Gas Constant Value
The gas constant R also known as universal, molar or ideal gas constant is found in many contexts.
It relates energy and temperature.
It is equivalent to the Boltzmann constant, but expressed in units of energy per temperature increment per mole i.e., the pressure–volume, PV ,where energy is a product of pressure and volume.
In physics, the gas constant is a proportionality constant.
It relates the energy scale to the temperature scale, where a mole of particles at a given temperature is being considered.
The gas constant R is defined as the product of Avagadro’s number and the Boltzmann’s constant K given by,
R = Na x K
The value of R in typical energy units of Joules is calculated by taking exact numerical values of K and Na, expressed in SI units is,
R = 8.314 J /mol.K
Gas Constant R Value
The value of gas constant R is calculated by taking P at pascal or N/m^2, V at m^3, T in K and n in mol.
Where P is the pressure in Pa = 1.01325 x 105 Pa or N/m^2
V = 22.4 L at STP
Where V is the Molar volume of a gas at standard temperature and pressure.
= 22.4 x 10-3 m3
T = 273 K
n =1
Using ideal gas law: PV = nRT
(Images to be added soon)
R = PV/ nT = 1.01325 x 105 N/m2 x 22.4 x 10-3m3/1 mol x 273 K
1.01325 x 105 N.m x 22.4 x 10-3/1 mol x 273 K
Cancelling out common terms we get 1 N-m = 1 Joule
1.01325 x 105 x 22.4 x 10-3 J/1 mol x 273 K
On solving we get the value of gas constant R in SI unit
R = 0.083138 x 102 J/mol.K 〜 8.314 J/mol.K….(1)
Gas Constant In Calories
Since the value of 1 Calorie = 4.2 Joule
If 4.2 J = 1 calorie
Then, 1 J = 1/ 4.2 calories
Putting it in eq(1), we get,
R = 8.314/ 4.2 cal.mol-1 K-1
On solving we get,
R =1.975 Cal mol-1 K-1
Gas constant has various units corresponding to their values that is given below in tabular form:
Gas Constant Units
Universal Gas Constant
The universal constant is an ideal gas constant that we use to quantify the relationship between the properties of a gas.
The constant is symbolized as ‘R.’
Typically, R relates the pressure in atmospheres (atm), volume in liters (L), and temperature in Kelvin (K).
In this case, it has the value and units of:
R = 0.08206 L. atm / mol.K
R is same for all the gases.
Unit Of Universal Gas Constant
Let’s find out the value of R by using the ideal gas law:
PV = nRT
R = PV/nT
Unit of each quantity
P = Pressure and its unit is atm
V = Volume, unit = L
n = no of moles and unit is mol
T = Temperature in kelvin
= L.atm/ mol x K
Unit of universal gas constant R = L.atm/ mol.K
The dimensional formula for universal gas constant = [ML2T-2K-1]
Universal Gas Constant R Value
Taking n = 1
T = 273 K
P = 1 atm (atmospheric pressure)
V = 22.4 L at STP
Using ideal gas law equation and putting the values, we get
R = PV/nT
= 1 atmx 22.4 L/ 1 mol x 273 K
On solving we get the value of universal gas constant R in SI unit as:
R = 0.08206 atm L/ mol.K
FAQs on Gas Constant
1. What is the universal gas constant (R)?
The universal gas constant, denoted by the symbol 'R', is a fundamental physical constant that appears in the ideal gas law (PV = nRT). It serves as a constant of proportionality, linking the energy scale in physics to the temperature scale when a mole of particles is considered. It essentially quantifies the amount of work done by one mole of an ideal gas when its temperature increases by one Kelvin.
2. Why is the gas constant 'R' considered 'universal'?
The gas constant 'R' is called 'universal' because its value is the same for all ideal gases, regardless of their chemical composition, mass, or type. This universality arises because, under ideal conditions, the pressure and volume of a gas depend only on the number of particles (moles) and the temperature, not on the nature of the particles themselves.
3. What are the common values of the gas constant 'R' in different units?
The numerical value of 'R' depends on the units used for pressure, volume, and temperature. For the CBSE/NCERT 2025-26 syllabus, the most important values to know are:
- 8.314 J·K⁻¹·mol⁻¹ (in SI units, when pressure is in Pascals and volume is in cubic meters)
- 0.0821 L·atm·K⁻¹·mol⁻¹ (when pressure is in atmospheres and volume is in litres)
- 1.987 cal·K⁻¹·mol⁻¹ (approximately 2 cal·K⁻¹·mol⁻¹, when energy is measured in calories)
4. How is the gas constant 'R' related to the Boltzmann constant (k)?
The universal gas constant (R) and the Boltzmann constant (k) are deeply connected. 'R' is the gas constant on a per mole basis, while 'k' is the gas constant on a per molecule basis. The relationship is given by the formula R = Nₐk, where Nₐ is Avogadro's number (the number of particles in one mole). This equation bridges the macroscopic scale (moles) with the microscopic scale (individual molecules).
5. What is the difference between the universal gas constant (R) and a specific gas constant (R_specific)?
The key difference lies in what they apply to:
- The Universal Gas Constant (R) is the same for every ideal gas and is used in the ideal gas equation when the amount of gas is measured in moles (n).
- A Specific Gas Constant (R_specific) is different for each gas. It is used when the amount of gas is measured in mass (m). It is calculated by dividing the universal gas constant by the molar mass (M) of that specific gas: R_specific = R / M.
6. How do the gas laws lead to the concept of the gas constant?
The gas constant 'R' emerges from combining the three primary gas laws:
- Boyle's Law: V ∝ 1/P
- Charles's Law: V ∝ T
- Avogadro's Law: V ∝ n
When these proportionalities are combined into a single equation, we get V ∝ nT/P. To turn this proportionality into an equality, a constant is introduced, which is the universal gas constant 'R'. This gives us the final ideal gas equation: PV = nRT.
7. Can we use the ideal gas constant 'R' for real gases like air or oxygen?
While the ideal gas constant 'R' is strictly defined for ideal gases, it is often used as a close approximation for real gases under conditions of high temperature and low pressure. In these states, the interactions between gas molecules and their volume are minimal, causing them to behave much like an ideal gas. However, for high-precision calculations or at low temperatures and high pressures, more complex equations like the van der Waals equation, which includes correction factors, must be used.
