Download Review for Chapter 16

Brief review and overview of thermodynamics
The system is the part of the universe we are interested in. The surrounding is the rest of the universe.
For all thermodynamic parameters (let Y be any thermodynamic parameter)
Yuniverse = Ysystem + Ysurroundings
Thermodynamic Quantities of Interest:
E, U
S
internal energy
entropy
units (J/mol)
units (J/mol x K)
H
G
enthalpy
Gibb’s free energy
units (J/mol)
units (J/mol)
A)
Thermodynamic quantities are extensive properties – the value will depend on how much material there is.
The quantities are additive (i.e. can use Hess’s law)
B)
Thermodynamic quantities are functions of state – the value depends only on the current state, not on the path
taken to get there. In general the change in any thermodynamic quantity will be Y = Yproduct - Yreactant
First Law of Thermodynamics – the internal energy of the universe is constant; energy can be neither created
nor destroyed.
The internal energy of the molecule is the total energy of the molecule. This includes translational, rotational, vibrational and
electronic energy.
Enthalpy:
H = U + PV
At constant pressure, enthalpy equals q and Hp = qp
Spontaneous Processes
1)
Spontaneity: The spontaneity of a reaction has always been of interest to scientists. Spontaneous means the process of
interest occurs without outside intervention. This does not mean the reaction will occur rapidly.
One can think of a spontaneous process as one that will proceed forward.
Initially it was thought that enthalpy changes associated with processes would correspond to the spontaneity of a reaction.
It was thought that an exothermic reaction would be spontaneous and an endothermic reaction would not be (or would be
spontaneous in the opposite direction). It was found that some endothermic processes are spontaneous so enthalpy
was not the only component.
2)
Entropy: It was determined that the entropy change of the universe was a good predictor of whether or not a process
would be spontaneous.
What is entropy? It is often described as a measure of disorder or randomness. It is better to describe entropy in terms of
the number of arrangements of components that have the same energy. The larger the number of arrangements, the greater
the entropy. Each arrangement is a microstate. The number of microstates is related to entropy by S = klnW, where k is the
Boltzman constant and w is the number of microstates and ΔS = kln(Wf/Wi)
3)
Second Law of Thermodynamics – in any spontaneous process, there is an increase of entropy in the
universe OR the entropy of the universe is increasing.
Thus, if
Suniv = (+), the process is spontaneous, proceeds forward
Suniv = (-), the process is spontaneous in the reverse direction
Suniv = 0, the reaction is at equilibrium and progresses neither forward nor reverse.
Suniv = Ssys + Ssurr
4)
In general, the number of microstates for a process is not determined, instead standard entropy values are employed.
Standard entropy is the absolute entropy of a substance at 1 atm and 250 C. In contrast to enthalpy, where values are
relative, an absolute value can be given for entropy. Entropy of a pure substance at absolute zero is 0. This is the third
law of thermodynamics. The entropy of a perfect crystalline substance is zero at the absolute zero of
temperature.
The units of entropy are J/K x mol
5)
The general trends of entropy for reactions or particles:
A)
B)
C)
D)
E)
entropy (gas) > entropy (liquid) > entropy (solid)
The more particles, the more the entropy
For a gas, the greater the volume, the greater the entropy
The more massive a particle, the greater the entropy.
Mixing results in an increase of entropy
6)
Entropy is dependent on the heat exchanged between system and surrounding and the temperature at which this
occurs. The magnitude of the entropy change associated with any process is dependent on the temperature at which
that process occurs.
S = q/T for a reversible process
If the process occurs at constant pressure, qp =Hp, Sp = Hp/T
H is equal and opposite for system and surroundings. Hsys = (-) and Hsurr = (+) since heat will leave the system
and enter the surrounding.
Entropy changes of the surrounding are difficult to determine and are usually expressed relative to changes in enthalpy of
the system. Ssurr = Hsurr/T = (-)ΔHsys/T
Entropy Changes in Chemical Reactions
How can the entropy changes of the system be determined?
1)
Standard molar entropies - Sorxn = nproductSoproduct - nreactantSoreactant
Note
2)
a) Standard absolute entropy values are employed.
b) n is the number of moles of compound used in one round of the reaction
c) The superscript o means the reaction is at standard state. One molar for solutions and 1 atm for gases.
Calculation of S from S of other reactions. Hess’s law can be applied.
Srxn = S1 + S2 + S3
The Free Energy
While ΔSuniv (+) is one way to determine the spontaneity of a reaction, it was found that another quantity, the change in Gibb’s free
energy (G) is a more convenient to determine. Free energy is a state function and is an extensive property G = H – TS.
Since absolute levels of G and H are not determined, the equation is written in terms of change: Grxn = Hrxn - TSrxn
For any case:
Grxn = (-) the reaction is spontaneous in the forward direction, proceeds in the forward direction
Grxn = (+) the reaction is not spontaneous as written, but is spontaneous in the reverse direction
Grxn = 0 the reaction is at equilibrium and will not proceed in either direction
The relationship between H and S will determine the sign and magnitude of G. Note that in addition to the signs of H and S,
the temperature can determine whether a reaction is spontaneous or not.
Examine Grxn = Hrxn - TSrxn. If the reaction is at equilibrium, then Grxn = 0 and the equation can be arranged to
-Hrxn = -TSrxn and further to Srxn = Hrxn/T. So, Srxn = Hrxn/T at equilibrium. This equation could be used to determine the T at
which a reaction is at equilibrium.
Free Energy and Chemical Reactions:
For any chemical reaction the following equation will hold true:
Grxn = Hrxn - TSrxn
This can be applied to reactions at standard state or reactions not at standard state. The only criteria is that all values are obtained
under the same conditions.
Gorxn – this is the change in free energy for a reaction that is associated with “one round” of the reaction occurring to
change reactants to products under standard conditions (1 M or 1 atm).
N2(g) + 3H2(g)  2NH3(g)
One round would convert 1 mole of N2 and 3 moles of H2 into 2 moles of NH3.
If Grxn = 34.4 kJ, this means 34.4 kJ is required for “one round”
How much free energy
a) per mol N2: 34.4 kJ/reaction x 1 reaction/mol N2 = 34.3 kJ/mol N2
b) per mol H2: 34.4 kJ/reaction x 1 reaction/3 mol H2 = 5.7 kJ/mol H2
How to determine Gorxn
1)
Determine standard entropy and standard enthalpy values first and plug values into Grxn = Hrxn - TSrxn
(Sorxn = nproductSoproduct - nreactantSoreactant Horxn = nproductHoproduct - nreactantHoreactant)
2)
Gorxn could be determined from Goformation values.
Goformation values – the free energy change that occurs when 1 mol of a substance is synthesized from its
elements in their standard states.
Gorxn = nproductGoproduct - nreactantGoreactant
3)
Gorxn could be determined from G values of other reactions.
Grxn = G1 + G2 + G3
The Dependence of Free Energy on Pressure/Concentration:
Most values in tables in thermodynamics are for standard state conditions. That means solutes present at 1 M and gases present
at 1 atm. However, very rarely are any reactions run under those conditions. Thus, there must be a correction for the difference in
concentrations employed between standard state and actual conditions.
The equation for a reaction, not at standard state conditions is:
Grxn = Gorxn + RTlnQ
Gorxn is the standard state value and gives information about the energetics of the reaction.
RTlnQ is the correction for not having reactants and products at standard state values.
Grxn will give you information on which direction the reaction will go to reach equilibrium
If Grxn = 0, the reaction is already at equilibrium
If Grxn is (-), the reaction is spontaneous in the forward direction and will go forward to reach equilibrium.
If Grxn is (+), the reaction will go in the reverse to reach equilibrium and is spontaneous in the reverse direction.
Free Energy and Equilibrium:
Equilibrium is defined kinetically as the point where the rates of the forward and reverse reactions are equal.
Thermodynamically, equilibrium where the total energy of the reactants equals the total energy of the products and Grxn = 0.
It is the point where the reaction system is at lowest energy.
The free energy change of a reaction can be related to Keq.
Consider the following reaction and subsequent points:
1)
Grxn = Gorxn + RTlnQ
2)
At equilibrium Grxn = 0
3)
At equilibrium Q = Keq
Substituting in information from 2 and 3 into 1, one gets 0 = Gorxn + RTlnKeq and rearranging one gets
Gorxn = -RTlnKeq
What do we know about Keq?
When Keq > 1, we know that at equilibrium, there will be more products than reactants
When Keq <1, we know that at equilibrium, there will be more reactants than products.
What do we know about Grxn?
Grxn = 0 at equilibrium
Grxn = (-) the reaction is spontaneous in the forward direction
Grxn = (+) the reaction is spontaneous in the reverse direction
The following correlations can be made:
Gorxn = 0 and Keq =1
Gorxn is + and Keq <1 – more reactants than products
Gorxn is – and Keq >1 – more products than reactants
The temperature dependence of Keq
Earlier it was noted that temperature is the only thing that will change the value of Keq.
As follows:
lnKeq1/lnKeq2 =( -H/R x 1/T1)/(-H/R x 1/T2)
Another equation that relates Keq and temperature will allow determination of H and S.
Since Grxn = -RTlnKeq and Grxn = Hrxn - TSrxn, then
-RTlnKeq = Hrxn - TSrxn Rearrange: lnKeq = -H/R x 1/T + S/R
A plot of lnKeq vs 1/T will give a line with slope = -H/R and an intercept of S/R
Differences between Go and G
Go – gives information on what the concentrations of reactant and product are AT equilibrium
G – gives information on which direction the reaction will go to reach equilibrium