Module Tag CHE_P10_M6

Size: px

Start display at page:

Download "Module Tag CHE_P10_M6"

Mabel Howard
5 years ago
Views:

1 Subject Chemistry Paper No and Title 10: Physical Chemistry- III (Classical Thermodynamics, Non-Equilibrium Thermodynamics, Module No and 6, Thermochemistry and Hess s law Title Module Tag CHE_P10_M6

2 TABLE OF CONTENTS 1. Learning outcomes 2. Introduction 3. Change in thermodynamic quantities during a chemical reaction 3.1 Change in internal energy of a chemical reaction 3.2 Change in enthalpy of a chemical reaction 4. Relation between the enthalpy at constant volume and enthalpy at constant pressure 5. Enthalpy of a chemical reaction 6. Determination of enthalpies of a reaction 7. Kirchhoff equation: Variation of enthalpy of reaction with temperature 8. Flame and explosion temperatures 9. Hess s law 10. Extension of Hess s law 11. Application of Hess s law 12. Summary

3 1. Learning Outcomes After studying this module you shall be able to: Depict the change in thermodynamic quantities during a chemical reaction Derive the relation between enthalpy at constant pressure and enthalpy at constant volume Know about Kirchhoff equation Learn about Flame and Explosion temperature Learn about Hess s law of constant heat summation Know how Hess s law is extended to find entropy and free energy change Know the applications of Hess s law 2. Introduction The branch of chemistry which deals with the energy changes involved in chemical reaction is called thermochemistry. It is the study of energy and heat associated with chemical reactions. Thermochemistry focuses on the energy changes, primarily on the system s energy exchange with its surroundings. Thermochemistry can predict the quantities of reactants and products during the course of the reaction. It is also useful in prediction of the spontaneity of the reaction. It merges the concepts of thermodynamics with the concept of energy in the form of chemical bonds. The quantities like enthalpy, heat capacity, entropy, free energy, heat of formation are mainly calculated through this. According to thermochemistry, the change in energy which occurs in chemical reaction is mainly because of the change of bond energy, i.e., it results from the breaking of bonds in the reactants and formation of new bonds in products. Thermochemistry is based on two laws: Lavoisier and Laplace s law: This law states that the change in energy accompanying any transformation is equal and opposite to change in energy accompanying the reverse process. Hess s law: This law states that the change in energy accompanying any transformation is same whether the process occurs in one step or many steps.

4 Lavoisier, Laplace and Hess have also done investigation on specific heat and latent heat. 3. Change in thermodynamic quantities during a chemical reaction 3.1 Change in internal energy of a chemical reaction Consider a chemical reaction during which the temperature and volume is kept constant, i.e., dv=0. Thus, work done (w) is also equal to zero as w=pdv. Therefore, equation of the First law (viz., U = q + w) becomes: U = q v (1) where q v stands for the heat exchanged at constant volume. Let UR be the internal energy of the reactants and UP be the internal energy of the products, thus change in internal energy will be ΔU= UP UR = qv (2) 3.2 Change in enthalpy of a chemical reaction The heat exchanged at constant pressure is known as the enthalpy change. Suppose q p be the heat exchanged during a chemical reaction which is occurring at constant pressure. Therefore, H q p (3) Let HR be the enthalpy of the reactants and HP be the enthalpy of the products, thus change in enthalpy will be ΔH = HP HR = qp (4) Thermochemistry enables us to predict the amount of heat that would be evolved or absorbed in a process without actually performing a tedious set of experiments in the laboratory. The energy changes for the processes which are not feasible experimentally can also be calculated through thermochemistry. Sign convention: Reactions in which heat is absorbed by the system are called endothermic reactions. In such reactions HP > HR, so ΔH is positive. Since the energy of the system also increases by the absorption of heat thus ΔU is also positive in endothermic reactions. While the reactions

5 in which heat is evolved, are called exothermic reactions. In such reactions HP < HR so ΔH is negative. In such reactions ΔU is also negative. 4. Relation between enthalpy at constant volume (qv) and enthalpy at constant pressure (qp) The relation between ΔH and ΔU is given by: H U P V (5) where ΔV is the volume change taking place in a reaction. Since qv U and qp H, therefore we can write equation (5) as q q P V (6) p v Now writing the above equation in simplified manner; For n moles of an ideal gas, PV = nrt (7) Suppose n1 be the number of moles for gaseous reactants and n2 be the number of moles of gaseous products. Let n2 > n1. Thus increase in the number of moles is given by n 2 n 1= n g. The corresponding increase in volume ( V ) will be given by (V/n) n g. Therefore, P V P(V / n) n RT n (8) g g Thus, P V RT ng (9) Substituting equation (8) in equation (6), qp qv ngrt In the above equation n g (10) stands for the difference between the number of moles of gaseous products and gaseous reactants. 5. Enthalpy of a chemical reaction Standard Enthalpy change of a reaction is defined as the enthalpy change of reaction determined at 25ºC and at 1atm pressure and is denoted by ΔHº

6 Considering various enthalpy changes: (a) Enthalpy of formation The enthalpy of formation can be defined as the amount of heat exchanged at constant temperature and pressure during the formation of one mole of the substance from its constituent elements in their standard states. It is represented by ΔfH. Its unit is kj mol 1. For example, the enthalpy of formation of CO2 is equal to the enthalpy change for the following reaction C(s) + O2(g) CO2(g) ΔfH = kj mol 1 H 2 (g) O 2(g) H 2 O(l) ΔfH = kj mol -1 H 2 O(l) H 2 (g) O 2(g) ΔfH = kj mol -1 (b) Enthalpy of combustion It is defined as the enthalpy change that takes place when one mole of a substance is burnt completely in the presence of oxygen at a given temperature and pressure. It is denoted by ΔcH and the unit is kj mol 1. The combustion is always an exothermic process. For example, combustion of methane CH4(g) + 2O2(g) CO2(g) + 2H2O(l) ΔcH ө (298 K)= 890 kj mol 1 C 2 H 6 (g) O 2(s) 2CO 2 (g) + 3H 2 O(l) H (298 K) = 1560 kj mol 1 (c) Enthalpy of solution The amount of heat exchanged when 1 mole of solute is dissolved in a sufficient amount of solvent at a specified temperature and pressure is known as enthalpy of solution. For example, HCl (g) + 10 H2O(l) HCl.10H2O(aq) HCl (g) + 40 H2O(l) HCl.40H2O(aq) ΔH = kj mol 1 ΔH = 72.79k J mol 1 These values of ΔH show the general dependence of the heat of solution on the amount of the solvent. As more and more solvent is used the value of heat of solution changes. As the amount of the solvent increases the resulting solution becomes more dilute and ultimately it becomes so dilute that further addition of solvent produces no enthalpy change. This solution is known as infinitely dilute solution. (d) Enthalpy of Sublimation

7 It is the amount of enthalpy change to convert one mole of a solid to vapor state at a given temperature and pressure. H2O (l) H2O(g) ΔsubH ө (298 K)= 50.0 kjmol 1 (e) Enthalpy of Fusion It is the change in enthalpy to convert one mole of a solid to its liquid state at a given temperature and pressure. H2O (s) H2O(l) ΔfusH ө (298 K)= 6.0 kj mol 1 (f) Enthalpy of Atomization It is the amount of heat required to convert one mole of a substance into its constituent atoms in the gaseous state. atomizatio n C(graphite) C(g) ah(c) = kjmol 1 H2(g) atomizatio n 2H(g) ah(h)= 436 kj mol 1 6. Determination of Enthalpies of reactions Enthalpies of reactions at 25ºC can be determined if ΔHºf values of the reactants and products involved in the reactions are known as ΔHº = ΣΔHºf (products) - ΣΔHºf (reactants) (11) By convention, ΔHºf values for the elements in their standard states are taken as zero. 7. Kirchhoff Equation: Variation of Enthalpy of reaction with Temperature The change in enthalpy of any physical or chemical process varies with temperature at constant pressure. The effect of temperature on the enthalpy can be understood as follows: Consider a reaction, aa + bb cc + dd The enthalpy change for the above reaction will be: H Hproducts H reac tan ts (chc dh D) (ah A bh B) (12)

8 Differentiating equation (12) with respect to temperature, keeping pressure constant ( H) HC HD HA H c d a b B T T T T T P P P P P Since, C P ( H / T) P Therefore, equation (13) can be written as [ ( H) ] = C T P (products) C P (reactants) P ( H) T where P cc dc ac bc C P, C P, D P, A P, B P (13) (14) C P = Sum of heat capacities of products Sum of heat capacities of reactants. Equation (14) is known as Kirchhoff equation. This equation states that the variation of of a reaction with a temperature at constant pressure is equal to [ ( H) / T] P CP Rearranging the above equation, H CP of the system, i.e., (15) d( H) CPdT (16) Similarly, the dependence of enthalpy on temperature at constant volume is given by, [ ( H) / T] V CV or d( U) CVdT (17) If the temperature range is small, then change in heat capacity is given by, (assuming heat capacities are not dependent on temperature) T2 T2 T2 P P T1 T1 T1 d( H) C dt C dt or H2 H1 C P(T2 T 1) (18) Similarly, U2 U1 C V(T2 T 1) (19) If the temperature range is not small then the heat capacities will vary with temperature. Thus it is convenient to express the heat capacity as a power series in Temperature (T) i.e. 2 C T T (20) P where, and are constants for a given species. Similarly, C P = = 2 T T... (21) Substituting equation (21) in equation (15) and integrating between T1 and T2, we get

9 T2 T2 2 d( H) ( T T )dt (22) Or, T1 T H2 H 1 (T2 T 1) (1/ 2) (T2 T 1 ) (T2 T 1 ) (23) 3 Equation (23) is the integrated Kirchhoff equation. 8. Flame and Explosion Temperatures The combustion of a gaseous fuel in air occurs so rapidly that the heat produced during combustion does not get enough time to dissipate into the surroundings. Thus, combustion process is found to be equivalent to an adiabatic process. The entire amount of heat produced is used up to heat the gases which are produced during combustion. Maximum flame temperature is defined as the maximum temperature attained by the flame zone (containing the resultant gases) due to the heat evolved by the combustion of the fuel under adiabatic conditions at constant pressure. On the other hand, if the combustion is carried out under adiabatic conditions at constant volume, the maximum temperature attained is called maximum explosion temperature. Kirchhoff equation is used to calculate the maximum flame temperature for an isobaric adiabatic process. This is done as follows, d( H) / dt C P or d( H) CPdT (24) Integrating the above equation gives, T f d( H) CP dt or H C P (Tf T i) Ti In the above equation C P integral sign. Thus, if the values of the final temperature T f (25) is assumed to be constant that is why it is taken outside the H, C P and the initial temperature (maximum flame temperature ) can be calculated. T i are known then 9. Hess s law Hess s law was established by the Russian chemist German H. Hess in This law is known as Hess s law of constant heat summation. This law states that the amount of heat evolved and absorbed in a process, including a chemical change, is the same whether the process takes place in one or several steps, i.e., total change in enthalpy does not change during the course of the reaction. Thus Hess s law is also known as principle of conservation

10 of energy. The change in enthalpy does not depend on the path taken from the initial to the final state ( i.e. enthalpy is a state function). Reaction enthalpy changes can be determined by calorimetry for many reactions. It is of particular utility in calculations of the heat of reactions which are difficult for practical calorimetric measurements. The overall energy needed for a chemical reaction can be determined by Hess s law. Hess s law states that the enthalpy change (i.e., heat of reaction at constant pressure) in a chemical reaction does not depend on the path between the initial and final states of the system. That is the overall change in enthalpy is same during a chemical change of a reaction regardless of the number of steps through which the reaction has been taken place. For example, for a change from reactant to product that can take place in four steps or a single step, the total enthalpy change will be same. Single step process: Reactant Product Multiple step process: Reactant A A B B C C Product ΔH ΔH1 ΔH2 ΔH3 ΔH4 According to Hess s law ΔH = ΔH1 + ΔH2 + ΔH3 + ΔH4 This can also be shown by following diagram:

11 This generalization means that enthalpy of the reaction depends only on the initial reactants and the final products and not at all on the intermediate products that can be formed. Thus, enthalpy change which cannot be measured directly is calculated by Hess s law. If the net enthalpy change of the reaction is negative, then the reaction is said to be exothermic; positive value for enthalpy change corresponds to endothermic reactions. Hess s law states that changes in enthalpy are additive. Thus for a single reaction change in enthalpy ΔH is given by: º ΔH reaction º = ΔH f(products) º ΔH f(reactants) where ΔHf stands for the enthalpy of formation and superscripts º represent standard state values. The above equation is the combination of two reactions. These are: Reactants Elements ΔH º = H f(reactants) Elements Products H = H f(products) 10. Extension of Hess s law The changes in entropy and in Gibbs free energy can also be calculated by applying the concepts of Hess s law. The Bordwell thermodynamic cycle is an example of such an extension which takes advantage of easily measured equilibria and redox potentials to determine experimentally inaccessible Gibbs free energy values. Thus the change in free energy can be determined by: G reaction = G f(products) G f(reactants) But entropy can be measured as an absolute value thus entropy of formation is not required, simply absolute values of entropy are used. = S products S reactants Ext S reaction 11. Applications of Hess s law Hess s law of constant heat summation is useful in the determination of enthalpies of the following: Calculation of enthalpies of reactions Determination of enthalpy changes of slow reactions Calculation of enthalpies of formation

12 Enthalpy of formation of reactive intermediates It helps in determining the lattice energies of ionic substances by building Born-Haber cycles if the electron affinity to form the anion is known Exercise: The heat of dissociation per mole of a gaseous water at 18º C and 1 atm is J, calculate its value at 68º C. Data given are: C P (H 2 O) = 33.56; C P (H 2 ) = 28.83; C P (O 2 ) = JK 1 mol 1 Solution: The dissociation reaction is: H 2 O (g) H 2 (g) O 2(g) H (291 K) = J C P = C P (H 2 ) + 1 C 2 P(O 2 ) C P (H 2 O) = ( ) J 2 K 1 mol 1 = 9.83 J K 1 mol 1 Therefore, C P T = (9.83J K 1 mol 1 ) (50 K) = J mol 1 H (341 K) = H (291 K) + C P T = = J mol 1

13 12. Summary The branch of chemistry which deals with the energy changes involved in chemical reaction is called thermochemistry The relation between enthalpy at constant volume (qv) and enthalpy at constant pressure (qp) is given by: qp qv ngrt Enthalpies of reactions at 25ºC can be determined if ΔHºf values of the reactants and products involved in the reactions are known as ΔHº = ΣΔHºf (products) - ΣΔHºf (reactants) Kirchhoff equation is given by ( H) T P cc dc ac bc C P, C P, D P, A P, B P Maximum flame temperature is defined as the maximum temperature attained by the flame zone (containing the resultant gases) due to the heat evolved by the combustion of the fuel under adiabatic conditions at constant pressure If the combustion is carried out under adiabatic conditions at constant volume, the maximum temperature attained is called maximum explosion temperature Hess s law was established by the Russian chemist German H. Hess in 1840 Hess s law states that the amount of heat evolved and absorbed in a process, including a chemical change, is the same whether the process takes place in one or several steps, i.e., total change in enthalpy do not change during the course of the reaction Hess s law states that changes in enthalpy are additive. Thus for a single reaction change in enthalpy ΔH is given by: º ΔH reaction º = ΔH f(products) º ΔH f(reactants)

10-1 Heat 10-2 Calorimetry 10-3 Enthalpy 10-4 Standard-State Enthalpies 10-5 Bond Enthalpies 10-6 The First Law of Thermodynamics

Chapter 10 Thermochemistry 10-1 Heat 10-2 Calorimetry 10-3 Enthalpy 10-4 Standard-State Enthalpies 10-5 Bond Enthalpies 10-6 The First Law of Thermodynamics OFB Chap. 10 1 OFB Chap. 10 2 Thermite Reaction