Matter and Energy

Gas Constant

The gaseous state is the most simplified state of matter. Gas is highly compressible in nature, however, it has a uniform distribution of pressure on all sides. Being shapeless and without any fixed volume, they take the shape of the container they are placed into. Additionally gas is very easily mixable due to the negligible interaction of the intermolecular forces.  The characteristic trait of all Gases is mainly governed by a few sets of laws. These laws were derived on the basis of the experimental studies conducted on the behavioural pattern of gas under various conditions like pressure, temperature, and volume. Further, we will study about gas constant in detail.

Gas Constant

Gas Constant

Introduction to Gas Constant

Definition: Gas constant is the general constant in an equation of a gaseous state which is equivalent to the product of the pressure and volume of one mole divided by absolute temperature. 

Gas constant is also referred to by other scientific names like Molar Gas Constant, Universal Gas Consent, and Ideal Gas Constant. It is denoted by the symbol R. Gas constant is similar to Boltzman constant, however, it is represented in energy per degree temperature increment per mole.

  • Boltzmann Constant is defined as the proportional factor that relates the average relative kinetic energy of particles and the temperature in a gas.

However, in the case of the Boltzmann constant instead of mole value (product of volume and pressure) particle value is used.

Gas Constant is an important relatable factor of numerous laws and Principles of Physics. It is used as a combination constant in various laws and as fundamental factors in equations.

  • Boyle’s Law – The pressure (P) of a gas increases as the volume (V) decreases. Mathematically it can be expressed as P is inversely proportional to V
  • Charles Law – Gas volume expands due to the rising temperature (T) despite the constant pressure. Hence mathematically V is proportional to T.
  • Avogadro’s Law – Equal volume of all gas at the same temperature and pressure have the same number of molecules
  • Gay Lussac’s law – The pressure of a given mass of gas varies directly with the absolute temperature of the gas when the volume is kept constant.

Ideal Gas Law

It is a combination of Boyle’s Law, Charles Law, and Avogadro’s law.  However every gas has its own innate features and properties, so it is difficult to acknowledge all the gases under these 3 laws. Therefore an ideal gas that combines the 3 laws, as well as binds with the structural integrity of all gases, is considered the specimen data for analysis.

Ideal Gas

An Ideal Gas is a theoretical representation of a gas that is composed of point particles that do not show any changes during intermolecular movements. This gas represents all the 3 primary laws as stated by Boyle, Charles, Gay Lussac and Avogadro

Hence,

From Boyle’ law – V ∝ 1/P where T and n are constant

From Charle’s Law – V ∝ T where P and n are constant

Finally, from Avogadro’s Law – V ∝ n where T and n are constant

Thus combining all will give us V ∝ n X T/P

Therefore, mathematically we can express it as:

PV = nRT 

Where,

P stands for pressure

V stands for Volume

T stands for temperature

R stands for Ideal Gas Constant

&

n stands for the amount of substance

An Ideal gas equation occurs when all the 3 laws can be combined together in a single equation. It is referred to as the relation between four variables and it describes the state of any gas, therefore, it is also called the equation of state.

Gas Constant Value

Gas constant Value is the denominating constant value used to show the relations between energy and temperature scale. One mole at a predefined temperature is considered the proportionality constant value.

As mentioned before Gas constant is a combination of various laws that results in the final value of R (gas constant).

Hence,

R = 8.3144598(48) J⋅mol−1⋅K−1

However, PV= RT is only valid under low temperatures. 

For dilute gas, the equation will be

PV = μRT where μ denotes the number of moles in the given quantity of sample gas. With increasing pressure, on a constant volume of gas, the temperature change can be seen is in a linear manner. This is known as the Absolute Temperature.

Valuation of the Universal Gas Constant R

As mentioned above, Universal Gas Constant is represented as R, also known as Ideal Gas Constant.

The representation unit of R is energy per mole per Temperature. The value of R is directly dependent on the units of measurement of P, V, and T. Thus, if the value of the 3 is known, calculating R is also possible.

As we know PV = nRT

Therefore R = n T V P 

The volume of one mole of an Ideal gas is 22.710981 L mol–1

Therefore as per the SI Unit, the standard value of R is 8.314 joule/mole/kelvin 

R = 8.31432joules mol−1⋅K−1.

As energy is represented using various other terms also, therefore the value changes from joules to calories also in some other format.

The Dimensional Formula of Gas Constant

Gas constant has a specific dimensional formula that is represented as 

[M1L2T-2K-1]

Where,

M stands for Mass, L stands for Length, & T stands for Time

We know that, 

The product of Pressure and Volume is equivalent to the product of total mole, temperature, and the Gas Constant

Therefore, Gas Constant is equal to the product of pressure, and  volume  along with the inverse value of  total mole and temperature

Or

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

FAQ on Gas Constant

Question 1: What is an Ideal gas?

Answer 1: Ideal Gas is a theoretical representation of a gas that is composed of point particles that do not show any changes during intermolecular movements.

There are three types of Ideal gas:

  1. Maxwell Boltzmann Ideal gas
  2. Bose Gas
  3. Fermi Gas

Question 2: What is R?

Answer 2: Universal Gas constant is represented as R. Due to its constant presence in various equations R can be represented as various units

Question 3: What is Avogadro’s Hypothesis?

Answer 3: Avogadro’s Hypothesis states that ‘for a given mass of an ideal gas, the volume of gas is directly proportional to the amount (mole) of gas when the pressure and temperature are constant.

Avogadro’s Hypothesis is one of the primary factors for determining the Ideal Gas Constant.

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