# The dimensional formula of gas constant 'R' is

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The dimensional formula of gas constant 'R' is
1. MLT2K-1
2. ML2T-2
3. ML-1T-1K-1
4. ML2T-2K-1

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Correct Answer - Option 4 : ML2T-2K-1

Concept:

• Gas constant(R): It is the constant of proportionality that relates the energy scale in physics to the temperature scale, when a mole of particles at the stated temperature is being considered.
•  As a consequence, the value of the gas constant is also exactly defined, at precisely 8.3144 J/mol-K.
• Ideal gas: It is a hypothetical gas, consisting of molecules that are having negligible volume and their collision is perfectly elastically (means no loss of energy) and obeys gas law.

The gas law P V = n R T

Where P = pressure of the gas, V = volume of the gas, n = moles of the gas, R = 8.31 J/mol-K (Universal gas constant), and T = temperature of the gas.

Explanation:

We have the gas law

P V = n R T

⇒ Pressure × Volume = Total moles × Temperature × Gas Constant

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

The dimensional formula of temperature and volume = [M0 L0 T0 K1] and [M0 LT0] . . . . (2)

Since, Pressure = Force × [Area]-1

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

∴ the dimensions of pressure = [M1 L-1 T-2] . . . . (3)

On substituting equation (2) and (3) in equation (1) 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 gas constant is dimensionally represented as [M1 LT-2 K-1].