THER 003- Ideal Gas Law

Engr. Lina D. dela CruzChemical Engineering DepartmentTechnological Institute of the Philippines

GassesIndefinite volumeIndefinite shape Take the shape and

volume of containerParticles are far apartParticles move fastHigh Kinetic Energy -

particles can separate and move throughout container..

An ideal gas is defined as one in which all collisions between atoms or molecules are perfectly elastic and in which there are no intermolecular attractive forces.

One can visualize it as a collection of perfectly hard spheres which collide but which otherwise do not interact with each other.

In such  a gas, all the internal energy is in the form of kinetic energy and any change in internal energy is accompanied by a change in temperature.

An ideal gas can be characterized by three state variables: absolute pressure (P), volume (V), and absolute temperature (T). 

The relationship between them may be deduced from kinetic theory and is called the:

Where: n = number of molesR = universal gas constant = 8.3145 J/mol KN = number of moleculesk = Boltzmann constant = 1.38066 x 10-23 J/K

= 8.617385 x 10-5 eV/Kk = R/NANA = Avogadro's number = 6.0221 x

1023 /mol

Another way to describe an ideal gas is to describe it in mathematically. Consider the following equation:

PVnRT=1The four gas variables

are: pressure (P), volume (V), number of mole of gas (n), and temperature (T). 

Boyle's Law

Boyle’s Law describes the inverse proportional relationship between pressure and volume at a constant temperature and a fixed amount of gas. This law came from a manipulation of the Ideal Gas Law.

P∝1/V Equation: P1V1 = P2V2

State Variables

A state variable is a precisely measurable physical property which characterizes the state of a system, independently of how the system was brought to that state.

It must be inherently single-valued to characterize a state.

For example in the heat-work example, the final state is characterized by a specific temperature (a state variable) regardless of whether it was brought to that state by heating, or by having work done on it, or both.

Common examples of state variables are the pressure P, volume V, and temperature T. In the ideal gas law, the state of n moles of gas is precisely determined by these three state variables.

If a property, e.g., enthalpy H, is defined as a combination of other state variables, then it too is a state variable. Enthalpy is one of the four "thermodynamic potentials", and the other three, internal energy U, Helmholtz free energy F and Gibbs free energy G are also state variables.

The entropy S is also a state variable.

The Mole A mole (abbreviated mol) of a pure

substance is a mass of the material in grams that is numerically equal to the molecular mass in atomic mass units (amu).

A mole of any material will contain Avogadro's number of molecules. For example, carbon has an atomic mass of exactly 12.0 atomic mass units -- a mole of carbon is therefore 12 grams

For an isotope of a pure element, the mass number A is approximately equal to the mass in amu.

The accurate masses of pure elements with their normal isotopic concentrations can be obtained from the periodic table.

One mole of an ideal gas will occupy a volume of 22.4 liters at STP (Standard Temperature and Pressure, 0°C and one atmosphere pressure).

Avogadro's number NA = 6.0221367 x 1023/mole

Standard Temperature and Pressure

STP is used widely as a standard reference point for expression of the properties and processes of ideal gases.

The standard temperature is the freezing point of water and the standard pressure is one standard atmosphere. These can be quantified as follows:

Standard temperature: 0°C = 273.15 K

Standard pressure = 1 atmosphere = 760 mmHg = 101.3 kPa

Standard volume of 1 mole of an ideal gas at STP: 22.4 liters

Boyle's Law

Boyle's Law equation would be ideal when working with problem asking for the initial or final value of pressure or volume of a certain gas when one of the two factor is missing.

Charles' Law

Charles's Law describes the directly proportional relationship between the volume and temperature (in Kelvin) of a fixed amount of gas, when the pressure is held constant. 

V∝T

Equation:      V1/T1 =V2/T2

This equation can be used to solve for initial or final value of volume or temperature under the given condition that pressure and the number of mole of the gas stay the same.

Units of P, V and TThe table below lists the different units for each

property. 

Factor Variable UnitsPressure P atm Torr

Pa mmHg

Units of P, V and T

Factor Variable Units Volume V L m³ Moles n mol Temperature T KGas Constant R * see Values

of R table below 

Values of R 0.082057 L atm mol-1 K-1

62.364 L Torr mol-1 K-1

8.3145 m3  Pa mol-1 K-1

8.3145 J mol-1 K-1*

*note: This is the SI unit for the gas constant