Chemical thermodynamics I.

Medical Chemistry

László Csanády

Department of Medical Biochemistry

What is thermodynamics?Thermodynamics is the study of the effects of work,

heat, and energy on a system.

bodyfood

(energy inchemicalbonds)

longterm storage(energy in

chemical bonds)

constant body

temperature(heat)

physicalexercise

(mechanicalwork)

What is thermodynamics?

body

ATPfood

(energy inchemicalbonds)

longterm storage(energy in

chemical bonds)

physicalexercise

(mechanicalwork)

constantbody

temperature(heat)

F1-Fo-ATP synthase

ADP ATP

System and surroundingsThe "system" is the well defined part of the universe we are interested in.

The "surroundings" is the rest of the universe, which is in contact with the system.

system

surroundings

Internal energy

The internal energy (U) is the sum of all microscopic forms of energy of a system.

Uenergy of motion of e--s and moleculespotential energy from chemical bonding

potential energy from intermolecular attractions

Internal energyU is a state function

State function: a property of the system that depends only on its present state, not on the pathway taken to reach that state.E.g.: p, V, T

2421 m

1500 m

h=921 m

U = Uf - Ui

Therefore:

U is an extensive property

Extensive property: a property of the system which is directly proportional to the amount of material in the system. Such properties are addivitive.Examples: mass (m), electric charge (Q).

Internal energy

Intensive property: a property of the system which does not depend on the system size. Such properties are not additive.Examples: temperature (T), pressure (p), density ().

The change in internal energy of a system equals the heat absorbed by the system (q) plus the work performed on the system (w):

The first law of thermodynamics

system

surroundings

heat (q)

work (w)

Heat: energy that flowsbecause of a temperaturedifference

Work: energy transfer dueto mechanical movement

U = q + w

Mechanical work is done when a force F moves an object over a distance d: w = F · d

Heat and mechanical work

wp = - F· h

heating

qp

Mechanical work done at constant pressure:

wp

system

atmosphericpressure

= - (p·A)·h = - p· (A·h)= - p·V

Restatement of the first law at constant pressure:

Enthalpy

U = qP - pV

qP =U + pV

Let us define a quantity: enthalpy (H):

H =U + pV

At constant pressure the change in enthalpy ofthe system reflects the absorbed heat:

H =U + pV = qp

Enthalpy(i) H is a state function (because U, p, and V are all state functions)

(ii) H is an extensive property: the total enthalpy of the system is the sum of the enthalpies of all the components in the system: H = kHk

Enthalpy change for a reaction:

(i) H = Hfinal – Hinitial

(ii) H = H(products) - H(reactants)

Hess's law: The enthalpy change for a chemical reaction depends only on the initial and final states, but is independent from the pathway taken.

Standard enthalpy change (H˚):

The reaction heat for a reaction in which reactants in

their standard states yield products in their standard

states.

"Standard state": p=1 atm, and usually T=25oC.

Standard enthalpy change

H of physical processes

1.1. Standard enthalpy of fusion (H˚fus): the amountof heat required to change the state of 1 mol of substance from solid to liquid at its melting temperature.E.g.: H˚fus (H2O) = +6.0 kJ/mol1.2. Standard enthalpy of vaporization (H˚vap): the amount of heat required to change the state of 1 mol of substance from liquid to gas at its boiling temperature.E.g.: H˚vap (H2O) = +40.9 kJ/mol

1. H associated with phase transitions

1.3. Standard enthalpy of sublimation (H˚subl): the amount of heat required to change the state of 1 mol of substance from solid to gas at a fixed temperature.E.g.: H˚subl (ice) = +50.8 kJ/mol

H of physical processes

2.1. Molar heat capacity at constant pressure (Cm,p):the amount of heat required to raise the temperature ofone mole of substance by 1 oK.

E.g.: Cm,p (ice) = +38 J/(mol·oK) Cm,p (water) = +75 J/(mol·oK) Cm,p (steam) = +36 J/(mol·oK)

2. H associated with temperature change

H of physical processesH for converting 1 mol -10oC ice into 100oC steam:

ice-10oC

ice0oCCm,p(s)·T

0.4 kJ

water100oC

7.5 kJ

Cm,p(l)·T

4 kJCm,p(g)·T

steam-10oC

50.8 kJsublH˚

steam100oC

40.9 kJvap

H˚

water0oC

6 kJfus

H˚ H1=(50.8+4) kJ = 54.8 kJH2=(0.4+6+7.5+40.9) kJ = 54.8 kJH1 = H2

hea

t re

qu

ired

fo

r p

has

e tr

ansi

tio

n

heat required for temperature rise

H of physical processes3. Standard enthalpy of solution (H˚soln): the amount of heat required to dissolve 1 mol of substance in a large excess of solvent under standard conditions (T=25oC, p=1atm). E.g.: H˚soln(HCl)= -75 kJ/mol in H2O

ii. Breaking solvent-solvent attractions (endothermic) E.g.: H-bonds in water

H˚ of solvation(in water: H˚hyd):

C+(g)+A-

(g)C+(aq)+A-

(aq)

(exothermic)

Factors that contribute to H˚soln:

i. Breaking solute-solute attractions (endothermic) E.g., for ionic solids: lattice enthalpy (H˚lat) is the amount of heat required to break 1 mol of solid crystal into gaseous ions CA(s) C+

(g)+A-(g) (Note: sometimes defined vice versa!)

iii. Forming solvent-solute attractions (exothermic)

H of physical processesCalculate H˚soln for NaCl:

NaCl(s) + aq

Na+(aq) + Cl-(aq)

+4 kJ/molH˚soln

Na+(g) + Cl-(g) + aq

+787 kJ/molH˚lat

-783 kJ/molH˚hyd

H˚soln=H˚lat+H˚hyd=(+787 + (-783)) kJ/mol= +4 kJ/mol

H of chemical processes 4. Standard enthalpy of formation (H˚f): the amount of heat required to form 1 mol of a substance in its standard state (T=25oC, p=1atm) from its elements in their reference forms.

Reference forms of elements:The most stable form of the element under standardconditions (T=25oC, p=1atm).

Element Reference formhydrogen H2(g)carbon C(s, graphite)oxygen O2(g)nitrogen N2(g)

Element Reference formsulfur S8(s, rhombic)bromine Br2(l)electron e-(g)proton H+(aq)

H of chemical processes

Example standard enthalpies of formation:

Substance H˚f Reaction of formation (kJ/mol) .water -286 H2(g)+1/2 O2(g)H2O(l)

steam -242 H2(g)+1/2 O2(g)H2O(g)

sulfuric a. -808 H2(g)+1/8 S8(s)+2 O2(g)H2SO4(l)

methane -74 C(s)+2 H2(g)CH4(g)

glucose -1275 6 C(s)+6 H2(g)+3 O2(g)C6H12O6(s)

elements involved

reactants products

H˚f(reactants) H˚f(products)

H˚reaction=H˚f(prod)-H˚f(react)

H2(g)+1/2 O2(g)

H2O(l)

-286 kJ -242 kJ

+44 kJH2O(g)

H of chemical processes

5. Heat of combustion (H˚c): the enthalpy change for the complete combustion of 1 mol of compound with oxygen under standard conditions.

E.g.: CH4(g)+2O2(g)CO2(g)+2H2O(l) H˚c=-890 kJ/mol

H of chemical processes Combustion heat data can be used to calculate

standard enthalpies of formation

+ 2 O2(g)

+ 2 O2(g)

CO2(g) + 2 H2O(l)

H˚c(CH4)=-890 kJ/mol

H˚c(H2)=-284 kJ/mol

H˚c(C)=-396 kJ/mol

H˚c(C+2H2)=-964 kJ/mol

These can bedetermined

experimentally

H˚f for methane:

H˚f(CH4)=-74 kJ/mol

C(s) + 2 H2(g)

CH4(g)

H of chemical processes Combustion heat data can be used to calculate

standard reaction heat values

+ 5 O2(g)

+ 5 O2(g)

3 CO2(g) + 4 H2O(l)

H˚c(C3H8)=-2220 kJ/mol

H˚c(H2)=-284 kJ/mol

H˚c(C3H6)=-2060 kJ/mol

H˚c(C3H6+H2)=-2344 kJ/mol

H˚for propene hydrogenation: C3H6(g)+H2(g)C3H8(g)

H˚=-124 kJ/mol

C3H6(g) + H2(g)

C3H8(g)

These can bedetermined

experimentally

H of chemical processes

Because by definition reaction heat is the heatabsorbed during the reaction, H˚ appears on the left-hand side (as a "reactant"): reactants + H˚ products

Thermochemical equation: a chemical equation inwhich the reaction enthalpy is explicitly included.

Thermochemical equations can be added up to obtain the equation for a multistep reaction.

CH4(g)+2O2(g) - 890 kJ CO2(g)+2H2O(l) (exothermic)C3H8(g) + 124 kJ C3H6(g)+H2(g) (endothermic)

Alternatively: reactants products - H˚CH4(g)+2O2(g) CO2(g)+2H2O(l) + 890 kJ (exothermic)C3H8(g) C3H6(g)+H2(g) - 124 kJ (endothermic)

H of chemical processes Calculation of standard enthalpies of formation from

combustion heat data using the thermochemicalequation formalism

(i) C(s)+2H2(g)+2O2(g) CO2(g)+2H2O(l)+964 kJ

(ii) CH4(g)+2O2(g) CO2(g)+2H2O(l)+890 kJ

H˚f for methane:

C(s)+2H2(g) CH4(g)+74 kJ

C(s)+2H2(g) – CH4(g) (964 – 890) kJ (i) – (ii):

H of chemical processes Calculation of standard reaction heat values from combustion heat data using the thermochemical

equation formalism

(i) C3H6(g)+H2(g)+5O2(g) 3CO2(g)+4H2O(l)+2344 kJ

(ii) C3H8(g)+5O2(g) 3CO2(g) + 4H2O(l) + 2220 kJ

H˚ for propene hydrogenation:

C3H6(g)+H2(g) C3H8(g)+124 kJ/mol

C3H6(g)+H2(g) – C3H8(g) (2344 – 2220) kJ(i) – (ii):

H of chemical processes

6. Average bond enthalpy (H˚A-B): the average enthalpy change for breaking 1 mole of A-B bonds in a molecule in the gas phase under standard conditions.E.g.: CH4(g) C(g)+4H (g) H=+1648 kJ/mol=4·H˚C-H

A-B H˚A-B(kJ/mol)

C-H 412C-C 348O-H 463

A-B H˚A-B(kJ/mol)

C=C 611CC 833H-H 436

H of chemical processes Estimation of standard reaction heat values

from average bond enthalpies

H˚ 1047 – 1172 = - 125 kJ/mol

H˚ H˚A-B(bonds broken) - H˚A-B(bonds formed)

H˚ for propene hydrogenation:

HH

C CH

CH

H

H

HH

+ C CH

CH

H

H

HH

H HBonds broken: H˚A-B

1x(C=C) 6111x(H-H) 436H˚A-B(broken)=1047

Bonds formed: H˚A-B

1x(C-C) 3482x(C-H) 2·412H˚A-B(formed)=1172