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# Dimensions of Gas constant

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## Dimensional Formula of Gas Constant

The dimensional formula of Universal Gas Constant is represented as:

[M¹ L² T⁻² K⁻¹]

Where,

• M denotes the mass

• L denotes the length

• T denotes the time

### Derivation of Gas Constant

Since,

Pressure × Volume = Total moles × Temperature × Gas Constant

Therefore,  we calculate the dimension of universal gas constant with the use of the following:

Gas Constant = Pressure × Volume × [Total moles × Temperature]⁻¹ . . . .  (i)

The dimensional formula of temperature and volume = [M⁰ L⁰ T⁰ K¹] and [M⁰ L³ T⁰] . . .(ii)

Since, Pressure = Force × [Area]⁻¹

P = M × a × [Area]⁻¹ = [M × LT⁻² × L⁻²]

Therefore, the dimensions of pressure = [M¹ L⁻¹ T⁻²] . . . (iii)

On substituting equation (ii) and (iii) in equation (i) we get,

Gas Constant = Pressure × Volume × [Total moles × Temperature]⁻¹

Or, G = [M¹ L⁻¹ T⁻²] × [L³] × [K¹]-1 = [M¹ L² T⁻² K⁻¹].

Therefore, the universal gas constant dimensional formula is represented as

[M¹ L² T⁻² K⁻¹].

### Perfect Gas Equation of General Gas Equation and Specific and Universal Gas Constant

We know that,

According to Gay Lussacc’s law, P is directly proportional to T………(i)

According to Charle’s law, V is directly proportional to T…………..(ii)

Combining both the equations, PV is directly proportional to T or PV= Constant * T

If mass of the gas is measured in kg or gm, the constant used is ‘k’, then,

PV= KT (Ideal Gas Equation)

Here, k is a gas constant depending upon the mass of a gas.

For 1 kg or gas, K is called a specific gas constant if the mass of gas is 1 kg-mole or 1 gm-mole, then constant k will be the same as value for all gases.

Therefore, K is replaced by R, known as universal gas constant.

Therefore, PV = RT--------(iv)

It is the general gas equation.

R= $\frac{Mass \ast Length^{2}}{Amount \ast temperature\ast (time)^{2}}$

R = 8.314462618... kg⋅m2⋅s−2⋅K−1⋅mol−1.

### What is Universal Gas Constant?

Universal Gas Constant is also known as the molar gas constant, ideal gas constant or universal gas constant. It is denoted by the symbol R. It is equivalent to the Boltzmann constant and can be expressed in units of energy per temperature per mole.

PV= nRT or PV= mRT

N is the number of moles and M is the mass

Universal Gas constant is named so because it is the same for all gases. It can also be derived from another theory called microscopic kinetic theory, as it was achieved (apparently independently) by August Krönig in the year 1856 and Rudolf Clausius in the year 1857.

### Determination of Universal Gas Constant

Firstly, the experimental value of Boyle's law constant is determined with the help of the product of pressure P and volume V for a constant temperature T and a fixed mass m of air. After knowing these values, the universal gas law constant R is calculated from the equation PV = nRT.

### What is Specific Gas Constant?

The specific gas constant of a gas or for a mixture of gases (Rspecific) is represented by the molar gas constant divided by the molar mass (M) of the gas or mixture.

Rspecific = R/M