Сalorimetric measurements of thermal effects of chemical reactions and physicochemical processes. Laboratory training guidance

The Ministry of education and science of the Russian Federation Federal state budget educational

institution of higher education

«Kazan National Research Technological University»

СALORIMETRIC MEASUREMENTS OF THERMAL

EFFECTS OF CHEMICAL REACTIONS AND PHYSICOCHEMICAL PROCESSES

Laboratory Training Guidance

Kazan

KNRTU Publishing house 2016

LABORATORY PRACTICUM 1

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).

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,

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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:

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 type. Mathematically, it means that the integral

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final final

A pdV can have a solution if a dependence p=f(V,T) is

initial initial

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),

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.

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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 pressure-volume 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 1 atm.

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, 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;

( i Н f ,i ) prod. is the sum of reaction products formation heats; ( i Н f ,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:

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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:

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).

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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 difference T2 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:

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

of reaction products and the sum of molar heat capacities of

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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:

While integrating the Kirchhoff's equation within narrow limits of temperature (dozens degrees), the heat capacity c p 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:

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

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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.

When we add more substance to its solution, the intermediate

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.

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