# Ideal Gas Law Equation

A gas which obeys Boyle’s law, Charle’s law, etc. under all conditions of temperature and pressure is known as an ideal gas or a perfect gas.These laws can be combined to give a relationship between the three variables P, V and T. This relationship or equation called as Ideal Gas Law Equation. Ideal Gas Law Equation

When we combine four parameters P, V, T and n then,

 Boyle’s law V ∝ 1/P  (n, T constant) Charle’s law V ∝ T  (n, P constant) Avogadro’s law V ∝ n  (P, T constant)

Combining laws can be written as:

• V ∝ nT / P
• or PV ∝ nT

Law equation is expressed as:

PV = nRT

Further, since the gas equation (PV = nRT) is derived by combining Boyle’s law and Charle’s law, an ideal gas may be defined as a gas which obeys the gas equation (PV = nRT) under all conditions of temperature and pressure, and hence the gas equation is also known as ideal gas equation. ## Ideal Gas Law Equation Units (P, V, and T)

The characteristics of gases are described in terms of following four parameters

1. Mass
2. Volume
3. Pressure
4. Temperature

### Mass:

Mass is expressed in grams or kg.The relationship between moles and moles as:

n = w/M

Where

• n = number of moles.
• w = mass of gas in grams.
• M = molecular mass of the gas.

### Volume:

Volume is expressed in ml or cm3 and  dm3.

1m3 = 103 litre = 103 dm3 = 106 cm3.

### Pressure:

The pressure of a pure gas is measured by manometer while that of a mixture of gases by a barometer. Pressure (force per unit area) is expressed in different units, viz. atmosphere, bar, torr etc. One atmosphere is the pressure exerted by exactly 76 cm or 760 mm of mercury at 0°C (density = 13.5951 g/cm3) at standard gravity (9.81 ms-2). 1 atm = 760 torr, 1 mm = 1 torr,  1 atm  ≈ 1 bar

C.G.S. units of pressure is dynes cm-2.

SI units of pressure is Newtons m-2 (Nm-2) = Pascal (Pa)

• 1 atm = 1.013 x 106 dyne cm-2
• 1 atm = 1.013 x 105 Nm-2. (Pa)
•  1 atm= 101.321 x 103 Pa
• = 101321 kPa = 102k Pa

A higher unit of pressure is bar (1 atm = 1.01325 bar)

1 bar = 105 Pa = 105 Nm-2 = 1010dyne.
Refer to the video for pressure and volume of gases

### Temperature:

It is a degree of hotness or coldness.SI unit of temperature is Kelvin K.

• K = oC + 273.5
• F = (9/5) oC + 32

## Nature of R(Constant) in ideal gas law equation

From the gas equation, Thus R represents work done per degree per mole

The value of R.  The value of R (gas constant) in the various units are given below.

• R = 0.0821 litre-atm/KJ/mole
•     =  8.314 x 107 ergs/K/mole
•     =  8.314 joules/K/mole
•     =  1.99 calories/K/mole
•     =  0.002 kcal/K/mole
•     =  5.189 x 1019 eV/K/mole
•     =  8.314 Nm/K/mole
•     =  8,314 kPadm3/K/mole
• R =  8.314 MPa cm3/K/mole

Gas constant for a single molecule is called Boltzmann constant (k)

R/N =K

values of k

• k= 1.38 x 10-16 erg/deg-abs/molecule
• k= 1.38×10-23 Joule/deg-abs/molecule

For ‘n’ moles of a gas, the equation becomes PV = n RT

Initial pressure P1, volume V1 and temperature T1 of a gas may be related with the final pressure P2, volume V2 and temperature T2 as below. ## Application of ideal gas law equation

### Calculation of mass and molecular weight of the gas • where m = Mass of the gas.
• M = Mol. wt. of the gas.

### Calculation of density Since M and R are constant for a particular gas,

Thus dT/P = constant

P Thus, at two different temperature and pressure This is  Ideal Law Equation.

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