Chemistry 231Work, Heat and Internal

Energy: The First Law

System – the specific part of the universe of interest to us

Surroundings – the part of the universe not contained in the system

Systems and Surroundings

3 types of Systems• open system – exchanges mass and energy• closed system – exchanges energy but no

mass• isolated system – no exchange of either

mass or energy

State of a System (Continued)

Types of Systems (Continued)

Open system Closed System

corkinsulation

Isolated System

State of a system• the system is in a definite state when each of its

properties has a definite value. Change in state

• initial state• final state

Path• initial and final states• intermediate states

Some Definitions

Process• reversible or irreversible transformation

Cyclic transformation• begins and ends at the same state variables.

Some Definitions (Continued)

Isothermal• dT = 0

Isochoric• dV = 0

Isobaric• dP = 0

Some Definitions (Continued)

Work (w)• any quantity that flows across the system’s

boundary and is completely convertible into the lifting of a mass in the surroundings.

How much work was done?

Work

Unit of work = J = 1 kg m/s2

dzFdw z

0

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120

0 10 20 30 40 50 60

Distance / m

Fo

rce

/ N

A Force Vs. Displacement Curve

A single-stage expansion process

Work Done in a Closed, Fluid System

State 1 State 2

Piston(T, P1, V1)

mass (m)

Piston(T, P2, V2)

mass (m)

Dir

ecti

on

of p

isto

n

h2

h1

The work done in the surroundings• wsurr= Pext DV

The work done by the system• wsys = - wsurr = - Pext DV

For an infinitesimal volume change• dwsys = - Pext dV

System and Surroundings

If the system is in equilibrium• Fsys = -Fext

• P = Pext

For a simple system• d wrev = - P dV

Reversible (Multistage) Expansion

Ideal gas as the working fluid.

Reversible Transformation in an Ideal Gaseous System

cc revrev PdVdww

VnRT

P

For an isothermal process (ideal gas as working fluid)

Reversible Transformation (Continued)

1

2lnVV

nRTdwwc revrev

dwirr = -Pext dV for a constant external pressure

Irreversible Transformations

12

2

1

VVP

dVPdww

ext

extc irrirr

Heat - the quantity that flows across the boundary of the system during a change in state• due to temperature difference between

system and surroundings• HOT to COLD (never the other way

around)!!!

Heat

Measured by determining the temperature change of some known object

'Amount of Heat'

C - the heat capacity of the system.

CdTdq

Integrate the infinitesimal heat flow

Macroscopic Heat Flows

2

1

T

Tc c

CdTCdTdqq

TCq

Exothermic - system to surroundings Endothermic – surroundings to system

Heat Flows

surroundingssystem

heat

Heat flows during phase changes - latent heats• Latent heat of vapourisation• Latent heat of fusion

Latent Heats

Subject our system to a cyclic transformation

The Internal Energy

CdTCdTqcycle

cycle

dwdwwcycle

cycle

The following would be true for an exact differential

Cyclic Integrals of Exact Differentials

exact is df if 0df

The infinitesimal change in the internal energy

The Internal Energy

dwdqdU

wqdwdqUc

For a general process

In general, we write U as a function of T and V

The Properties of U

dVVU

dTTU

dUTV

Examine the first partial derivative

Isochoric Changes in U

0

dTTU

dUV

Define the constant volume heat capacity, CV

The Constant Volume Heat Capacity

VVV T

UdTdq

C

For a system undergoing an isochoric temperature change

Heat Flows Under Constant Volume Conditions

For a macroscopic system

dTCdU V

2

1

T

TVV dTCqU

Examine the second partial derivative

Isothermal Changes in U

dVVU

dUT

The Joule Experiment

AT1, Vm,1, P1

B

Stirrer

Valve

Thermal insulationFFOO

CO

CO

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The partial derivative

The Joule Coefficient

is known as the Joule coefficient, J. UV

T

The change in the internal energy under isothermal conditions is related to the Joule Coefficient

Internal Energy and the Joule Coefficient

VUT TU

VT

VU

JVT

CVU

For an adiabatic process, q = 0!! The first law becomes

Adiabatic Processes

wU

dTCdwdU V

Adiabatic Processes for an Ideal Gas

For an ideal gas undergoing a reversible, adiabatic process

1

2

/

2

1,

TT

VV

mvCR

,2 2

1 1

v m

RC RP T

P T

Defining the enthalpy of the system Re-examine the piston with the weight

on top

State Changes Under Constant Pressure Conditions

Piston(T, P, V)

mass (m)

The first law

A Constant Pressure Process

Integrating

PdVdqdU P

2

1

2

1

V

VcP dVPdqdU

Define the enthalpy of the system, H

Enthalpy

PVUH

In general, we write H as a function of T and P

The Properties of H

dPPH

dTTH

dHTP

Examine the first partial derivative

Isobaric Changes in H

0

dTTH

dHP

Define the constant pressure heat capacity, CP

The Constant Pressure Heat Capacity

PPP T

HdTdq

C

For a system undergoing an isobaric temperature change

Heat Flows Under Constant Pressure Conditions

For a macroscopic system

dTCdH P

2

1

T

TPP dTCqH

For an ideal gas

Relating CP and CV

nRCC VP

In general

TVP

TVCC

2

Examine the second partial derivative

Isothermal Changes in H

dPPH

dHT

0

The Joule-Thomson Experiment

Porous Plug

Thermal insulation

T1, P1, Vm,1T2, P2, Vm,2

FFOO

CO

CO

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0

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FFOO

CO

CO

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The partial derivative

The Joule-Thomson Coefficient

is known as the Joule-Thomson coefficient, JT.

HPT

The change in the enthalpy under constant pressure conditions is related to the Joule-Thomson Coefficient

Relating H to the Joule-Thompson Coefficient

PHT TH

PT

PH

JTPT

CPH

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

The Constant Volume (Bomb) Calorimeter

U = qv.

The Constant Pressure Calorimeter

H = qp

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.

Bond Energies

Examine the following reactions H2 (g) ® H (g) + H (g) DU° = 433.9 kJ

Cl2 (g) ® Cl (g) + Cl (g)DU° = 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)DU = 740 kJ DH of this reaction D(C=O) What about dissociating methane into C

+ 4 H’s?CH4(g) ® C(g) + 4 H(g) DU° = 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° S D(bonds broken) - S 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!!!