The Basic Concepts: the system

Thermodynamics The First Law Work, Heat, Energy

System

Matter Energy

System Matter Energy

Surroundings

Thermodynamics is the study of the transformations of energy.

Surroundings

(b) closed

(a) open System Matter Energy

Oxtoby, Chapter 10 (10.1-10.4)

(c) isolated

Surroundings

The Basic Concepts: state and path fns A state function, X, is a property that depends only on the current state of the system, and not on how it was prepared. Changes in a state function depend only on the start and end points of an experiment

The Conservation of Energy: Energy can neither be created not destroyed (experimental observation)

DX = Xfinal – Xinitial e.g. the duration of this lecture depends only when I start and when I finish A path function, Y, is a property that depends on the history of the system. e.g. the boredom/interest factor for this lecture depends on a lot more than just my first and last sentence

fl Energy is a state function

The principle of conservation of energy can be used to assess the energy changes that accompany physical and chemical processes.

Heat, q ICE +

heat

Liquid water Melting

SOLID

+

heat

When the energy of a system changes as a result of a temperature difference between it and its surroundings, it is said that energy has been transferred as Heat, q

Liquid

Processes that release energy as heat are exothermic; A C

+

O2

CO2 +

B + heat Combustion reactions

heat Processes that absorb energy as heat are endothermic; A + heat

B Melting, Vaporization of Water

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Work, Heat and Energy

Work, w

Work, w, is done when an object is moved against an opposing force

w=F. d

In general:

work

distance

Force along path

More specifically, for thermodynamics:

w=- F. d We focus on the force the system has to push against Work is a path function (how strong is gravity?)

Expanding gas pushes out piston against (e.g, atmospheric) pressure

Work and pressure Pressure Volume Work:

Work is done on system by the surroundings

The First Law In thermodynamics, the “total” energy of a system is called the internal energy, E.

External pressure, p

Experiments measure the change in energy between start and finish: ∆E = Ef - Ei

Area A

∆h

w = - Fext . d

The change in internal energy ∆E is the sum of work done on a system and the energy transferred as heat to a system according to;

w = - Fext ∆ h

∆E = w + q

w = - pext A ∆ h

Heat must be a path function: the system can gain/lose energy either as heat or as work.

w = - pext ∆ V

∆E = w + q &

w = - pext ∆V

If the system is kept at constant volume:

∆E = qv We measure ∆E usually using Calorimetry (the measurement of amounts of heat flowing into or out of a system and the accompanying temperature changes)

Calorimetry Adiabatic Bomb Calorimeter

Adiabatic means no heat is transferred from calorimeter to surroundings The change in temperature, ∆T, of the calorimeter is proportional to the heat that the reaction releases or absorbs.

q = Ccal ∆T Calorimeter Constant Calibrated using a process of known energy output (eg, burning of a substance of known mass) or from an electrical current, I, of known potential, V

q=VIt

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Heat Capacity

Heat Capacity Generally: C =

q ∆T

Units: J K-1, cal K-1 1 cal = 4.184 J

Molar Heat Capacity (J K-1 mol-1 or cal K-1 mol-1) q C Heat capacity of a sample divided by the c= = n chemical amount of substance, n ∆T n

The heat capacity C of a substance is the heat required to change its temperature by one Kelvin, and has units of energy per Kelvin. The heat capacity is an extensive variable: the quantity is proportional to the amount of matter present.

Specific Heat Capacity (in J K-1 kg-1 or cal K-1 kg-1) q C Heat capacity of a sample divided by the cs = ∆T m = m mass of substance, m c = M cs

Spontaneous Changes: Why do some processes happen spontaneously? •Why does a hot body get cooler (rather than hotter) when surrounded by a cooler medium? •Why does a gas expand into all available volume of a container rather than contract?

Entropy

The driving force for spontaneous change (change that happens without intervention — doing work or heating) is described in the second law of Thermodynamics

Chapter 11

No process is possible in which the sole result is the absorption of heat from a reservoir and its complete conversion into work. Kinetic energy converted into thermal motion

Energy is not accumulated in ball and thermal motion is not directional

Entropy, S, and the second law These spontaneous changes happen because they increase the randomness with which energy is spread through an isolated system The Entropy, S, a thermodynamic state function, is a measure of “molecular disorder”, or “freedom of movement” molecules have, and helps us to define the direction of spontaneous change The Entropy of an isolated system increases in the course of a spontaneous change ∆Ssystem + ∆Ssurroundings =

∆Stotal > 0

Hence, in a spontaneous process: ∆Suniverse > 0

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Entropy and Equilibrium

Entropy and Heat

Nothing changes when a system is at equilibrium, including the entropy of the system So, for any process ∆Ssystem + ∆Ssurroundings = ∆Suniverse r 0

Entropy measures dispersal of energy in a system Heat changes kinetic energy of molecules, i.e. disperses energy by increasing the velocities of all the molecules fl heat and entropy are related?

But, equilibrium is dynamic at a microscopic level For a reversible process

reactants Ý products This introduces the idea that changes can be reversible, i.e. a change can be made, and then exactly undone (“reversed”), so ∆Suniverse = 0

DS = qrev / T

= DU / T (at constant volume)

For an irreversible process DS > qrev / T

for a reversible process

In practice, reversible changes are an idealised limit in which changes happen infinitely slowly via a series of imperceptible shifts in the equilibrium

Entropy and Disorder

Reversible (infinitesimal) Changes qrev = TdS

The Entropy of the System

• First law becomes dU = TdS – PdV

Solid

Gas

Liquid Entropy of system increases

Other Energies • Legendre transformations enable us to define other energies which have exact differentials in terms of other state variables

Enthalpy H = U + PV

dH = TdS + VdP

Gibbs Free Energy G = U + PV − TS

Enthalpy

dG = −SdT + VdP

Helmholtz Free Energy A = U − TS

dA = −SdT − PdV

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Enthalpy of Reaction - ∆Hr

The Enthalpy, H

Example 1

For a system kept at constant pressure:

∆H = qp

where ∆H = Hf - Hi

A

B

HA

HB

Enthalpy of Reaction: ∆Hr = HB - HA

The Enthalpy, like the internal Energy, is a state function Example 2

2C + D 2 HC HD

E +3F HE 3 HF

Enthalpy of Reaction: ∆Hr = HE + 3 HF - HD - 2 HC

The Reaction Enthalpy, ∆Hr

Standard Enthalpies Enthalpy normally tabulated for substances in their standard state; Denotes standard condition these are called the standard enthalpy, Ho.

∆Hr = Hproducts - Hreactants

In General:

∆Hr = Σ ν Hproducts - Σ ν Hreactants Sum over all standard molar enthalpies taking into account their stochiometric factors, ν

The standard state of a substance at a specified temperature is its pure form at 1 atm (should now be 1 bar). For dissolved species, the standard state is the concentration of 1M under a pressure of 1 atm at a specified temperature.

Example: Standard enthalpies at T = 298 K are often denoted Hʅ

2 C2H6 + 7 O2 ν= 2 ν= 7

4 CO2 ν= 4

+

6 H2O ν= 6

Hence, the standard enthalpy of reaction is

∆Hr = 6H(H2O) + 4H(CO2) - 7H(O2) - 2H(C2H6)

Enthalpies of phase change

Being a state function: path doesn’t matter

Enthalpy changes also occur when a substance melts/freezes or condenses/evaporates

H2O(s)

kJ H2O(l) ∆Hofus(273)=+6.0 mol

Vaporisation (boiling): H O 2 (l)

kJ H2O(g) ∆Hovap(373)=+40.7 mol

Fusion (melting):

endothermic! Sublimation

H2O(s)

(direct conversion from solid to gas)

∆Hro = Σ ν Hoproducts - Σ ν Horeactants

kJ H2O(g) ∆Hosub(298.15)=+46.7 mol

H2O(s)

H2O(l)

∆Hofus = +6.0 kJ mol–1

H2O(l)

H2O(g)

∆Hovap = +40.7 kJ mol–1

Overall: H2O(s)

H2O(g)

∆Hosub = +6.0 + 40.7 kJ mol–1 = + 46.7 kJ mol–1

Because enthalpy is a state function, these rules apply to every type of reaction or change

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Standard Molar Enthalpies of Formation, ∆Hof

Hess’s Law The enthalpy of an overall reaction is the sum of the enthalpies of the individual reactions into which the reaction can be divided.

The enthalpy of formation is the enthalpy change when a compound is formed from its elements, and those elements are in their most stable form under the prevailing conditions. When the prevailing conditions are the standard state, this is called the standard enthalpy of formation, ∆Hof

Example: Calculate the enthalpy of combustion of benzene (C6H6) from its enthalpy of hydrogenation (-205 kJ/mol) to cyclohexane, and the enthalpy of combustion of cyclohexane (∆Ho (C6H12) = –3920 kJ/mol)). The enthalpy of the combustion for H2 is -286 kJ/mol.

H2(g) + 0.5 O2(g) 6 C(s, graphite) + 3 H2(g)

H2O(l)

∆Hof = - 286 kJ/mol

C6 H6(l) ∆Hof = + 49 kJ/mol

The standard enthalpies of elements in their reference states are zero at all temperatures (graphite is the reference state of carbon!).

Bond enthalpies A–B(g)

A(g) + B(g)

∆Hrxn = energy of the A–B bond

But bond enthalpies are affected by the neighbouring bonds CH4(g)

CH3(g)

+ H(g)

∆H = 439 kJ mol–1

C2H6(g)

C2H5(g) + H(g)

∆H = 410 kJ mol–1

CHCl3 (g)

CCl3(g

∆H = 380 kJ mol–1

)

+ H(g)

Gibbs Free Energy, G

fl usually tabulate average bond enthalpies (determined from A–B bond enthalpies in many different A–B containing molecules) Average bond enthalpies can be used to estimate the enthalpy of a compound: just count the number and type of bonds involved.

The Gibbs Free Energy, G

The Gibbs Free Energy: criterion for spontaneity

∆Suni = ∆Ssystem + ∆Ssurroundings Requires knowledge of both system and surroundings

At constant T: ∆Gsys = ∆ (Hsys - Tsys Ssys) = ∆Hsys - T ∆Ssys

∆G = ∆H - T ∆S

At constant pressure and temperature, and for reversible changes: T∆Ssurroundings = qp,rev = –∆Hsystem

But also: Define a new form of the energy function G = H – TS Called the Gibbs free energy. G is a state function

∆Hsys = - ∆Ssurr T

∆Gsys = - T ∆Ssurr - T ∆Ssys = - T (∆Ssurr + ∆Ssys) = - T (∆Suni) < 0 for spontaneous pr. and as ∆Suni > 0 Resulting in:

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Driving forces in chemistry

Criterion for Spontaneity

Two driving forces underpin Chemistry:

∆Suni > 0

Spontaneous

∆Gsys < 0

¾ Systems tend to a state of minimum enthalpy

∆Suni = 0

Equilibrium

∆Gsys = 0

¾ Systems tend to a state of maximum entropy

∆Suni < 0

Not spontaneous (reverse reaction is spontaneous)

∆Gsys > 0

The Gibbs free energy expresses the balance between these two driving forces DG = DH – T DS

(b 0 ?)

N.B. left hand describes the whole universe, but right hand is just the system. We can drive the system in the wrong direction (hence can have reactions where DG is positive, but cannot force the universe to show negative entropy

Gibbs Energy for Chemical Reaction As the Gibbs energy is a state function, the (standard) Gibbs energy of reaction is defined (in analogy to Hess’ law for the enthalpy) as: ∆Gro = Σ ν Goproducts - Σ ν Goreactants

Standard Molar Gibbs Energy of Formation By analogy with the definition of the standard molar Enthalpy of formation we define ∆Gfo = ∆ Hfo - T ∆ Sfo

o

Where as before indicates that all substances are in their standard states at the specified temperature. ∆Gro = ∆ Hro - T ∆ Sro

as the standard molar Gibbs energy of formation when 1 mole of a substance forms in a standard state at a specified temperature from the most stable forms of its constituent elements in standard states at the same temperature.

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