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!

Thermodynamics – the study of energy and its transformations Thermochemical changes – energy changes associated with chemical reactions

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

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

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.

Examples of state functions  H  G  V  T Examples of path functions work (w) heat (q)

Metastable - the progress towards the equilibrium state is slow Equilibrium state - state of the system is invariant with time

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

Gas - a substance that is characterised by widely separated molecules in rapid motion Mixtures of gases are uniform. Gases will expand to fill containers.

n Common gases include - O 2 and N 2, the major components of "air" n Other common gases - F 2, Cl 2, H 2, He, and N 2 O (laughing gas)

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/m 2 = (kg m/s 2 )/m 2

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 = kPa = bar 1 bar = 1 x 10 5 Pa (exactly)

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 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

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

V t /  C Absolute Zero (-273  C = 0 K)

Lord Kelvin – all temperature/volume plots intercepted the t c axis at °C). Kelvin termed this absolute 0 – the temperature where the volume of an ideal gas is 0 and all thermal motion ceases!

T (K) = [ t c (°C) °C] K/°C Freezing point of water: t c = 0 °C; T = K Boiling point of water: t c = 100 °C; T = K Room temperature: t c = 25 °C; T = 298 K NOTE t c = °C; T (K) = K NO DEGREE SIGN

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!

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

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

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

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

Define:STP (Standard Temperature and Pressure) Temperature °C = K Pressure atm The volume occupied by mole of an ideal gas at STP is L!

Define:SATP (Standard Ambient Temperature and Pressure) Temperature °C = K Pressure bar (10 5 Pa) The volume occupied by mole of an ideal gas at SATP is L!

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

The pressure exerted by gas #1 P 1 = n 1 RT / V The pressure exerted by gas #2 P 2 = n 2 RT / V The total pressure of the gases p T = n T RT / V n T represents the total number of moles of gas present in the mixture

P 1 and P 2 are the partial pressures of gas 1 and gas 2, respectively. P T = P 1 + P 2 = n T (R T /V) P T = P 1 + P 2 + P 3 =  j P J note P j is known as the partial pressure of gas j

Gaseous mixtures - gases exert the same pressure as if they were alone and occupied the same volume. The partial pressure of each gas, P i, is related to the total pressure by P i = X i P T X j is the mole fraction of gas i. X j = n j / n T

In the limit of low pressures

The Isothermal Compressibility

The coefficient of thermal expansion