Gas Constant: Exploring its Formula, Laws, and Applications

Gas Constant

One of the most important states of matter is the gaseous state or gas constant. Although gas is highly compressible, the pressure is uniformly distributed on all sides. Being without shape and volumeless, they adapt to the shape of the container they are in. Gases are also readily miscible as there is negligible interaction between the intermolecular forces.

A few sets of laws govern the characteristic traits of all gases. These laws were based on experimental studies on the behavioral pattern of gases under different conditions like temperature, pressure, and volume. This discussion is focused on this constant and its value. 

It is denoted by R. It is a physical constant expressed in terms of units of energy per temperature increase per mole. Also called the molar gas constant or universal gas constant, It has a value equal to that of the Boltzmann constant, but that one is expressed in terms of pressure-volume product. 

Gas Laws 

The gas constant r is a vital factor for numerous principles and laws of physics. It is used in various laws as a combination of a constant and equations as a fundamental factor. 

Boyle’s Law 

It states that as the volume of a gas decreases, its pressure increases. In mathematical terms, it is denoted by P and is inversely proportional to V.

Charles Law 

The volume of gas expands because of the increase in temperature (T) in spite of the constant pressure. Therefore, V is proportional to T in mathematical terms.

Avogadro’s Law 

All gases of equal volume at the same pressure and temperature have the same number of molecules.

Gay Lussac’s law

The pressure of a certain mass of a gas is directly proportional to the gas’s absolute temperature if we keep the volume constant.

Ideal Gas Law

The ideal gas law is a combination of Charles’ law, Boyle’s law, and Avogadro’s law. As every gas has unique properties, it is challenging to fit all gases under these three laws. Thus, an ideal gas that follows all three laws and binds with the structural integrity of all gases is taken as the specimen for analysis. 

Ideal Gas

An ideal gas can be defined as the theoretical representation of a gas comprising point particles that do not reveal any alterations during intermolecular movements. The ideal gas follows all three fundamental laws as given by Charles, Avogadro, Boyle, and Gay Lussac. 

V ∝ 1/P with T and n as constant (From Boyle’s law)

V ∝ T with P and n as constant (From Charles law)

Finally, V ∝ n with T and n as constant (From Avogadro’s law)

Combining all three of these gives V ∝ n X T/P

Mathematically, this can be expressed as,

PV = nRT 

Here, 

P is the pressure

V is the volume

T is the temperature

R is the Ideal Gas Constant, and

n is the amount of substance

When all three laws are combined into one equation, an ideal gas constant equation results; it implies the relation between four variables and describes any gas’s state. Therefore, it is also known as the equation of state. 

Gas Constant in Different Units

There are diverse applications of the gas constant r. Therefore, it is used in terms of many units. Some values of it in various units are given below: 

Value of Gas Constant	Units
8.3144598(48)	J⋅K−1⋅mol−1
8.3144598(48)×103	amu.m2.s-2.K
8.3144598(48)×10-2	L.bar.K-1.mo
8.3144598(48)	m3.Pa.K-1.mol-1
62.363577(36)	L.Torr.K-1.mol-1
1.9872036(11)×10-3	kcal.K-1.mol-1
8.2057338(47)×10-5	m3.atm.K-1.mol-1
0.082057338(47)	L.atm.K-1.mol-1

Gas Constant Value

 In Physics, it is a proportionality constant that relates the temperature scale to the energy scale when we consider one mole of particles at a defined temperature. The ideal gas constants have been derived by combining Avogadro’s number, Gay-Lussac’s law, Boyle’s law, and Charles’s. Therefore, the value of the gas constant R is given by: 

R = 8.3144598(48) J⋅mol⁻¹.k^-1

Inside the parentheses, the digits are the uncertainty in the measurement of the value of the ideal gas constants. 

R Constant for Atm

The R constant for atm in the US Standard Atmosphere is given as:

R = 8.31432joules mol⁻¹⋅K^−1.

Specific Gas Constant

It is the ratio of the molar gas constant or R to the molar mass or (molecular weight) M of the gas mixture. It is denoted by Specific and is expressed mathematically as:

Rspecific = R/M

Dimensions

The universal gas constant R can be expressed by using the ideal gas equation PV = nRT as,

R = PV/nT

Here,

P stands for pressure

n denotes the number of moles

V stands for volume

T stands for temperature 

The dimensional expression for R can be derived by writing pressure as force per unit area, 

Volume and area can be expressed in terms of length as,

Volume = (length)^{3, and}

Area = (length)²

R = work/ amount * temperature 

Therefore, we can interpret the universal gas constant as work per degree per mole. 

Valuation of the Universal Gas Constant R

As discussed earlier, the Universal Gas Constant is denoted by R. It is also called the Ideal Gas Constant. Its value directly depends on the units of measurement of V, P, and T. Therefore, if we know the value of these three, we can calculate R. 

We know that,

 PV = nRT

So, R = n T V P 

For an ideal gas, the volume of one mole is 22.710981 L mol^–1. Therefore according to the standard SI Unit, the value of R is 8.314 joule/mole/kelvin.

R = 8.31432joules mol⁻¹⋅K⁻¹.

As energy can be represented by using several other terms as well, the value alters from joules to calories in some other format as well. 

The Dimensional Formula of Gas Constant

There is a specific dimensional formula for it as follows:

[M¹L²T^-2K^-1]

Here,

M is for mass

L is for length

T is for time

We know, 

The product of volume and pressure is equal to that of the temperature, total mole, and Gas Constant. Thus, it equals the product of volume and pressure, along with the inverse value of total temperature and mole. 

Or, G = [M¹ L^-1 T^-2] × [L^3] × [K^1]-1 =[M¹L² T^-2 K^-1].

Specific Gas Constant

A specific of it may be indicated by R or Rgas. It is the universal gas constant divided by the molar mass (M) of pure gas or mixture. As the name suggests, the specificity of it is constant for a particular gas or mixture. On the other hand, the universal gas constant remains constant for an ideal gas.

Specific Gas Constant

Specific for dry air	Unit
287.058	J⋅kg−1⋅K−1
53.3533	ft⋅lbf⋅lb−1⋅R−1
1,716.49	ft⋅lbf⋅slug−1⋅R−1

The Specific Gas Constant of one or more gases is mathematically given by the division of the molar gas constant with the molar mass of the single gas or the mixture of gases. 

Rspecific = R/M

Just like we can relate the ideal gas constant to the constant of Boltzmann, can we relate the specific this by carrying out the division of the Boltzmann constant by the gas’s molecular mass? 

Rspecific = kB/m

Another significant relationship is established on the basis of thermodynamics. The specific of it is related by Mayer’s relation to the specific heat capacities for a calorically and thermally perfect gas. 

Rspecific = cp – cv

Here, at constant pressure, cp is the specific heat capacity, and at constant volume, cv is the specific heat capacity.

It is common to represent the specific gas constant by the symbol R, especially in engineering applications. In such situations, a different symbol such as R is usually given to the universal gas constant to distinguish it. 

Conclusion

Hope this discussion helped clear all your doubts and strengthened your fundamental understanding of the concepts regarding it. Try solving mathematical problems on this topic to broaden your knowledge of it further. 

Frequently Asked Questions

1. What is an ideal gas?

An ideal gas is a representation of a gas theoretically that comprises point particles that do not reveal any changes during intermolecular movements. Ideal gases are of three types— Bose Gas, Maxwell Boltzmann Ideal Gas, and Fermi Gas. 

2. What is Avogadro’s Hypothesis?

Avogadro’s hypothesis says that for an ideal gas of a given mass, the amount of the gas in moles is directly proportional to the volume of gas when the temperature and pressure are constant. This hypothesis is one of the major factors that determine the Ideal Gas Constants. 

3. Why is R used to denote gas constants?

It is assumed by many that the symbol R is employed to denote, to honor the French scientist Henri Regnault, who carried out experiments that first determined the constant. However, if his name was the real origin of the system to use R to denote the Gas Constants or not is unclear.