The Ministry of Education and Science of the Russian Federation Kazan National Research Technological University

N. M. Selivanova, A. N. Bezrukov, Y. G. Galyametdinov

PHYSICAL CHEMISTRY

Educational аid

Kazan

KNRTU Press

2017

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UDC 544.342-14

LBC Ш143.21-923

S45

Published by the decision of the Editorial Review Board of the Kazan National Research Technological University

Reviewers:

Prof., Leading Researcher Laboratory Diffraction Methods of Research

A.E. Arbuzov IOPC KSC RAS A. T. Gubaidullin

Head. Laboratory of Ultrafast Molecular Processes

E.K. Zavoisky KFTI KSC RAS V. S. Lobkov

Selivanova N. M.

S45 Physical Chemistry : Educational аid / N. M. Selivanova, A. N. Bezrukov, Y. G. Galyametdinov; The Ministry of Education and Science of the Russian Federation, Kazan National Research Technological University. – Kazan : KNRTU Press, 2017. –151 p.

ISBN 978-5-7882-2243-1

This manual represents laboratory practicums and individual tasks in the main areas of physical chemistry, which determine its subject matter: chemical thermodynamics, chemical equilibrium, phase equilibriums and the theory of solutions, kinetics and catalysis, and solutions of electrolytes.

The present teaching materials are addressed to undergraduate and graduate students majoring in chemical engineering, who study “Physical Chemistry” and “Supplementary Materials of Physical Chemistry” as academic disciplines.

Developed at the Department of Physical and Colloid Chemistry.

UDC 544.342-14

LBC Ш143.21-923

ISBN 978-5-7882-2243-1 © Selivanova N. M., Bezrukov A. N.,

Galyametdinov Y. G., 2017

©Kazan National Research Technological

University, 2017

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TABLE OF CONTENTS

1.Laboratory Practicum: Calorimetric Measurements of Thermal Effects

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INTRODUCTION

Physical chemistry is an important branch of science with its own research methods. It is quite important for various adjacent scientific disciplines. Physical chemistry plays a significant role in training of chemical engineers. Physical chemistry us usually preceded by inorganic, organic and analytical chemistry. It finalizes the cycle of general chemistry, and then physical chemistry is followed by theoretical foundations of special engineering courses. Thus, physical chemistry provides fundamental basis for these disciplines.

This study guide represents laboratory practicums and individual tasks in the main areas of physical chemistry, which determine its subject matter: chemical thermodynamics, chemical equilibrium, phase equilibriums and the theory of solutions, kinetics and catalysis, and solutions of electrolytes.

The Chemical Thermodynamics section considers the main equations for calculating the thermal balance of a chemical process and the amount of heat released or absorbed in chemical reactions or various physicochemical processes as well as for predicting spontaneous behavior of processes.

The Chemical Equilibrium section includes the theory of equilibrium states in chemical and physical processes and discusses the influence of external conditions on chemical equilibrium.

Chemical Kinetics studies rates of chemical reactions both in homogeneous and heterogeneous media as well as the phenomenon of catalysis.

Electrochemistry studies specific properties of electrolyte solutions, electrical conductivity, and galvanic elements.

The Theory of Solutions considers the nature of solutions, problems of solubility, and the dependence of properties on concentration and the nature of components.

This study guide includes the following laboratory practicums: “Determination of the Distribution Coefficient of a Solute between Two Immiscible Liquids”, “Equilibrium of Homogeneous Chemical Systems”, “Calorimetric Measurements of Thermal Effects of Chemical Reactions and Physicochemical Processes”, “Kinetics of Heterogeneous Catalytic Reactions”.

The guidelines to each laboratory practicum include the following obligatory components: theoretical introduction with general concepts and laws of the studied physical chemistry area, self-study and control

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questionnaire, and instructions for the experiments, the necessary bibliography, and the reference data tables.

Individual work block in “Kinetics of Homogeneous Processes” and “Electrolytes solutions” includes about 250 questions such as theoretical problems and self-study tasks.

These teaching materials are addressed to undergraduate and graduate students majoring in chemical engineering, who study “Physical Chemistry” and “Supplementary Materials on Physical Chemistry” as academic disciplines. They can be also useful for PhD students and faculty carrying out workshops.

The study guide has been developed at the Department of Physical and Colloid Chemistry.

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1. LABORATORY PRACTICUM:

CALORIMETRIC MEASUREMENTS OF THERMAL EFFECTS OF CHEMICAL REACTIONS AND PHYSICOCHEMICAL PROCESSES

Objective: to study the method of thermochemical measurements and calculations; to measure heat capacity of a calorimeter and (according to the task provided by a professor) the heat of a chemical or physicochemical process (for example, neutralization, salt dissolution or hydration heats).

1.2 THEORETICAL INTRODUCTION

FIRST LAW OF THERMODYNAMICS AND FOUNDATIONS OF

TERMOCHEMISTRY

Terms and Definitions

Thermodynamic system is a body or a group of bodies interacting with environment and considered separately from it. Systems exchanging energy (such as heat and work) and matter with environment are called open systems. Systems which exchange only energy are closed systems, while systems exchanging neither energy, nor matter are called isolated.

Let’s consider closed systems at the state of thermal and mechanical equilibrium with the environment, which means that temperature and pressure are the same in any part of such a system. A system can undergo transition from one state (initial one) to another (final state) due to occurrence of physical or chemical processes.

A parameter of state is generally a variable which can get a certain value in process conditions. Parameters of state can be subdivided into extensive (capacitive), quantitatively proportional to the size and mass of a system (volume, mass, heat capacity, internal energy and entropy) and intensive, which do not depend on mass and are determined by the specific nature of a system (pressure, temperature, chemical potential).

Thermodynamic parameters of state are the parameters which change directly and express intensive properties of a system. The most important of them are temperature (Т), pressure (р) and molar volume (V). Parameters of state are interdependent; an equation connecting them is an equation of state. The ideal gas state equation (Mendeleev-Clapeyron equation) is widely used in thermodynamics:

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where n is the number of moles of a gas, R is the universal gas constant.

First Law of Thermodynamics

First law of thermodynamic is the energy conservation law of an isolated system. It is an empirical equation and can be considered as a postulate valid for any isolated system. When the first law is applied to closed systems, it is assumed, that after heat transfer all the processes in closed systems occur in the same way as in isolated ones. (Energy exchange with environment is considered to be instantaneous: time is excluded from thermodynamic processes). First law of thermodynamic postulates that the heat transferred to a system is consumed for the increase of its internal energy dU and for work of a system against external pressure

δA=pdV:

Internal energy depends on state parameters only, so its change in a process occurring through any intermediate states is fully determined by its initial and final states. Internal energy is therefore a function of state, the differential of such a function is a full differential:

initial

The work of transfer from an initial to a final state depends on a process

a solution if a dependence p=f(V,T) is known. Therefore, in equation (2) the right part and, thus, the left one depend on the path of a process. In other words, heat and work are process functions.

Let’s consider particular cases of equation (2) application: In an isochoric process, V=const, then δQv=dU,

In an isobaric process, p=const, then δQv=dU+pdV=d(U+pV),

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Let’s introduce H=U+pV, where H is a state function called enthalpy, then:

Thus, heat obtains properties of a state function in isobaric and isochoric processes, it does not depend on process trajectory, but only on initial and final states of a system. This consequence of the first law of thermodynamics is called Hess’s law. Selecting reactions in a way that reactants and products as well as their states are the same and all the thermal effects are known except the required one, it is possible to calculate reaction heats which are unknown or cannot be measured directly.

As heat can release due to reduction of internal energy or enthalpy or be absorbed resulting in internal energy increase, ∆U<0 and ∆H<0 for exothermic reactions occurring with heat release, while ∆U>0 and ∆H>0 for endothermic reactions occurring with heat absorption.

A section of physical chemistry studying thermal effects of chemical reactions and physicochemical processes is called thermochemistry. Thermochemical data and related generalizing regulations can be used in engineering practice for thermal balancing of physicochemical processes and for calculation of heat constants. The results of thermochemical measurements in theoretical chemistry are used for the calculation of chemical bond energies in molecules.

Standard heat of a chemical reaction is an amount of heat that is released or absorbed in irreversible reaction conditions, when pressurevolume work is one type of work and the temperatures of initial substances and reaction products are the same.

Standard heats of formation, heats of combustion, heats of dissolution, heats of neutralization, and heats of crystallohydrate formation are the most important heat effects.

Standard heat of formation (∆H 0f ,298 )is a heat effect of formation of a

mole of a substance from elementary substances in stable modification and a state of mater under T = 298 К and P =1atm. Standard heats of

formation (∆H 0f ,298 )are listed in data tables of thermodynamic quantities.

Heat of elementary substances formation (N2, H2, O2, and etc.) is considered to be zero. While calculating heat effect from formation heats,

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the following rule is used: A standard heat of a chemical reaction is the difference between the sum of reaction product formation heats and the sum of reactant formation heats. Each formation heat is to be multiplied by corresponding stoichiometric coefficient. This rule is a consequence of the

Hess’s law. The mathematical representation of the rule:

where ∆H is a standard heat of reaction;

(∑νi∆Нf ,i )prod. is the sum of reaction products formation heats; (∑νi∆Нf ,i )itit. is the sum of reactant formation heats;

vi are stoichiometric coefficients in a chemical equation.

If a heat of formation of a chemical substance for one state of matter is provided, the heat of formation of this chemical substance in other state of matter can be calculated using the Hess’s law:

where ∆Нsublim. , ∆Нmelting , ∆Нevap. are the heats of sublimation, melting and evaporation, kJ/mole, respectively.

Standard combustion heat (∆Нcomb0 .298 ) is a heat of combustion reaction of a mole of a particular substance with the formation of higher oxides. The heat of a chemical reaction can be calculated from combustion heats in case if only organic substances are involved into a reaction.

The heat of a chemical reaction equals to the difference between sum of combustion heats of initial substances and sum of combustion heats of reaction products. Each combustion heat is to be multiplied by a corresponding stoichiometric coefficient:

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If a chemical reaction occurs at the temperature other than the standard temperature, heat capacities can be used to calculate the reaction heat. Heat capacity is one of the most important characteristics of an individual substance. Heat capacity of a substance is widely used to carry thermodynamic calculations (heat balance, entropy, chemical equilibrium and, and etc.)

Heat capacity can be specific and molar. Specific heat capacity is the heat required for heating up a gram of a substance by one degree. Molar heat capacity is the heat required for heating up a mole of a substance by one degree. The values of molar heat capacities are used for physicochemical and thermodynamic calculations. True heat capacity and mean heat capacity are also introduced.

True heat capacity (c) is a ratio between infinitely-small heat amount conducted to substance and subsequent infinitely-small temperature increase:

where с is a molar heat capacity, J/(mole∙К).

Mean heat capacity (c), corresponding to a temperature interval from T1 toT2 , is called a ratio of final heat amount conducted to one mole of substance and temperature differenceT2 −T1 :

The relation between true (ср) and mean ( c ) heat capacity at constant pressure is expressed by the following equation:

In general, heat capacity is a function of a process, but in case of isobaric and isochoric process heat capacity is a function of state.

Considering the fact that δQV = dU and δQP = dH , the equations for true heat capacity are represented as follows:

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For ideal gas cp – cv = R = 8.314 J/mole·degree.

Heat capacity is the temperature relationship described by the following empirical equations:

cp = a +bT +c′T −2 +... – for inorganic substances (18),

where a , b , c , c′ are numerical coefficients, that are listed in a references.

According to the Kirchhoff's law, the relationship between heat capacity and temperature is represented as follows: at a constant pressure a

difference (∆cp ) between the sum of molar heat capacities of reaction

products and the sum of molar heat capacities of reactants. Each heat capacity is to be multiplied by a corresponding stoichiometric coefficient:

The calculation formula is developed by integrating of Kirchhoff's equation between 298 K and temperature T:

T

∆HT = ∆H2980 + ∫∆cp dT (1.20).

298

While integrating the Kirchhoff's equation within narrow limits of temperature (dozens degrees), the heat capacity ∆cp is assumed as

constant value, then equation 18 is presented as follows:

Expanded Kirchhoff's equation is solved taking into account the dependence of each reaction step heat capacity on temperature:

After integration, the equation takes the following form:

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Heat is the main object of study of thermochemistry. In a framework of this laboratory practicum, neutralization heat, dissociation, dissolution and crystallohydrate formation are to be experimentally determined and calculated. Several types of heats of dissolution and dilution exist. Generally, the dissolution heat comprises the heats of lattice destruction (for solid materials), ionization and solvation. Processes with more intense energetic effect exert more intensive influence on a sign of dissolution heat value. For example, dissolution of gases is accompanied by the release of solvation hear, which is higher than the energy required for separation of solution molecules, regular distribution of gas molecules in a solution and ionization. For this reason, gas dissolution in liquids occurs with heat release.

For crystalline salts, a sign of dissolution heat value is determined by a ratio between the energy of lattice destruction and the energy of solvation. Lattice destruction requires energy, hydration of ions leads to energy release. If the amount of released solvation energy is less than the energy adsorbed during lattice destruction, a sign of dissolution heat value is positive. In the opposite case, exothermic dissolution occurs.

The value of dissolution heat depends on the process of solution preparation and its concentration. Solution of any given concentration can be prepared by mixing of pure components or by adding a component to solution of initial concentration. Heat released or adsorbed while one mole of a pure substance dissolves in a number of moles of a solvent required for preparation of a solution of the desired concentration is the integral heat

of dissolution ( ∆Hm ). Depending on the nature of a dissolving substance

and a solvent, the value of integral dissolution heat can amount to dozens kJ per mole of a dissolved substance. Integral dissolution heat depends on the temperature and concentration. Heats of gas dissolution are similar to their condensation heats; heats of dissolution of some solid substances are similar to their melting heats.

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When we add more substance to its solution, the intermediate integral dissolution heat ( ∆Hmm12 ) is released or absorbed (where m1 is the initial

solution concentration, m2 is the final solution concentration). For m2 – ∆Hm2 , the integral heat of dissolution equals to:

where g1 and g2 are the weights of samples dissolved in a pure solvent

and the solution with m1 concentration.

Addition of a solvent to corresponding solutions with final concentration is also accompanied by thermal effects (dilution heat), because of changes in interparticle interactions. Lower dilution heats are observed for more dilute solutions.

There are the following types of dilution heats:

Integral dilution heat ( ∆Hm0 ) is a heat effect occurs while solution

contained a mole of dissolved substance dilutes from concentration m to an infinitely small concentration m → 0 .

Intermediate integral dilution heat ( ∆Hmm21 ) is a heat effect occurs while solution contained one mole of dissolved substance dilutes from concentration m2 to an infinitely small concentration m1 (m2 > m1 ).

Ratios between integral dilution heat and integral dissolution heat are represented by the following equations:

Differential (partial) molar heats of dissolution and dilution are also used in calculations. Differential molar heats are calculated from the

integral heats. Differential molar heat of dilution ( ∆H1,m ) describes an

addition of a mole of solvent to infinite large amount of solution of concentration m. Differential molar heat of dissociation ( ∆H2,m )

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describes an addition of a mole of dissolved substance to infinitely large amount of solution of concentration m.

Integral heats of dissolution are determined experimentally, differential heats are determined by calculations.

Along with heats of dissolution heats of neutralization, dissociation, and crystallohydrate formation are used in thermochemistry.

Neutralization heat (Δ Hneutr) is a heat effect of neutralization reaction between one mole of any strong mono acid ( HCl, HNO3 , etc.) and strong

base ( NaOH, KOH , etc). Neutralization reaction is as follows:

H + +Cl − + K + +OH − =Cl − + K + + H2O

While mole equivalent of a strong acid interacts with a strong base in dilute water solutions, almost the same heat amount is released. The neutralization heats are constant due to the formation of water molecules under interaction of strong acids and bases that are fully dissociated in water solutions. At 298 K thermal effect of liquid water formation from hydrogen ions and hydroxyl is equal to:

H+ + OH- → H2O (liq), ΔHteor = -55.9 kJ/mole

Neutralization of a weak acid by a strong base (or neutralization of weak base by strong acid) is attended by simultaneous dissociation of weak electrolyte with thermal effect that is called dissociation heat (ΔHdiss). Neutralization heat comprises of endothermic dissociation heat and exothermic heat of ions hydration. Depending on the nature of electrolytes, the sum of these two heats can have different signs and values. The dissociation heat is calculated by the following equation:

Heat of crystallohydrate formation (ΔHcr.h.) is a heat released while an anhydrous salt and crystallization water interact. It is calculated from

integral heats of dissolution that characterize dissolution of anhydrous salt and crystallization water in an amount of water required to prepare solutions with the same concentration in both cases.

Thermal effect of the process, temperature change, heat capacity and the weights substances form by a heat-balance equation:

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where mi and ci are weight and heat capacity of a studied substance and calorimeter parts involved in heat exchange.

Calorimeters and Their Application

Calorimeters (or calorimetric systems) are used to measure heat effects. Calorimetric system is a reactor placed into a container. A container works in one of two possible regimes: it prevents heat exchange between reactor and environment (an isolated system) or it makes the control of heat exchange easier (a closed system).

In general, calorimeters are subdivided into calorimeters with constant or varying temperature. In the first case, a container includes melting solid substances (such calorimeters are called ice calorimeters) or a vaporizing liquid. During an experiment in such a calorimeter, the temperature is constant, because all obtained heat is consumed for a phase transition. Heat is evaluated using the amount of melted of evaporated substance.

In case of calorimeters with varying temperature, two following measurement methods are possible:

Adiabatic method is a method when a container temperature is varied during the experiment in such a way, that it equals to a reactor temperature at any time; in this case heat exchange does not proceed, so reactor is an isolated system; these calorimeters are applied for measuring small thermal effects or thermal effects of slow processes;

Diathermic method when the heat exchange occurs between a reactor and an isothermal container (a reactor is the closed system); container has the almost constant temperature, because it contains a significant amount of water that has a relatively high heat capacity.

These calorimeters are usually applied for measuring heat capacity, heat of dissolution, dilution, neutralization, state change, and combustion. In the latter case, the reaction runs in a calorimeter bomb with a constant volume.

At this practicum, a calorimeter with an air isothermal container is used; its schematic configuration is presented at the Figure 1.1.

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Cup 1 is an external container of calorimeter. Inside isothermal container, there is calorimeter cup 2, where thermochemical process runs.

The cup is covered with the thermal insulating lid 3. Air layer between cups serves for protective layer that decrease heat exchange between calorimeter and environment.

There are holes in the calorimeter lid: for mixer 4, for thermometer 5 and the testing tube 6 with studied reagent. Electric motor driven mixer 4 provides rapid temperature equalization and active mixing of studied substances. During the thermochemical experiment the temperature change is measured with Beckman thermometer.

Beck man thermometer (Figure 1.2) serves to measure

small temperature changes and consists of main 1 and additional 2 mercury reservoirs connected with capillary 3. Additional reservoir makes it possible to adjust the thermometer by mercury transferring from one reservoir to another at the temperature from - 20 to 15 ºC. Beckman thermometer used at this practicum can measure the temperature changes in the range from 5 to 0.005 ºC.

Fig. 1.2. Beckman thermometer

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