This introductory physical chemistry course examines the connections between molecular properties and the behavior of macroscopic chemical systems.

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Из курса от партнера University of Minnesota

Statistical Molecular Thermodynamics

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This introductory physical chemistry course examines the connections between molecular properties and the behavior of macroscopic chemical systems.

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Module 5

This module is the most extensive in the course, so you may want to set aside a little extra time this week to address all of the material. We will encounter the First Law of Thermodynamics and discuss the nature of internal energy, heat, and work. Especially, we will focus on internal energy as a state function and heat and work as path functions. We will examine how gases can do (or have done on them) pressure-volume (PV) work and how the nature of gas expansion (or compression) affects that work as well as possible heat transfer between the gas and its surroundings. We will examine the molecular level details of pressure that permit its derivation from the partition function. Finally, we will consider another state function, enthalpy, its associated constant pressure heat capacity, and their utilities in the context of making predictions of standard thermochemistries of reaction or phase change. Homework problems will provide you the opportunity to demonstrate mastery in the application of the above concepts.

- Dr. Christopher J. CramerDistinguished McKnight and University Teaching Professor of Chemistry and Chemical Physics

Chemistry

We've come to the end of week 5, a full week, a lot of material mostly devoted to

the first law of thermodynamics. So I'd like to finish then, with a review

of what I think the high points were. So, stated in words, the first law of

thermodynamics most simply would be, energy is conserved.

And mathematically, we go beyond that to express dU is equal to delta q plus delta

w. Where u is the internal energy, q is the

heat, and w is work. And there are conventions for the signs

of heat and work. By convention, heat is positive when it's

absorbed by the system. Work is positive when it's done on the

system, and vise versa. Energy is a state function.

That is, it depends only on the variables defining the state, temperature,

pressure, number of particles, for instance.

Heat and work on the other hand are path functions.

The amount of heat or work that changes depends on how you go from one state

point to another state point. Work, when it's done by expanding a gas,

is equal to minus the external pressure times dv, the change in volume.

Where p ext is, indeed, the external pressure against which the gas expands.

A reversible process is one that happens in infinitesimally small steps.

And the maximum work that can be extracted from the isothermal expansion

of a gas, is the reversible work. Where the external pressure is going to

be equal to the pressure of the ideal gas itself.

Another term that we define is an adiabatic process.

Adiabatic implies that the heat transfer delta q is equal to 0.

And under those circumstances, since du is equal to delta w, and since u is a

state function, W is also a state function for an adiabatic process.

If you expand a gas adiabatically against an external pressure it must cool.

Another state function is enthalpy. Enthalpy is written capital H.

It's defined as the sum of the internal energy plus pressure times volume.

Delta H for a constant pressure process, is equal to the heat transferred at

constant pressure, which is represented by putting a p as a subscript on q.

That also leads to a definition for a constant pressure heat capacity.

And that's defined as the change in enthalpy with respect to the change in

temperature at a constant pressure. Another way of thinking of it, is the

amount of heat that's required to raise the temperature of the substance by one

degree. For an ideal gas, the difference between

the heat capacity at constant pressure Cp, and the heat capacity at constant

volume Cv, when we talk about the molar quantities, they differ by r.

So the Cp is greater than Cv by r. Enthalpy itself can be measured, or most

more accurately enthalpy changes can be measured.

And in particular, if you want to talk about the change in enthalpy as you go

from absolute zero to some non-zero temperature, that's computed by looking

at the heat capacity as a function of temperature, which since it's a

measurement of how much heat is required to raise the temperature by one degree,

you can measure that degree by degree. And when you integrate all of that heat

that has been transferred, of course that's all contributing to the enthalpy.

That integration gives you the enthalpy change, and then when there are phase

transitions between say a solid and a liquid, or a liquid and a gas phase,

additional heat is required. That's defined as the heat of fusion, or

the heat of vaporization, integration of the heat capacities for the various

phases, also contributes as you get up to the next phase change.

And that allows you then to, through experiment define the enthalpy at a given

temperature relative to that at zero. And I showed an example that I've just

re-capitulated here in these slides for the case of benzene.

So, these are the measured heat capacities, these are the integrated heat

capacities which is the enthalpy. Enthalpy being a state function that

implies that it is a additive property, and so that leads to the convenient Hess'

Law. Which says if you'd like to know the

enthalpy change for a given reaction, if you can construct that reaction out of

other reactions, adding them or subtracting them, for which you know the

heat of reaction, then that unknown one will be the sum of those various other

reactions. Standard enthalpy of reactions, unlike

Just a general enthalpy of reaction which is an extensive process it depends on how

much you have a standard enthalpy of reaction is intensive.

It refers to one mole of a certain specified quantity, and such standard

enthalpies are tabulated for defined standard states where definition requires

a choice of convention. And in particular that convention is that

the standard molar enthalpy of formation for a pure element, in its most stable

form, at a given temperature, is defined to have a heat of formation of zero.

And given that definition, looking at the changes in enthalpy as you transform pure

elements into chemical compounds Allows you to define the heat of formation for

those chemical compounds. Given heats of formation and heat

capacities, one can then determine, as long as all of the participants in a

chemical reaction have known heats of formation and heat capacities, One can

determine the enthalpy change for that process, as the heat of formation of the

products minus the heat of formation of the reactant.

That's sufficient if you already have tabulated data for the temperature you're

interested in. If the temperature of interest for the

reaction is not the same as that the heats of formation are tabulated for.

That's when you can use the difference in heat capacities of products versus

reactants to add to that an integrated term from the temperature you know to the

temperature of interest, in order again to determine the heat of reaction at the

final temperature. So a lot of tools that are now in our

toolbox. That allow us to, understand changes in

energy, changes in work, changes in heat and changes in enthalpy.

That wraps up what I think are the most important points in week five.

We're going to move on from the first law of thermodynamics next week.

We're going to address a new state function and a key thermodynamic

property, and that is entropy. I look forward to seeing you then.

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