How to Apply the Molar Gas Constant in Physics Problems
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: Complete Guide for Students
1. What is the Molar Gas Constant (R) and what does it represent?
The Molar Gas Constant, denoted by the symbol R, is a fundamental physical constant that appears in many fundamental equations, most notably the Ideal Gas Law (PV = nRT). It acts as a proportionality constant that links the energy scale to the temperature scale for one mole of a substance. In essence, it represents the amount of work or energy per mole per unit of temperature change. It is also known as the universal gas constant or ideal gas constant.
2. What is the accepted value of the Molar Gas Constant (R) in SI units?
The officially accepted value of the Molar Gas Constant (R) in SI units is approximately 8.314 J·K⁻¹·mol⁻¹. This value is used when pressure is measured in Pascals (Pa), volume in cubic metres (m³), temperature in Kelvin (K), and the amount of substance in moles (mol). It is a crucial value for calculations in thermodynamics and physical chemistry as per the CBSE 2025-26 syllabus.
3. Why does the Molar Gas Constant (R) have different numerical values like 8.314 and 0.0821?
The Molar Gas Constant (R) is a universal constant, meaning its actual physical value doesn't change. However, its numerical value depends entirely on the units used for pressure, volume, and temperature in a calculation. The choice of which value to use depends on the units given in a problem.
- Use R = 8.314 J·K⁻¹·mol⁻¹ when pressure is in Pascals (Pa) and volume is in cubic metres (m³).
- Use R = 0.0821 L·atm·K⁻¹·mol⁻¹ when pressure is in atmospheres (atm) and volume is in litres (L).
- Use R ≈ 2 cal·K⁻¹·mol⁻¹ when dealing with energy in calories.
4. How is the dimensional formula for the Molar Gas Constant, [ML²T⁻²K⁻¹mol⁻¹], derived?
The dimensional formula for R is derived from the Ideal Gas Law equation, PV = nRT. By rearranging the formula to R = PV / nT, we can substitute the dimensions for each quantity:
- Pressure (P) = Force/Area = [MLT⁻²] / [L²] = [ML⁻¹T⁻²]
- Volume (V) = [L³]
- Amount of substance (n) = [mol]
- Temperature (T) = [K]
Substituting these into the equation for R gives:
R = ( [ML⁻¹T⁻²] × [L³] ) / ( [mol] × [K] )
Simplifying the terms, we get the final dimensional formula for R as [ML²T⁻²K⁻¹mol⁻¹].
5. What is the Ideal Gas Law and how does it relate to the Molar Gas Constant?
The Ideal Gas Law is a fundamental equation of state for a hypothetical ideal gas, expressed as PV = nRT. It describes the relationship between four key variables: pressure (P), volume (V), number of moles (n), and temperature (T). The Molar Gas Constant (R) is the constant of proportionality in this relationship. It serves as the essential bridge that connects these variables, ensuring the equation remains balanced across different units and conditions.
6. How does the Molar Gas Constant (R) differ from the Specific Gas Constant (R_specific)?
The primary difference lies in their scope of application.
- The Molar Gas Constant (R) is universal. It is the same for all ideal gases because it is based on the number of moles (a count of particles), not the mass or type of gas. Its value is approximately 8.314 J·K⁻¹·mol⁻¹.
- The Specific Gas Constant (R_specific) is not universal. Its value is different for each gas because it is defined per unit mass of the gas, not per mole. It is calculated by dividing the universal gas constant (R) by the molar mass (M) of the specific gas: R_specific = R / M.
7. Beyond the Ideal Gas Law, where else is the Molar Gas Constant applied in Physics and Chemistry?
While famous for its role in the Ideal Gas Law, the Molar Gas Constant (R) is a cornerstone in various other scientific principles and equations. Some key applications include:
- The Nernst Equation: In electrochemistry, it helps determine the cell potential under non-standard conditions.
- The Arrhenius Equation: In chemical kinetics, it relates the rate of a chemical reaction to temperature and the activation energy.
- Boltzmann's Constant (k_B): R is directly related to Boltzmann's constant through Avogadro's number (N_A), where R = k_B × N_A. This connects macroscopic gas properties to the kinetic energy of individual particles.
8. What is the physical significance of the Molar Gas Constant? Why is it called a "universal" constant?
The physical significance of the Molar Gas Constant (R) is that it represents the amount of work that one mole of an ideal gas performs when its temperature increases by one Kelvin under constant pressure. It's called "universal" because its value is the same for any gas that behaves ideally. This is because, according to Avogadro's Law, equal volumes of ideal gases at the same temperature and pressure contain the same number of molecules (moles), regardless of the gas's chemical identity or mass. Therefore, R is a property of a mole of particles, not the particles themselves, making it a universal value.
