\( \newcommand{\xrightleftharpoons}[2]{\overset{#1}{\underset{#2}{\rightleftharpoons}}} \) \( \newcommand{\conc}[1]{\left[\mathrm{#1}\right]} \) \( \newcommand{\chem}[1]{\mathrm{#1}} \) \( \newcommand{\expect}[1]{\left< #1 \right>} \)

Classical Physical Chemistry Sets the Stage

Shaun Williams, PhD

The Classical Properties of Matter

What do we measure?

Which is ice and which is diamond?

  • By observation they appear the same
A cubic sample of diamond and ice appear identical.

Which is ice and which is diamond? Can we tell by mass?

  • For equal volumes of each, the two substances will compress the spring different amounts
A cubic sample of diamond will have more mass than an equal volume of ice.

Which is ice and which is diamond? Can we tell by heating the samples?

  • The ice will melt at a lower temperature.
A cubic sample of diamond will increase its temperature when heated while a sample of ice will remain at the same temperature when heating as it melts.

Classical Parameters - Volume

Classical Parameters - Mass and Moles

Classical Parameters - Pressure

Classical Parameters - Temperature

Measuring Temperature

Thermodynamics

What is thermodynamics?

Energy

Zero Energy

The First Law

Signs

First Law Graphically

Heat enters the gas in a cylinder so the sign of the q is positive. The heated gas expands, pushing a piston upwards so the sign of the work done is negative.

A Steam Example

A Steam Example, Signs

Enthalpy

Back to the steam pipe

Blocks of diamond and ice

Entropy and the Second Law

An engine

Heat enters the engine through a pipe. This heat heats up steam which expands pushing up a piston and driving the engine. Throughout the entire process, heat is being lost from the engine into the surroundings.

Defining Entropy

Alternative Entropy Definition

Explanation

  • Understanding $$ T \equiv \left( \frac{\partial E}{\partial S} \right)_{V,n} $$
  • \(\partial \) is like a tiny \(\Delta\)
  • So we have a tiny (infinitesimal) change in energy on top
  • On the bottom is a tiny change in entropy
  • Ratio these two tiny changes
  • This ratio is temperature when the volume and number of moles are held constant

Melting Ice

$$ T\equiv \left( \frac{\partial E}{\partial S} \right)_{V,n} $$

Another Clausius realization

The Kinetic Theory of Ideal Gases

Towards our modern molecular theory of matter

The Maxwell-Boltzmann Distribution

Example: Flipping 50 coins

  • About 11% of the time we actually get the average
  • Less probability away from the average
  • This is holds for all random events
A gaussian curve (bell curve) of the result of flipping 50 coins. The curves peaks (highest probability outcome) with 25 heads and 25 tails. The probability fall of boths sides of the peak.

Derivation of Maxwell-Boltzmann Distribution

Summary of Maxwell-Boltzmann Distribution Derivation

The Maxwell-Boltzmann Distribution at 300 K

The distribution of the velocities of nitrogen gas and helium gas. Because it is lighter, the helium gas curve peaks (reaches maximum probability) at a higher velocity than does nitrogen gas.

The Ideal Gas Law

  • Reflections are totally elastic
  • These reflection allow us to define the forces acting in the box
  • The time-averaged force \(F_1\) exerted on wall 1 by a single particle with mass \(m\) traveling along the \(x\) axis at speed \(v_x\) is balanced by an equal and opposite force on the particle of \(–F_1\)
Gas molecules in a box that has walls of area A. The gas molecules exhibit a simple elastic collision with the walls bouncing back and forth between them.

Continuing with the force

Working with the velocity part of the expression

Continuing on...

Another Maxwell-Boltzmann Distribution

Chemical Equilibrium

Other Conditions

Time-Dependent Chemical Reactions

Final Thoughts

/