Definition
The relationship between pressure, absolute
temperature and the volume of a gas is called general gas equation. It is the
combined form of Boyle’s law, Charles law and Avogadro’s law in which neither
temperature nor pressure is constant. It gives the simultaneous effect of
pressure and temperature on the volume of a gas.
Derivation of 1st Form of Equation of State/Ideal Gas
Equation
Equation of state is an equation in which four state variables of gas like pressure, volume, absolute temperature and number of moles are specified i.e. it describes the behaviour of all gases under any combination of amount (n), T, P and V. It is also called ideal gas equation. The ABC gas laws i.e. Avogadro’s law, Boyle’s law and Charles law are combined to formulate ideal gas equation.
Ideal
gas equation is a relation between four variables and it describes the
state of any gas, therefore, it is also called equation of state.
Combining above three relationships into a single relationship and then removing proportionality sign by introducing a constant, we get:
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Where R is proportionality
constant and is called General or Universal Gas Constant. This equation
is called Equation of State also
known as Ideal Gas Equation.
Derivation of Second Form of Equation of State/General Gas
Equation
Since for one mole of a
gas; n = 1
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For two set of conditions i.e. initial and final states set of conditions (i.e. if pressure changes to P1 and temperature changes to T1 then volume also changes to V1). Then,
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 Comparing equation (1) and (2): |
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This equation is called General Gas Equation. | |||||||
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If moles of gas changed from n1 to n2, then |
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Derivation
of Density from Ideal gas equation
The density of a gas at a given temperature and pressure is measured by using ideal gas equation:
Alternative Derivation of Density from Ideal gas equation
Another way to derive gas density is:
Factors
affecting density of gas
The density of a gas depends on its molar mass, pressure and temperature.
The density of a gas varies directly with to
its pressure and molar mass i.e. the higher the molar mass and pressure, the
more dense the gas. A less dense gas will lie above a more dense one. e.g. CO2
has a higher molar mass (44 amu) than N2 (28 amu) or O2
(32 amu) and is therefore more dense than air. When CO2 is released
from a CO2 fire extinguisher, it will blanket a fire, preventing O2
from reaching the combustible material.
Determination of Numerical Value of ‘R’
“R” is a gas law constant or gas constant or molar gas constant. Its value
is independent of the nature of the gas. The value and units of R depends on the units
chosen for P, V, T and n.
Since PV (and also liter-atm) has the dimension of energy, therefore, R can include energy units such as joule, ergs, cal etc.
The value of R is calculated for one mole of a gas at standard conditions of temperature and pressure.
Nature of R
The nature of R for 1 mole of a gas
is determined by examining the nature of various quantities making up it.
Thus R is work divided by temperature. Its value therefore, will be expressed in units of work per degree per mol. In SI unit, the value is expressed in joule per degree per mole.
Different Numerical Values of ‘R’
“R” in N-m or J when pressure is expressed in N/m2
and volume in m3 (SI Value)
When pressure is expressed in N/m2 (SI unit) and volume in m3 (SI
unit), then value of ‘R’ at standard conditions for one mole of a gas
is calculated as:
“R” in dyne-cm or ergs when
pressure is expressed in dyne/cm2 and volume in cm3 (cgs
Value)
In cgs system, pressure is expressed in dyne/cm2 and volume in cm3,
then value of ‘R’ at standard conditions for one mole of a gas is
calculated as
“R” in cal
“R” in atm-dm3 or atm-liter when pressure is
expressed in atm and volume in dm3 (Non SI Unit)
When pressure is expressed in atmosphere and volume in dm3, the
value of R is calculated for one mole of a gas at standard condition
of temperature and pressure as follows:
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