Chemical Thinking - Unit 1: How do we distinguish substances?

Searching for Differences

• Central goal of Unit 1:
  • Understand and apply basic ideas to distinguish different substances in a system.
• Module 1: Searching for Differences
  • Identifying differences that allow separation of components.
• Module 2: Modeling Matter
  • Using the particulate model of matter to explain differences.

Chemical Thinking: Zooming In and Out

• Scales of observation:
  • Particulate
  • Macro
  • Molecular
  • Atomic
  • Electronic
• Unit Focus:
  • Unit 1: How do we distinguish substances?
  • Unit 2: How do we determine structure?
  • Unit 3: How do we predict properties?
• Relating Structure to Properties
  • Particulate level to Macro properties via Structure.

Modeling Matter

• Central Goal:
  • Explain diversity in properties and behaviors of substances based on the particulate model of matter.

The Challenge of Modeling

• Each substance has unique differentiating characteristics.
• The question is how to explain these differences.
• Example given:
  • Why does water form clouds in the atmosphere, but not nitrogen or carbon dioxide?

Models of Matter: Simplifying Substance Differentiation

• Models are developed about the internal structure of substances.
• These models allow us to:
  • Explain and predict the properties of matter.
  • Develop better techniques to detect and identify them.

Particulate Model of Matter (PMM)

• Definition:
  • A powerful model to explain and predict physical properties and behavior of substances.
  • Basic Assumptions:
    1. Any macroscopic sample of a substance is composed of a large number of very small particles.
       • How small are these particles?

Scale of Smallness

• Illustrating the scale of smallness with powers of ten, from 1 meter down to 1 nanometer.
• $0.1 m = 10^{-1} m$
• $0.01 m = 10^{-2} m$
• $0.001 m = 10^{-3} m$
• $0.00001 m = 10^{-5} m$
• $0.0000001 m = 10^{-7} m$
• $0.000000001 m = 1 \times 10^{-9} m = 1 nm$
• Most substances are made of particles of "nanometer" size.

Representing Particles

• Particles can represent atoms, molecules, or ions.
• Cautions about representations:
  • They are static.
  • Have unrealistic proportions.
  • Represent particles as solid objects.
  • Mix levels of representation.

Dynamic Nature of Particles

• Particles are constantly moving in random directions through empty space.
• Pressure (P) is determined by the force of particle collisions on the walls:
  • $Pressure = \frac{Force}{Area}$

Temperature and Kinetic Energy

• Temperature is a measure of average kinetic energy per particle.
• $\langle K \rangle = \frac{1}{2} m \frac{(v<em>1^2 + v</em>2^2 + v_3^2 + …)}{N}$

Particle Speed and Mass Relationship

• At any fixed temperature (T), average particle speed decreases with increasing mass (m).
• $\langle v \rangle^2 \sim \frac{\langle K \rangle}{m} \sim \frac{T}{m}$

Applying the PMM to Gases

• In a first approximation, gases at high T and low P can be modeled by assuming that particles do not interact with each other at all.
  • No repulsions.
  • No attractions.
  • Only wall collisions.

Predictions of the Ideal Gas Model

• The model predicts the following type of behavior:
  • $P \propto T$
  • $P \propto N$
  • $P \propto \frac{1}{V}$
  • This behavior is observed in all gases at high temperatures and low pressures.

Ideal Gas Law

• The particulate model of matter predicts a relationship of the following type for gases at high T and Low P:
• $P = k_B \frac{(N T)}{ V }$
  • where the proportionality constant $k_B = 1.380 \times 10^{-23} J/K$ is known as Boltzmann constant.

Limitations of the Ideal Gas Model

• In the absence of interactions among particles (intermolecular forces, or IMF), the model does not predict the existence of phase transitions as we change T.
• Analyze the behavior of the model when intermolecular forces (IMF) among particles are introduced.

Refining the Particulate Model: Intermolecular Forces

• Basic Assumptions:
  1. Any macroscopic sample of a substance is composed of a large number of very small particles.
  2. Particles are constantly moving in random directions through empty space.
  3. Particles interact with each other. The strength of the interactions depends on the distance between particles.

Modeling Phase Changes

• To explain the existence of phase transitions, we assume that there are intermolecular forces among particles.
• When temperature decreases…
  • The average kinetic energy per particle decreases.
  • Attractive forces between particles are then able to hold them together.

Kinetic and Potential Energy in Dynamic Systems

• In a dynamic system with interacting components, these components have both kinetic (KE) and potential (PE) energies.
  • $KE \rightarrow \frac{1}{2} m v^2$ (Energy due to movement)
  • $PE \rightarrow$ (Energy due to interactions)

Potential Energy Explained

• The potential energy of a system of interacting particles is a measure of the kinetic energy that could potentially be gained by the particles due to the forces acting on them.

Potential Energy (Ep) vs Distance Separated (r)

• Situation A: Particles are infinitely apart → Ep = 0
• Situation B: Particles get closer → Ep becomes negative
• Situation C: Particles get even closer → Ep becomes more negative
• Why is Ep = 0 when particles are far apart?
• Why is Ep negative when close together?

Factors Affecting Potential Energy

• In systems of particles that interact with each other, the potential energy depends on:
  • a) the distance between particles
  • b) the strength of their interactions

Potential vs. Kinetic Energy During Phase Transitions

• During a phase transition all the energy is invested (or lost) in the form of POTENTIAL ENERGY.
• The average KINETIC ENERGY per particle does not change during a phase change.

Central Idea: Two Competing Phenomena

• Changes that we observe in our surrounding, can be seen as the result of two competing phenomena:
  1. particles that make up a system are constantly moving in random directions.
  2. There exist attractive interactions between particles.
• The outcome of the competition will depend on the strength of interactions and on factors that impact the movement of particles.

Predicting Changes in a System: Two Critical Elements

• Predicting the changes that a system may undergo can be simplified by analyzing two critical elements:
  • The POTENTIAL ENERGY of its particles
  • The NUMBER OF CONFIGURATIONS that its particles can adopt

Potential Energy: Evaluating Energy Cost

• Comparing the potential energy allows us to evaluate the energy cost associated with a change.

Number of Configurations: Evaluating Probability and Ease

• Comparing the number of configurations allows us to evaluate the probability and the ease they rearrange.

Configurations and Probability

• There are more configurations that particles can take in the gas phase than in the liquid phase
• Random motion is more likely to induce a change to the gas phase

PEC Diagram

• The phase depends on factors like temperature and pressure
• The POTENTIAL ENERGY of its particles vs
• The NUMBER OF CONFIGURATIONS that its particles can adopt

Competition Between Potential Energy and Number of Configurations

• In this case, PE and # of configurations compete
  Who is favored at higher temperatures? Why?
  Who is favored at lower pressures? Why?

Modeling Matter: Summary

• The particulate model of matter allows us to explain and predict the properties of chemical substances.
• Useful to analyze, synthesize, and transform chemical substances.
• Differences in the intermolecular forces among the particles of different substances can be used to explain their different physical properties.