Chemistry 231 Introduction and Gases

Physics - study of the properties of matter that are shared by all substances

Chemistry - the study of the properties of the substances that make up the universe and the changes that these substances undergo

Physical Chemistry - the best of both worlds!

Physical Chemistry

Thermodynamics – the study of energy and its transformations

Thermochemical changes – energy changes associated with chemical reactions

Thermodynamics and Thermochemistry

Interested in the numerical values of the state variables (defined later) that quantify the systems at that point in time.

Systems can be either• macroscopic• microscopic

Studying Systems

Described by variables such as• temperature (T)• pressure (P)• volume (V)• energy (U) • enthalpy (H)• Gibbs energy (G)

State of a System

State Variables • system quantity whose values are fixed at constant

temperature, pressure, composition State Function

• a system property whose values depends only on the initial and final states of the system.

Path Functions • system quantity whose value is dependent on the

manner in which the transformation is carried out.

State and Path Functions

Examples of state functions• H• G• V• T

Examples of path functions• work (w)• heat (q)

State and Path Functions (Continued)

Metastable - the progress towards the equilibrium state is slow

Equilibrium state - state of the system is invariant with time

Equilibrium vs. Metastable

Reversible transformation - the direction of the transformation can be reversed at any time by some infinitesimal change in the surroundings

Irreversible transformation - the system does not attain equilibrium at each step of the process

Reversible and Irreversible

Gas - a substance that is characterised by widely separated molecules in rapid motion

Mixtures of gases are uniform. Gases will expand to fill containers.

The Definition of a Gas

Common gases include - O2 and N2, the major components of "air"

Other common gases - F2, Cl2, H2, He, and N2O (laughing gas)

Examples of Gaseous Substances

The pressure of a gas is best defined as the forces exerted by gas on the walls of the container

Define P = force/area The SI unit of pressure is the Pascal 1 Pa = N/m2 = (kg m/s2)/m2

The Definition of Pressure

How do we measure gas pressure? We use an instrument called the

barometer - invented by Torricelli Gas pressure conversion factors

• 1 atm = 760 mm Hg = 760 torr• 1 atm = 101.325 kPa = 1.01325 bar• 1 bar = 1 x 105 Pa (exactly)

The Measurement of Pressure

Experiments with a wide variety of gases revealed that four variables were sufficient to fully describe the state of a gas • Pressure (P)• Volume (V) • Temperature (T)• The amount of the gas in moles (n)

The Gas Laws

The gas volume/pressure relationship The volume occupied by the gas is

inversely proportional to the pressure V 1/P

• note temperature and the amount of the gas are fixed

Boyle's Law

Boyle's Law

V

1/P

V

P

Defines the gas volume/temperature relationship.

V T (constant pressure and amount of gas)

Note T represents the temperature on the absolute (Kelvin) temperature scale

Charles and Gay-Lussac's Law

Charles and Gay-Lussac's Law

V

t / CAbsolute Zero

(-273C = 0 K)

Lord Kelvin – all temperature/volume plots intercepted the tc axis at -273.15°C).

Kelvin termed this absolute 0 – the temperature where the volume of an ideal gas is 0 and all thermal motion ceases!

The Kelvin temperature scale

T (K) = [ tc (°C) + 273.15°C] K/°C• Freezing point of water: tc = 0 °C; T = 273.15

K

• Boiling point of water: tc = 100 °C; T = 373.15 K

• Room temperature: tc = 25 °C; T = 298 K

• NOTE tc = °C; T (K) = K NO DEGREE SIGN

The Temperatures Scales

The pressure/temperature relationship For a given quantity of gas at a fixed

volume, P T, i.e., if we heat a gas cylinder, P increases!

Amonton’s Law

The volume of a gas at constant T and P is directly proportional to the number of moles of gas

V n => n = number of moles of gas

Avogadro’s Law

We have four relationships• V 1/P; Boyle’s law • V T; Charles’ and Gay-Lussac's law • V n; Avogadro’s law• P T; Amonton’s law

The Ideal Gas Equation of State

Combine these relationships into a single fundamental equation of state - the ideal gas equation of state

The Ideal Gas Law

mole Katm

08206.0

314.8L

moleKJ

R

nRTPV

An ideal gas is a gas that obeys totally the ideal gas law over its entire P-V-T range

Ideal gases – molecules have negligible intermolecular attractive forces and they occupy a negligible volume compared with the container volume

The Definition of an Ideal Gas

Define: STP (Standard Temperature and Pressure)• Temperature - 0.00 °C = 273.15 K• Pressure - 1.000 atm• The volume occupied by 1.000 mole of an

ideal gas at STP is 22.41 L!

Standard Temperature and Pressure

Define: SATP (Standard Ambient Temperature and Pressure)• Temperature - 25.00 °C = 273.15 K• Pressure - 1.000 bar (105 Pa)• The volume occupied by 1.000 mole of an

ideal gas at SATP is 24.78 L!

Standard Ambient Temperature and Pressure

Let's consider two ideal gases (gas 1 and gas 2) in a container of volume V.

Partial Pressures

1

2

2 2

22 1

1

1

1

11

2

2

The pressure exerted by gas #1 • P1 = n1 RT / V

The pressure exerted by gas #2 • P2= n2 RT / V

The total pressure of the gases • pT = nT RT / V

nT represents the total number of moles of gas present in the mixture

Partial Pressures

P1 and P2 are the partial pressures of gas 1 and gas 2, respectively. • PT = P1 + P2 = nT (RT/V)

• PT = P1 + P2 + P3 = j PJ

• note Pj is known as the partial pressure of gas j

Partial Pressures (continued)

Gaseous mixtures - gases exert the same pressure as if they were alone and occupied the same volume.

The partial pressure of each gas, Pi, is related to the total pressure by Pi = Xi PT

Xj is the mole fraction of gas i.• Xj= nj / nT

Dalton's Law of Partial Pressure

In the limit of low pressures

Ideal Gas Temperature Scale

0lim p

PVT

nR

The Isothermal Compressibility

The Isothermal Compressibility

TT P

VV

1

The coefficient of thermal expansion

Coefficient of Thermal Expansion

PTV

V

1