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# Molar Gas Constant

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Last updated date: 12th Aug 2024
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## What is R in Physics?

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 the 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:

$R= \frac{PV}{nt}$

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

Now, $R= \frac{\frac{\text{Force}}{\text{Area}}\times \text{volume}}{\text{Mole} \times \text{Temperature}}$ ……(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.

$R= \frac{\frac{\text{mass} \times \text{length}}{{\text{length}^{2}}\times \text{time}^{2}}\times \text{(length)}^3}{\text{mole} \times \text{temperature} }$

$R = \frac{[ML^{-1}T^{-2}]\times[L^3] }{mole} \times K$

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

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

$R= \frac{\frac{\text{force}}{\text{length}^{2}}\times \text{length}^3}{\text{mole} \times \text{temperature}}$

$R= \frac{\text{force}\times \text{length}}{\text{mole}\times \text{temperature}}$

$R = \frac{\text{work}}{\text{mole}}\times \text{temperature}$

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.

R$_{specific} = \frac{R}{M}$

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.

R$_{specific} = \frac{k_{b}}{m}$

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

R$_{specific} = c_{p} - c_{v}$

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)$^{\frac{1}{2}}$

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.

## FAQs on Molar Gas Constant

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 gas

• An ideal gas has no definite volume.

• Ideal gases experience a perfectly elastic collision of particles.

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

• Ideal gases obey the ideal gas laws.

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

Real gas

• Real gas has a definite volume.

• Real gas experiences non-elastic collisions between particles

• Real gas has interactive molecule attractions operating between the molecules.

• Real gas does not obey the ideal gas laws.

• Real gas exists in the environment.

3. What is an ideal gas?

We can define an ideal gas as a gas that 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.

4. What is the ideal gas law?

The ideal gas law also known as the general gas equation, is an equation of the state of a hypothetical ideal gas. The ideal gas law was derived by the French engineer and physicist Benoit Paul Émile Clapeyron in 1834 as a combination of the empirical Charles’s law, Avogadro’s law and Boyle’s Law.

The ideal gas law has several limitations, but it is good for deriving the approximate behaviour of many gases under several conditions.

The ideal gas law basically says that the product of the pressure and the volume of one gram molecule of an ideal gas is equal to the product of the universal gas constant and absolute temperature of the gas.

Ideal gas law units

When we use the gas constant R = 8.31 J/K.mol, then the pressure (P) is in the unit of pascals (Pa), volume in the unit of m3 and the temperature T in the unit of kelvin K.

When we use the gas constant R = 0.082 L.atm/K.mol then pressure is in the unit of atmospheres (atm), volume is the unit of a litre (L) and the temperature T in the unit of kelvin (K).

Derivation of the Ideal Gas Law

The ideal gas law combines the observations of Robert Boyle, Gay-Lussac and Amedeo Avogadro. Combining them in a single expression we get the Ideal gas equation which describes all the relationships simultaneously.

The three individual expressions are as follows:

Boyle’s Law

V ∝ 1/P

Charles’s Law

V ∝ T

V ∝ nT/P

Combining these three expressions, we get

V ∝ nT/P

This equation presents that volume is proportional to the moles and the temperature, and inversely proportional to the pressure.

V = RnT/P = nRT/P

From this, we get the ideal gas equation which is:

PV = nRT

5. What is the molar mass of the gas?

Molar mass (M) is equal to the mass of one mole of a particular element or compound. Molar mass, also referred to as molecular weight, is expressed in units of grams per mole (g mol–1). The molar volume of all gases is the same when they are measured at the same temperature and pressure, but the molar mass of different gases mostly varies. Knowing the molar mass of a compound or an element helps balance a reaction equation.

The molar mass of any gas is equal to the mass of a single particle of that gas multiplied by Avogadro’s number, which is 6.02 x 1023

Here’s how to calculate the Molar Mass using the Ideal Gas Equation:

The molar mass of an ideal gas can be calculated using a derivation of the Ideal Gas Law: PV = nRT

But how do you find the molar mass of a mixture of gases? Well, you need to take into account the molar mass of each gas in the mixture, and also their relative proportion. So, the average molar mass of a mixture of gases is equal to the sum of the mole fractions of each gas (xi), multiplied by their respective molar masses (Mi). Therefore, ⁻M = ∑i xi Mi.