THE STATES OF GASES Chapter 1

Bulk Variables Volume - m3 Pressure - Pa Temperature - K Composition - moles

Volume length3 units molar volume Vm= V/n m3 or cm3 liter = 1000 cm3

Pressure Force/Area units Pascal = Newton/m2 = Joule/m3 atmosphere = 101325 Pa bar = 100000 Pa – Standard Pressure mm Hg torr h

Mechanical Equilibrium High P Low P High pressure gas will tend to compress a low pressure gas Movable wall or “piston” Equal P

Temperature Thermometry - relate temperature to other properties. Fahrenheit (°F) Celsius (°C) Kelvin (K)

Thermal Equilibrium High T Low T Heat or energy will flow from the high T gas to the low T gas Rigid diathermic wall Equal T

Zeroth Law of Thermodynamics Two systems that are separately in thermal equilibrium with a third system are also in thermal equilibrium with one another. The zeroth law is the basis for thermometry, i.e. the use of a third body (the thermometer) to measure an equilibrium property (the temperature) of other systems.

Zeroth Law of Thermodynamics Thermal Equilibrium Thermal Equilibrium B C Thermal Equilibrium

CHARLES’S LAW

Absolute zero = -273.15 °C T/K = θ/°C + 273.15 CHARLES’S LAW

Composition moles: ni S ni = n mole fraction: xi S xi = 1 partial pressure: pi S pi = p

Gas Laws Boyle’s Law: pV = constant at constant n, T

Equations of State P,V,T, and n are not independent. Any three will determine the fourth. An equation of state is an equation that relates P,V,T, and n for a given substance. Gases have the simplest equations of state. The simplest equation of state is the ideal gas law, pV = nRT

Ideal Gas Law p = pressure V = volume n = moles T = temperature R = universal gas constant = 0.08206 L-atm/mol-K (Table 1.2)

Ideal Gas Model Molecules may be treated as point masses relative to the volume of the system. Molecular collisions are elastic, i.e. kinetic energy is conserved. Intermolecular forces of attraction and repulsion have negligible on the molecular motion. Real gases approximately behave as ideal gases at higher temperatures and low pressures.

Ideal Gas Model http://intro.chem.okstate.edu/1314F00/Laboratory/GLP.htm

Ideal Gas Problem Gas in a vessel of constant volume is heated to 600 K. If it initially entered the vessel at 300 K and 1 atm, what is the pressure after heating?

Ideal Gas Problem Gas in a vessel of constant volume is heated to 600 K. If it initially entered the vessel at 300 K and 1 atm, what is the pressure after heating?

Ideal Gas Problem Gas in a vessel of constant volume is heated to 600 K. If it initially entered the vessel at 300 K and 1 atm, what is the pressure after heating?

Partial Pressure pA = partial pressure of gas A V = total volume nA = moles of gas A T = temperature R = universal gas contant = 0.08206 L-atm/mol-K

Dalton’s Law The total pressure is the sum of all the partial pressure.

Dalton’s Law Problem Earth’s atmosphere is ~ 75.5% N2, 23.2 % O2, and 1.3 % Ar by mass. What is the partial pressure of each component when the total pressure is 1.00 atm?

Dalton’s Law Problem Earth’s atmosphere is ~ 75.5% N2, 23.2 % O2, and 1.3 % Ar by mass. What is the partial pressure of each component when the total pressure is 1.00 atm? STOP HERE

Real Gases Real gases do not obey the ideal gas law. Deviations at low temperature and high pressure. Especially near point of condensation.

Molecular Interactions Real gases are not point masses – they have volume. Real gases do interact. Two forces of interaction Attractive forces Repulsive forces.

Molecular Interactions Attractive forces are “long” range forces Long = several molecular diameters Beyond this attractive forces are not significant “Low” temperature Low = T near condensation point.

Molecular Interactions Repulsive forces are “short” range forces Short = ~ less than 1 molecular diameter At low T, attractive forces overcomes repulsive forces.

Intermolecular Forces

Summary At low pressures and large volumes, there is little interaction ~ Ideal Gas. At moderate pressure, attractive forces start to dominate – gas more compressible. At high pressure, repulsive forces dominate – gas less compressible.

Compressibility The compressibility of a gas is defined by:

Compressibility If the gas behaves ideally, then Z=1 at all pressures and temperatures. For real gases, however, Z varies with pressure, and deviates from its ideal value.

Compressibility

Isotherms, isobars and isochores

Ideal Gas Isotherm