Molar Gas Constant

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What is R in Physics?

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Molar gas constant also known as gas constant, the universal gas constant, or the ideal gas constant is a fundamental physical constant that arises in the formulation of general gas laws. The molar gas constant is denoted by the symbol R. It is equivalent to the Boltzmann Constant. R can also be defined as Avogadro Number multiplied by Boltzmann Constant. However, instead of energy per temperature increment of a particle, it is expressed in terms of energy per temperature increment per mole which is also equivalent to the pressure-volume product. This constant features in fundamental equations of physics like the ideal gas laws equations, the Arrhenius Equation and the Nernst equation.

The origin of the symbol R for the ideal gas constant is probably in honour of French chemist Henry Regnault who is known for his measurements of thermal properties of gases.

Units of Ideal Gas Constant

The SI unit of the ideal gas constant is Pascal or newton per metre. It can also be written as joule per mole per Kelvin.

Molar Gas Constant Value

The molar gas constant is a combination of Boyle's law, Charles law, Gay-Lussac’s law and Avogadro's number. It relates the energy scale to the temperature scale in physics. The value of gas constant:

R = 8.3144598(48) J.mol−1.K−1

Dimension of Gas Constant

We find the dimensions of the ideal gas constant from the ideal gas equation which is given by:

PV=nRT, Here P is the pressure of the gas, V is the volume of the gas, T is the temperature of the gas on an absolute scale and n is the number of moles of the given gas. 

Hence, Gas Constant Formula can be written as:

R= PV/nT

Now substitute pressure as force per unit area for deriving the dimensions of R. 

Now, R= {(force/ area) × volume}/{mole × temperature)  ……(i)

For volume, we take it as the cube of length and for the area, we take it as length square. We substitute n as the mole. Force can be written as mass per unit acceleration which is equal to mass into length per unit square of time. 

R= {(mass × length/ length2 × time2) × (length)3}/ mole × temperature;

R= [ML-1T-2] × [L3]/ [mol] × [K]

Hence the dimensions of R is [ML2T-2K-1mol-1]

Also, from equation (i) we can see that, 

R= {(force/ length2) × length3}/ {mole × temperature}

R= force × length/ mole × temperature

R= work/ mole × temperature

Thus, the universal gas constant can be defined also in terms of work. It is work per unit mole per degree. Hence the expression of gas constant in Joules per mole per Kelvin is justified. 

Specific Gas Constant

The Specific Gas Constant of a particular gas or a mixture of gases is calculated by dividing the molar gas constant by the molar mass of the gas or the mixture. The application of specific gas constants is in the field of engineering especially. 

Rspecific = R/M

The specific gas constant can be related to the Boltzmann constant just like the Universal gas constant, by dividing it with the molecular mass of the gas or the mixture. 

Rspecific = kb/m

Well, another important thermodynamic equation related to the specific gas constant is Mayer’s relation. 

Rspecific = cp- c

Here cp is the specific heat capacity of gas at constant pressure whereas cv is the specific heat capacity of the gas at constant volume. 

The knowledge of the universal gas constant is indispensable for various calculations related to the ideal gas formula and other applications in physical sciences.

Did You Know?

In 2006, the most precise measurement of R was done by measuring the speed of sound ca(P, T)  in  room temperature of the triple point of water at various pressures and on extrapolating the value of R obtained was 

Ca(0,T)= (Y0RT/AR (Ar) Mu)1/2

Here, Y0 is the heat capacity ratio which is 5/3 for monoatomic gases like argon. T is the temperature which is the triple point of water, AR (Ar) is the relative atomic mass of argon and Mu is 10-3 kg per mole. 

This equation gives the exact precise value of R.

FAQ (Frequently Asked Questions)

1. What is the Molar Gas Constant?

Molar gas constant or universal gas constant is a constant obtained from combining Boyle's law, Charles law, Gay-Lussac’s law and Avogadro's number to solve various equations in physical sciences like ideal gas laws, Arrhenius equation and the Nernst equation. The value of the universal gas constant is 8.3144598(48) J.mol−1.K−1 This proportionality constant relates the energy scale in physics to the temperature scale. It is an essential constant for the calculation of various thermodynamic properties like entropy, molar heat capacities, etc.

2. What are the Differences Between Ideal Gas and Real Gas?

The differences between real gas and ideal gas are as follows: 

Ideal Gases

Real Gases

An ideal gas has no definite volume

Real gases have a definite volume

Ideal gases experience a perfectly elastic collision of particles.

Real gases experience non-elastic collisions between particles.

Ideal gases do not have any interactive molecular forces operating between them.

Real gases have interactive molecule attractions operating between the molecules.

Ideal gases obey the ideal gas laws 

Real gases do not obey the ideal gas laws.

Ideal gas doesn't exist in reality. The concept is hypothetical.

Real gases exist in the environment.

3. What is an Ideal Gas?

We can define an ideal gas as a gas which obeys all the gas laws at all conditions of pressure and temperature. Ideal gases have mass and velocity while they lack volume. Ideal gases do not condense and lack a triple point. Ideal gases are said to have no intermolecular forces of attraction between the gas molecules and the particles experience a completely elastic collision. However, the concept of an ideal gas is hypothetical and they do not exist in the environment. Instead, real gases exist in the environment which has a certain volume and intermolecular forces amongst them. These gases do not obey the gas laws completely. The gas laws need certain modifications for the real gases to obey them.