its decrease in the course of the reaction is to be found. One Fe+3 ion is required to form one ion of Fe+2. The equilibrium concentration of iron (III) ions equals the difference between the initial concentration of these ions and the equilibrium concentration of iron (II) ions:

СFe+3 =С0,Fe+3 −СFe+2 , mol/L,

Considering that the reaction requires two iron (III) ions per two iodine ions, their concentrations decrease equally in the course of the reaction. The equilibrium concentration of iodine ions equals to the difference between the initial concentration of these ions and the equilibrium concentration of iron (II) ions:

СI − = С0,I − −СFe+2 , mol/L,

4.Calculate the equilibrium constant according to the equation (2.20).

5.Calculate the variation of the Gibbs function in the course of the reaction in accordance with the equation (2.7). Considering that the reaction proceeds in solution, i.e. without any change in the number of gaseous products moles, KC = KP. Add the calculated data to the Table 2.4.

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Measurement Error Assessment

Maximum relative error for КС is calculated as follows:

Burette reading of volume V is accurate to ∆V = 0.1 ml. Na2S2O3 concentration measurement error during the solution preparation equals to:

∆СNa2S2O3 = 0.0001.

СNa2S2O3

Other Types of Tasks

1. Evaluation of influence of the temperature and concentration on equilibrium

Divide the mixture remained in the Erlenmeyer flask after the last titration into three parts.

a) Put the first part on ice. Put the second part in water bath and heat it up to 50оС. Observe the color of the liquid and write down the observation results. Draw conclusions regarding a direction of the reaction equilibrium shift when heating and cooling the solution. Indicate how they conform to Le Chatelier principle. Specify which reaction (forward or reverse) is the

endothermic one (∆rH > 0).

b) Add 5 ml of potassium iodide to the third part of the solution. Observe the color of the liquid and write down the results. Draw conclusions regarding the change in equilibrium concentrations of the

components, the value of equilibrium constant KC , and the equilibrium

shift in the system. Specify how the obtained results conform to Le Chatelier principle and the law of mass action.

2. The law of mass action justification test

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