Gas Constant: Value, Dimension, Law and Sample Questions

The Gas Constant is a universal constant expressed in terms of units of energy per temperature increment per mole. It is denoted by the symbol ‘R’. The ideal gas constant is the combination of Gas Laws i.e. Boyle’s law, Charles’s law, Avogadro’s Law, and Gay-Lussac’s law.

• It is also known as the Molar gas constant or Ideal gas constant.
• The gas constant is molar equivalent to the Boltzmann constant, expressed in units of energy per amount of substance per increment in temperature.

• It is a physical constant featured in many fundamental equations in the physical sciences. These equations include the ideal gas law, the Nernst equation, and the Arrhenius equation.

Key Terms: Pressure, Volume Temperature, Avogadro constant, Boltzmann constant, Energy, Mole, Boyle’s law, Charles’s law, Gay-Lussac’s law.

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Gas Constant

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The Gas Constant (also known as Molar Gas Constant, Ideal Gas Constant, or Universal Gas Constant) is a universal constant denoted by the symbol ‘R’. It is expressed in terms of units of energy per temperature increment per mole.

• The gas Constant is the molar equivalent to the Boltzmann Constant with the pressure-volume product.
• The gas constant is the constant of proportionality that links energy, temperature, and substance amounts in physics.
• The gas constant value derives ultimately from historical decisions and accidents in the definition of units of energy, temperature, and substance amount.
• The gas constant R is defined as the product of Avogadro constant N_A and the Boltzmann constant k (or k_B):

R = N_Ak

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Value of Gas Constant

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The gas constant is a proportionality constant that is used to relate the energy scale to the temperature scale when one mole of gas particles is considered at a definite temperature.

• The value of the Gas Constant depends on the Gas Laws i.e. Boyle’s Law, Charle’s Law, Gay-Lussac’s Law, and Avagadro’s Law.
• It is defined as the product of Avogadro's Constant (NA) and Boltzmann Constant (k). 

R = N_ak

Putting in the values of Avagadro’s Constant and Boltzmann Constant, we get

R = 8.31446261815324 JK^-1mol^-1

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Value of Gas Constant in Different Units

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The value of the Gas Constant is used differently in different equations. The value of the Gas Constant in different units is as follows:

U.S. Standard Atmosphere

The Gas Constant R is defined by the U.S. Standard Atmosphere (USAA 1976) as follows: 

R = 8.31432 x 10³ N m kmol^-1 K^-1 = 8.31432 J K⁻¹ mol⁻¹

• This value is not consistent with the cited values for the Boltzmann constant and Avogadro constant, according to the acknowledgment of the USSA1976.
• Despite this discrepancy, USSA1976 uses this value of R for all calculations of the standard atmosphere.

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Dimensions of Gas Constant

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Consider the Ideal Gas Equation

PV=nRT 

⇒ R = PV / nT

where

• P = Pressure
• V = Volume
• T = Temperature
• n = Number of Moles

We know that Pressure = Force / Area. Therefore, the expression becomes

Converting area and volume into length, we get 

Now, force multiplied by length is work. Therefore 

\(R = \frac {work} {amount * temperature}\)

Finally, we can interpret the Gas Constant as work per degree per mole. 

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Specific Gas Constant

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Specific Gas Constant can be obtained by dividing the molar gas constant by molar mass (M). It is denoted by R_Specific and mathematically expressed as:

R_Specific = R / M

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Gas Laws

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There are four Gas Laws which when combined give a universal relation that holds to approximation for all gases. These four Gas Laws are listed below. 

Boyle’s Law: 

Boyle’s Law states that the volume of a gas is inversely proportional to the pressure exerted by the gas at a constant temperature.

V ∝ 1 / P

P ∝ 1 / V

⇒ PV = constant 

⇒​ P₁V₁ = P₂V₂ 

where 

• P = Pressure
• V = Volume

Charle's Law 

Charle’s Law states that the volume of a gas is directly proportional to the temperature (in Kelvin) of the gas in a closed container. 

V ∝ T

V / T = constant 

⇒ V₁ / T₁ = V₂ / T₂

where 

• V = Volume
• T = Temperature

Gay-Lussac’s Law

Gay-Lussac’s Law states that the temperature of a gas (in Kelvin) is directly proportional to the pressure exerted by the gas. 

P ∝ T

⇒ P / T = constant

⇒ P₁ / T₁ = P₂ / T₂

where 

• P = Pressure
• T = Temperature

Avogadro’s Law

Avogadro's Law states that the volume occupied by a gas is directly proportional to the number of moles of the gas at constant temperature and pressure. 

V ∝ n

⇒ V / n = constant

⇒ V₁ / n₁ = V₂ / n₂

where 

• V = Volume
• n = Number of Moles

Ideal Gas Equation

After combining all four Gas Laws, the final expression is 

PV = nRT

where 

• P = Pressure
• V = Volume
• n = Number of Moles
• R = Gas Constant
• T = Temperature 

The above-mentioned expression is called the Ideal Gas Equation. 

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Things to Remember

• The gas Constant is a universal constant denoted by R.
• The Gas Constant is also known as Molar Gas Constant, Ideal Gas Constant, and Universal Gas Constant.
• The value of the Gas Constant is R = 8.31446261815324 JK^-1 mol^-1. 
• The dimensions of the Gas Constant can be interpreted as work per degree per mole.
• Specific Gas Constant is denoted as RSpecific = R / M. 
• There are four Gas Laws: Boyle’s Law, Charle’s Law, Gay-Lussac’s Law, and Avagadro’s Law.
• Boyle’s Law states that the volume of a gas is inversely proportional to the pressure exerted by the gas at a constant temperature and mathematically, it is derived as, P₁V1 = P₂V₂ 
• Charle’s Law states that the volume of a gas is directly proportional to the temperature (in Kelvin) of the gas in a closed container. Mathematically, V₁ / T₁ = V₂ / T₂
• Gay-Lussac’s Law states that the temperature of a gas (in Kelvin) is directly proportional to the pressure exerted by the gas. It can be further derived as, P₁ / T₁ = P₂ / T₂
• Avogadro's Law states that the volume occupied by a gas is directly proportional to the number of moles of the gas at constant temperature and pressure. Also, expressed as V₁ / n₁ = V₂ / n₂
• Ideal Gas Equation- PV = nRT. Where, P = Pressure, V = Volume, n = Number of Moles, R = Gas Constant and T = Temperature