Chemistry 231

Thermodynamics in Reacting Systems

Enthalpy Changes for Reactions

The shorthand form for a chemical reaction

J

JJ0

J = chemical formula for substance JJ = stoichiometric coefficient for J

Reaction Enthalpy Changes

The enthalpy change for a chemical reaction

JHnHJ

mJr

Hm [J] = molar enthalpies of substance J

nJ = number of moles of J in the reaction

The Enthalpy Change Reaction beginning and ending with

equilibrium or metastable states

JHn

HHH

JmJ

initialfinalr

Note – Initial and final states have the same temperature and pressure!

Reaction Enthalpies (cont’d)

We note that 1 mole of a reaction occurs if

JJn

JHHJ

mJr

A Standard State Reaction

A reaction that begins and ends with all substances in their standard states

The degree sign, either or P = 1.00 bar [aqueous species] = 1.00 mol/ kg T = temperature of interest (in data

tables - 25C or 298 K).

Standard Reaction Enthalpies

We note that for 1 mole of a reaction under standard conditions

JHHJ

mJr

The Formation Reaction

A "chemical thermodynamic reference point."

For CO and CO2

C (s) + O2 (g) CO2 (g)

C (s) + ½ O2 (g) CO (g)

The Formation Reaction The formation reaction

1 mole of a compound constituent elements stable state of aggregation at that

temperature. Formation of 1.00 mole of Na2SO3(s)

2 Na(s) + S(s) + 3/2 O2 (g) Na2SO3 (s) ‘Formation enthalpy of Na2SO3(s)’,

fH°[Na2SO3 (s)]

The Significance of the Formation Enthalpy

fH° is a measurable quantity! Compare CO (g) with CO2 (g)

C (s) + 1/2 O2 (g) CO (g)

fH° [CO(g)] = -110.5 kJ/mole

C (s) + O2 (g) CO2 (g)

fH° [CO2(g)] = - 393.5 kJ/mole

Formation Enthalpies

Formation enthalpies - thermodynamic reference point! Ho

m [J] = fH [J] Hm [elements] = 0 kJ / mole.

Use the tabulated values of the formation enthalpies

The General Equation

The enthalpy change for a given reaction is calculated from the formation enthalpies as

Notes Reverse a reaction Multiply a reaction by an integer

JHHJ

fJr

The Calorimeter

A calorimeter - device containing water and/or another substance with a known heat capacity

Calorimeters – either truly or approximately adiabatic systems

Two major types of calorimeters.

The constant volume (bomb) calorimeter. U = qv.

The constant pressure calorimeter. H = qp.

The Constant Volume (Bomb) Calorimeter

The Constant Pressure Calorimeter

Relating H and U

The enthalpy and the internal energy both represent quantities of heat.

U = qv.

H = qp.

Relate the two state functions using the following relationship

U = H - PV

Other Important Enthalpy Changes

Enthalpy of solution Enthalpy of dilution Enthalpy of fusion Enthalpy of vapourisation

The Solution Enthalpy solH - heat absorbed or released

when a quantity of solute is dissolved in fixed amount of solvent

solH = Hm(sol’n) – Hm(component) H(component) = Hm(solid) +

Hm(solvent) Two definitions

Standard Limiting

The Dilution Enthalpy

For the process,HCl (aq, 6 M) HCl (aq, 1 M).

The Enthalpy of dilution of the acid. dilH = Hm(sol’n 2) – Hm(sol’n ,1)

Reaction Enthalpy Changes With Temperature

Differentiate the reaction enthalpy with temperature

JHHJ

mJr

JHdTd

dTHd

JmJ

r

The Result

rCp

- the heat capacity change for the reaction

TCKHTH prrr 298

J

pJpr JCC

Internal Energy Changes in Chemical Reactions Examine a chemical reaction.

C (s) + O2 (g) CO2 (g)

U = U[CO2 (g)] – U[C(s)] – U[O2(g)] Note - rH = -393.5 kJ/mole

RTnUH

JUU

grr

JfJr

Enthalpies and Hess’s Law

Use tabulated values of formation enthalpies to obtain rH°.

May also estimate reaction enthalpies using an indirect method.

Hess’s Law

Hess’s Law – the enthalpy change for a given

reaction is the same whether the reaction occurs in a single step or in many steps.

The Entropy Change in a Chemical Reaction

Burning ethane! C2H6 (g) + 7/2 O2 (g) 2 CO2 (g) + 3 H2O (l)

The entropy change is calculated in a similar fashion to that of the enthalpies

JS SJ

mJr

Some Generalizations For any gaseous reaction (or a

reaction involving gases).ng > 0, rS > 0 J/(K mole).

ng < 0, rS < 0 J/(K mole).

ng = 0, rS 0 J/(K mole). For reactions involving only solids

and liquids – depends on the entropy values of the substances.

The Gibbs Energy Change for a Chemical Reaction

The standard Gibbs energy change for a chemical reaction is obtained as follows

JGGJ

fJr

The Gibbs Energy Change

For the methane combustion reaction1 CH4(g) + 2 O2(g) 1 CO2(g) + 2

H2O(l)

rG = np fG (products) - nr fG (reactants)

= 2 fG [H2O(l)] + 1 fG [CO2(g)] - (7/2 fG [O2(g)] + 1 fG [CH4(g)] )

The Formation Gibbs Energies

fG (elements) = 0 kJ / mole. Tabulated values at SATP used to

obtain the Gibbs energy changes for chemical reactions.

A Caveat!!!

rG° refers to standard conditions only! For non-standard conditions - rG

rG < 0 - reaction moves in the forward direction

rG > 0 - reaction moves in the reverse direction

rG = 0 - reaction is at equilibrium

Bond Energies

Examine the following reactions H2 (g) H (g) + H (g) U° = 433.9

kJCl2 (g) Cl (g) + Cl (g) U° = 239.5

kJ Bond dissociation energies. Enthalpy changes are designated

D (H-H) and D (Cl-Cl).

For Polyatomic Molecules

CO2 (g) C (g) + 2 O (g) U = 740 kJ H of this reaction D(C=O) What about dissociating methane

into C + 4 H’s?CH4(g) C(g) + 4 H(g) U° = 1640 kJ

4 C-H bonds in CH4 D (C-H) 410 kJ/mol

Make or Break!! Note: all chemical reactions involve the

breaking and reforming of chemical bonds Bonds break - we add energy. Bonds form - energy is released.

rU° D(bonds broken) - D(bonds formed)

A Word of Caution These are close but not quite exact.

Why? The bond energies we use are averaged

bond energies ! This is a good approximation for

reactions involving diatomic species.Can only use the above procedure for GAS PHASE REACTIONS ONLY!!!