Chemistry 17 Reviewer

U P K E M

M E M B E R S ’ A C A D E M I C D E V E L O P M E N T

Chem 171st Long Exam Reviewer

R. DangananT. Delos Santos

J. Quintos

1 Thermochemistry

Thermochemistry is concerned with the heat pro-duced in a chemical reaction. It is a field underthe discipline thermodynamics.

1.1 Thermodynamic Systems

A thermodynamic system is the content of amacroscopic volume in space, along with its wallsand surroundings that undergoes thermodynamicprocesses and can be adequately described by ther-modynamic variables such as temperature, entropy,internal energy and pressure [1].

There are the common types of thermodynamicsystems in thermochemistry. Table 1.1.1 summar-ises the properties of each.

Table 1.1.1: Summary of different thermodynamic sys-tems

System Energy exchange Material exchange

Open Yes YesClosed Yes NoIsolated No No

1.2 Heat

Heat is the transfer of energy due to temperaturedifference between a system and its surroundings.Energy transfers in the form of heat can causetemperature change, phase change, or both.

The following diagram shows a solid substance(A) heated until it becomes vapour (F).

Time, minutes

A

BC

DE

F

Tem

pera

ture

, °C

Figure 1.2.1: Phase transformations. The line BC showsa phase change from solid to liquid (melt-ing/fusion). While line DE shows a liquidto vapour phase change (vaporization)

1.2.1 Latent heat

Latent heat is the amount of energy released orabsorbed during a phase change.

The amount of latent heat q for transformationsBC and DE can be expressed as.

qBC = ∆Hfusion · n (1.2.1a)

qDE = ∆Hvap · n (1.2.1b)

where ∆Hfus/vap is the specific latent heat of thesubstance in Jmol−1 and n is the amount of thatsubstance in moles.

1

University of the Philippines Chemical Engineering Society, Inc. (UP KEM)Chem 17 - 1st Long Exam Reviewer

Notes:

(1) There is no temperature change when a sub-stance undergoes a change in phase.

(2) ∆Hvap is not necessarily equal to ∆Hfustion

for the same substance.

(3) A change from C to B (freezing) or from E toD (condensation) require the same amount ofheat but of opposite sign, i.e. freezing releasesheat (q is negative) while melting absorbs heat(q is positive).

1.2.2 Sensible heat

In contrast with latent heat, sensible heat is theheat absorbed or released by the substance due totemperature change.

In the diagram, line AB, CD, and EF involvesensible heat. This amount of heat, q, can be ex-pressed as:

q = mc∆T = C∆T (1.2.2)

where

m : mass of substance (g)

c : specific heat capacity (J g−1 K−1)

C : heat capacity (JK−1)

∆T : Temperature change (K)

1.2.3 Heat capacities

Heat capacity is the amount of heat required tochange the temperature of a system by 1K.

Specific Heat capacity is the amount of heatrequired to change the temperature of one gramof a substance by 1K.

Molar Heat capacityis the amount of heat re-quired to change the temperature of one mole ofa substance by 1K.

1.2.4 Heat of reaction, ∆Hrxn

It is the amount of heat transferred between asystem and its surroundings when a chemical re-action occurs at constant temperature, i.e. at dif-ferent temperatures, the same chemical reactionwill have different heats of reaction

Exothermic reactions. Heat is released to thesurroundings, ∆Hrxn < 0.

Endothermic reactions. Heat is gained fromthe surroundings, ∆Hrxn > 0.

1.3 Law of Conservation of Energy,Calorimetry

This law states that

qsystem + qsurroundings = 0 (1.3.1)

For an isolated system such as the coffee-cup calor-imeter, the system is the reaction while thesurroundings consist of the test-tube, the liquidsolution and any of its solid contents, and the ther-mometer.

The coffee-cup calorimeter is a useful tool to meas-ure heats of reaction indirectly by measuring theheat evolved to the surroundings instead. Notice:

qsurr = qcal (1.3.2a)

qsurr = −qsys (by 1.3.1)

qsys = −qcal (1.3.2b)

By definition,

qcal = Ccal∆T (1.3.3)

Where the coffe-cup calorimeter heat capacity, Ccal,can be obtained by performing standardisation us-ing a chemical reaction with known heat of reac-tion.

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1.4 Work

Work is the energy transferred by a force actingon a distance. Thermodynamically, it is any formof energy transfer that is not heat.

A particular type of work often present in thermo-chemistry is the Pressure-volume work definedbelow.

W = −P∆V (1.4.1)

Where

W : PV work on the system

P : External pressure

V : Volume of the system

1.5 First Law of Thermodynamics

1.5.1 State and Process Functions

State functions or state variables are propertiesthat only depend on the final and initial state of aparticular system, e.g. Internal Energy (U), En-thalpy (H), Entropy (S), Gibbs Free Energy (G).

Process functions or path-dependent functionsare quantities dependendent on the path from ini-tial state to final state, e.g. heat (Q) and work(W ).

1.5.2 Internal energy

The internal energy, U or sometimes E, is the statefunction of the total energy of a system. A systemonly contains internal energy.

1.5.3 First Law formulation

The first law of thermodynamics states that, fora closed system:

∆U = Q+W (1.5.1)

Where

∆U = Change in internal energy

Q = Heat supplied to the system

W = Work done on the sytem

Q :

(+) if heat is gained by the system

(−) if heat is lost by the system

W :

(+) if work is done on the system

(−) if work is done by the system

Often we deal with PV-work so that

∆U = Q− P∆V (1.5.2)

For isolated systems, note that ∆U = 0.

Remark. This follows the IUPAC sign conven-tion.

1.5.4 Enthalpy

A useful quantity for open systems defined as

H = U + PV (1.5.3)

In terms of state changes,

∆H = ∆U + ∆(PV )

= ∆U + P∆V + V∆P (product rule)

= (Q− P∆V ) + P∆V + V∆P (by 1.5.2)

= Q+ V∆P (1.5.4)

Since U , P , and V are state functions, enthalpy isalso a state function.

1.5.5 Heats of reaction

At constant volume (∆V = 0), by equation 1.5.2,

QV = ∆U

At constant volume (∆P = 0), by equation 1.5.4,

QP = ∆H

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Standard Enthalpy of Formation, ∆H◦f . The

change in enthalpy that occurs when one mole ofa substance is produced from the reference formsof its elements in their standard states (1 bar anda specific temperature of interest). These valuesare tabulated for each compound, and are zero forelemental substances like O2.

Standard Enthalpies of Reaction, ∆rHΘ. The

enthalpy change in a reaction, the reactants andproducts are in their standard states (1 bar and aspecific temperature of interest). Mathematically,

∆rHΘ =

∑νp∆H◦

f

products−∑

νr∆H◦f

reactants(1.5.5)

Where ν is the appropriate stoichiometric coeffi-cient

1.5.6 Hess’s Law

Considering a process with many steps, the en-thalpy change of the entire process is equal tothe summation of the enthalpy change of the in-dividual steps.

∆Htot =∑

∆Hi (1.5.6)

Notes:

(1) Change in specific enthalpy (enthalpy per moleor enthalpy per mass) is an intensive prop-erty of a reaction as written, and is multipliedalong with stoichiometric coefficients

(2) If a step is reversed, ∆H reverses sign

1.6 Spontaneity

Spontaneous Process. A process which canproceed by itself, no external force is needed inorder for the process to be sustained.

Nonspontaneous Process. A process whichwill not occur without the presence of an externaldrive

1.6.1 Entropy

Entropy is quantitative measure of disorder, mean-ing the higher number of arrangements (micro-states), the greater the entropy of the system. TheBoltzmann formulation of entropy is:

S = k ln (W ) (1.6.1)

Where k = 1.381× 10−23 JK−1 (Boltzmann con-stant) andW is number of ways that the atoms ormolecule can be arranged in the available statesresulting to the same total energy.

1.6.2 Second and Third Law of Thermo-dynamics

The second law generally states that there is anincrease in the sum of the entropies of the parti-cipating systems or that all spontaneous changeincreases the entropy of the universe. That is,

∆Suniv = ∆Ssys + ∆Ssurr ≥ 0 (1.6.2)

The third law states that the entropy of a pureperfect crystal at 0K is zero.

1.6.3 Entropy change

Entropy change depends on heat and temperat-ure.

∆S :

(+)if the products have higher degreeof disorder than that of the react-ants.

(−)if the reactants have higher de-gree of disorder than that of theproducts.

For a reversible process

∆S = dQrev

T(1.6.3)

For a phase change

∆S =∫ ∆Htrans

T(1.6.4)

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Standard Molar Entropy, S◦. The absoluteentropy of a substance at its standard state (1bar and a specific temperature of interest). For areaction,

∆S◦rxn =

∑νpS

◦p

products−∑

νrS◦r

preactants(1.6.5)

1.6.4 Gibbs Free Energy, G

It is thermodynamic function that (for Chem 17purposes!) determines the spontaneity of a pro-cess. Defined as

G = H − TS (1.6.6)

The Gibbs free energy change is then

∆G = ∆H − T∆S (1.6.7)

Process :

spontaneous : ∆G < 0

in equilibrium : ∆G = 0

non-spontaneous : ∆G > 0

The Standard Gibbs Energy Change (∆G◦)for a reaction is expressed as:

∆G◦ =∑

νp∆G◦p

products−∑

νr∆G◦r

preactants(1.6.8)

For a reaction

aA + bB cC + dD

The Gibbs free energy change for an arbitrarynon-equilibirium state is

∆G = ∆G◦ +RT lnQ (1.6.9)

Where

R : Universal gas constant

Q : Reaction quotient

= [C]c[D]d

[A]a[B]b

1.6.5 Coupled Reactions

A combination of spontaneous and non-spontaneousreactions such that ∆Gnet < 0. Informally we canthink of this like: the Gibbs free energy releasedby the spontaneous process is utilised by the non-spontaneous process thereby forcing it to proceed.

2 Chemical Kinetics

2.0.1 Rates of Chemical Reaction

A measure of how fast a reaction occurs. It canbe either based on the formation of a product ordisappearance of a reactant. For a particular re-action

aA + bB cC + dD

rate = −1a

(∆A∆t

)= 1c

(∆C∆t

)= −1

b

(∆B∆t

)= 1d

(∆D∆t

)

2.0.2 Measurement of Reaction Rates

There are several methods of measurement. Theseinclude

(i) Follow the progress of the reaction. Requirescontinuous analysis of the disappearing/formingchemical species.

(ii) Rate of reaction as change in concentrationover time.

(iii) The rate as the slope of the tangent line ina concentration-time graph

(iv) Based on the concept of initial rates of reac-tion.

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2.0.3 The Rate Law

Chemical kinetics aims to find a distinct relation-ship between the rate of a reaction and the con-centration of the present chemical species.

The relationship between these two is expressedthrough rate laws/equations

rate of reaction = −r = k[A]m[B]n

[A] and [B] are the concentration, in molarities,of the reactants. The exponents, m and n, arethe order of reaction with respect to A and B

respectively. The sum of the exponents is equalto the overall order of reaction. The constant k,the rate constant, relates the rate of reaction tothe concentration of the reactants.

2.0.4 Method of Initial Rates

Given experimental data involving initial rates andreactant concentration. The rate constant and theorder of reactions can be determined using themethods of initial rates. The values of m andn are experimentally determined.

Given:A −−→ B + C

Zero-Order Reaction. The rate is constant, in-dependent of the concentration of A. Half-life islinear in [A]◦

−r = k (rate law)

[A] = −kt+ [A]◦ (∫

rate law)

thalf = [A]◦2k (half-life)

First-Order Reaction. The rate is linear in A.Half-life is constant regardless of initial concentra-tion [A]◦

−r = k[A] (rate law)

ln ([A]) = −kt+ ln ([A]◦) (∫

rate law)

thalf = ln 2k

(half-life)

For gas-phase reactions,

ln PA

PA◦

= −kt

Second-Order Reaction. The rate is quadraticin A. Half-life is inversely proportional to the ini-tial concentration [A]◦

−r = k[A]2 (rate law)1

[A] = kt+ 1[A]◦

(∫

rate law)

thalf = 1k[A]◦

(half-life)

2.0.5 Theoretical Models for Chemical Kin-etics

Collision Theory For a reaction to proceed afterthe collision between two molecules, energy of col-lision must be at least equal to the activation en-ergy (Ea) of the reaction, minimum kinetic energyrequired for reaction to occur.

Transition State theory. Involves a transitionstate which is a hypothetical species that are presentbetween the reactant and product state.

Activated Complex is a hypothetical and un-stable species.

Reaction Profile displays the progress of the re-action. Potential energy vs progress of reaction.

Arrhenius Equation. A mathematical formu-lation for the dependence of the rate constant ontemperature.

k = Ae− EaRT (2.0.10)

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Given two sets of ordered pairs (T, k),

ln k1k2 = Ea

R

(1T1 −

1T2

)(2.0.11)

2.0.6 Reaction Mechanisms

A reaction mechanism is a detailed descriptionof a chemical reaction. Each step involved is calledan elementary process.

Elementary reactions. These reactions haverate laws with exponents having stoichiometriccorrespondence. Elementary reactions are revers-ible, some involve the production and consump-tion of intermediates.

Some notes

(1) Unimolecular reactions. a single molecule dis-sociates

(2) Bimolecular reactions. collision of two mo-lecules

(3) Termolecular reactions. collision of three mo-lecules

(4) An elementary process occurring at a slowrate is the rate determining step.

Steady-State Approximation.

2 A + BC −−→ AB + CA (slow)

CA + BC −−→ AB + 2 C (fast)

The rate of formation of CA is equal to the rateof consumption of CA.

References

[1] Wikipedia, the Free Encyclopedia.

[2] R H Petrucci, F G Herring, J D Madura, andC Bissonnette. General Chemistry: Principlesand Modern Applications. Prentice Hall PTR,2011.

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Chemistry 17 Reviewer