Lecture 1.
The equation of state Divide the world in two parts: the system and the environment (the medium). The system is in equilibrium with its environment (properties of the system and the medium do not change in time)
environment
SYSTEM
To specify th
Chemical equilibrium continued We have derived the general relationship describing chemical equilibrium for any chemical reaction:
x = exp(G /RT) = K
i
i
0
where K is equilibrium constant and G0 =
! ! = ! "G
0 ii
f ,i
! i
Chemical kinetics We saw that the equilibrium constant K of the reaction N2 + 3H2 = 2NH3 is large at room T and atmospheric pressure. Yet if you mix hydrogen and nitrogen under those conditions
Reversible first order reactions Although some processes can be approximately viewed as being irreversible, strictly speaking, there is no such thing as an irreversible reaction. If A can be converted to B then B can a
The principle of detailed balance For the reaction A=B in equilibrium we have k1[A] = k1[B] or [B]/[A] = k1/k1 = KAB, where KAB is the equilibrium constant. Imagine now that we have a system, in which reactio
The temperature dependence of the rate constant For most chemical reactions, the temperature dependence of the rate constant is given by the Arrhenius law: k(T) = a Tn exp(Ea/RT) where the activation energy Ea is exp
Diffusion A molecule in a gas or a liquid frequently collides with other molecules and, as a result, its trajectory looks like a random walk. Here we will derive some properties of such motion. First, consider a rand
Superheated and supercooled materials (continued from the last lecture). In the last lecture we have explained why gases can be supercooled below their condensation point: it has to do with the energetic penalty to create
Thermodynamics of mixtures continued For a mixture, we have learned: dG = VdP-SdT + and G(P, T, n1, n2, ) =
dn
i
i
n
ii
where i ( P, T , n1, n2 , .) is the chemical potential of a component in the mixture. The last expression is deceptively simple becau
The Boltzmann distribution: the probability to have an energy i is given by:
pi i exp( i / kBT )
Examples of this 1. A piece of chalk on the table has the probability to be above the table ~exp(mgh/kBT). The surround
Phase equilibrium involving mixtures
Suppose we mix two liquids. What is the composition of the vapor that is in equilibrium with the liquid mixture? What is the boiling point of the mixture? To answer this kind of questio
Protein folding
k A B k B A
d[ A] / dt = kA B [ A] + k B A [ B] d[ B] / dt = k A B [ A] kB A [ B]
A
B
Drive system out of equilibrium by rapid mixing, T-jump etc.
Signal, e.g.~[A]
~ exp ( k A B + k B A )t
time
Single-molecule fluorescence resonance energ
More examples of using thermochemistry
Example 1.
Calculate H and S for the process applied to one mole of water at P = 1 atm:
H2O(s, -10C) H2O(l, +10C)
The melting point of ice at P = 1 atm is 0
CH353 Final Review
1) The Carnot cycle is a theoretical example of a perfect engine consisting of 4 steps:
i. Reversible isothermal expansion from state A to B at a hot temperature (Th)
ii. Reversible adiabatic expansion from state B to C
iii. Reversible
CH353 Physical Chemistry I, Spring 2016
Thermodynamics, Statistical Mechanics, Chemical Equilibria
2/15/16 Lecture Summary
In last Fridays lecture, I introduced a new state function, called entropy, that counts the number
of ways that we can arrange a sys
CH353 Physical Chemistry I, Spring 2016
Thermodynamics, Statistical Mechanics, & Chemical Equilibria
2/8/16 Lecture Summary
At the beginning of todays lecture, I continued our discussion of thermochemistry and showed
that if we know the change in the enth
Chemical equilibrium continued: the general approach
Extent of reaction
First of all, we will write any chemical reaction in the following general form:
A = 0
i i i
Here is are the stoichiometric coefficients, which are
Chemical equilibrium
A chemical reaction reactants = products can go from left to right or from right to left. Many reactions however have a preferred direction: It is easy, for example, to burn wood but hard to unb
Lecture 3.
Going from one state to another (thermodynamic transformations). In thermodynamics, we will be generally interested in how the system behaves when it goes from one state to another. This question can be answered if we specify the initial state
Work (path dependent quantities and functions of state) From physics you know that mechanical work = force displacement
Consider gas in equilibrium with the weight of the piston F. Now consider a process where the piston goes down by -dh. The work done by
The 1st Law of thermodynamics q + W = dU U is a function of state (while q or W are not). U is called energy (or internal energy) of the system. If q = 0 this is the standard energy conservation law from t
What conditions should a process satisfy to be reversible? Are there any reversible processes to begin with?
To find out, consider the following example: a vertical cylinder covered with a piston of mass m1 with one mole of gas ins
The 2nd Law For any equilibrium (= reversible) process the quantity dS = q/T is an exact differential (i.e. an increment of a function of state). In other words, = S(2) S(1)
where S is a function of
More examples of the 2nd law: 2nd law and heat engines: It is impossible to take heat q from a reservoir, convert it all into work, and return into the original state (no cyclically operating heat engine with an effi
The microscopic origins of irreversibility and entropy in statistical mechanics For more on this issue, see the video of Feynmans lecture The Distinction Between Past and Future from his Character of Physical Law series:
In the previous lecture we have introduced the Boltzmann formula for the entropy:
S = kB ln
Examples of using this: Example 1. (see previous lecture). Irreversible gas expansion Example 2. We have also seen that hot
The Gibbs free energy and nonPV work So far in our discussion of the work we have assumed it is associated with the expansion or compression of some material, in which case it is given by the formula W = PdV. We w
Relating thermodynamic quantities A,G,H,U,S to measurable quantities (equation of state and heat capacities) If A(V,T) or G(P,T) is known for some material , all of its other thermodynamic properties can be determined
An example of using our general relationships for U(V,T), S(V,T) etc. : Entropy of a nonideal gas. Consider irreversible expansion of one mole of a gas, in which it occupies the volume 2V where V is its initial volume
Thermochemistry Many chemical reactions are accompanied by heat release. In others, the chemicals tend to get colder so one has to provide heat to maintain the temperature. How can one predict these things? For example,