# 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

- Mass
- Volume
- Pressure
- 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 cm** ^{3} **and

**dm**

^{3}.

1m^{3} = 10^{3} litre = 10^{3} dm^{3} = 10^{6} cm^{3}.

### 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/cm** ^{3}**) 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

**) = Pascal (Pa)**

^{-2}- 1 atm = 1.013 x 10
dyne cm^{6}^{-2} - 1 atm = 1.013 x 10
Nm^{5}. (Pa)^{-2} - 1 atm= 101.321 x 10
^{3}Pa - = 101321 kPa = 10
^{2}k Pa

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

1 bar = 10^{5} Pa = 10** ^{5}** Nm

**= 10**

^{-2}^{10}dyne.

**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 =
^{o}C + 273.5 - F = (9/5)
^{o}C + 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 10
^{7}ergs/K/mole - = 8.314 joules/K/mole
- = 1.99 calories/K/mole
- = 0.002 kcal/K/mole
- = 5.189 x 10
^{19}eV/K/mole - = 8.314 Nm/K/mole
- = 8,314 kPadm
/K/mole^{3} - R = 8.314 MPa cm
/K/mole^{3}

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

*R/N =K*

values of k

- k= 1.38 x 10
erg/deg-abs/molecule^{-16} - k= 1.38×10
Joule/deg-abs/molecule^{-23}

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

Initial pressure P_{1}, volume V_{1} and temperature T_{1} of a gas may be related with the final pressure P_{2}, volume V_{2} and temperature T_{2} 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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