Gas Constant - Definition, Value, Units, FAQs

Gas Constant Value

The gas constant ( $\mathbf{R}$ ) is a fundamental physical constant used in the ideal gas equation to relate the pressure, volume, temperature, and amount of gas. It is obtained by combining Boyle's law, Charles's law, Gay-Lussac's law, and Avogadro's law. For one mole of an ideal gas, the equation is written as $P V=R T$.

The value of the ideal gas constant is:

$
R=8.3144598(48) \mathrm{J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}
$

where:

• J (Joules) is the unit of energy
• mol refers to the amount of substance in moles
• K is the unit of temperature (Kelvin)

What is Gas Constant?

A gas constant is a physical phenomenon defined by R and expressed in units of energy by the increase in temperature per molecule. It is also known as an Ideal gas constant or molar gas constant or even universal gas constant. The fixed amount of gas is equivalent to the constant durability of Boltzmann but is expressed as a product of volume pressure instead of the force with each temperature increase of the particles.

Units of Gas Constant

The gas constant R is the proportionality constant that relates the energy scale in thermodynamic equations, particularly in the equation of state for gases.

The gas constant can be expressed in various units depending on the system of measurement:
1. In Joules per mole per Kelvin (J/mol-K), as it is used in the SI system.
2. In liter-atmospheres per mole per Kelvin (L•atm/mol-K) for gas law calculations in terms of pressure in atmospheres and volume in liters.

Gas Constant in Different Units in Table Form

The gas constant is widely used in different branches of physics, chemistry, and engineering. Since calculations may involve different units of pressure, volume, and energy, the gas constant is expressed in various unit systems. Some commonly used values of the gas constant in different units are given below:

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Dimensions of Gas Constant (R)

From the ideal gas equation,

$
P V=n R T
$

For one mole of gas ( $n=1$ ),

$
R=\frac{P V}{T}
$

Now,
Pressure $P=\frac{\text { Force }}{\text { Area }}$

$
[P]=M L^{-1} T^{-2}
$

Volume $V=L^3$

Temperature $T=K$

So,

$
\begin{aligned}
{[R] } & =\frac{\left(M L^{-1} T^{-2}\right)\left(L^3\right)}{K} \\
{[R] } & =M L^2 T^{-2} K^{-1}
\end{aligned}
$

Relationship with Boltzmann Constant

The universal gas constant can be related to the Boltzmann constant (k), which applies to individual gas molecules, by the following relationship:

$
R=N_A \cdot k
$
Where:

• $N_A$ is Avogadro's number (the number of particles per mole, approximately $6.022 \times 10^{23}$ )
• $k$ is the Boltzmann constant (approximately $1.38 \times 10^{-23} \mathrm{~J} / \mathrm{K}$ )

What is an ideal gas?

An ideal gas is a theoretical gas formed by a group of randomly charged particles that meet only in an elastic collision. An ideal gas is one that follows the gas laws at all conditions of temperature and pressure. The gas needs to completely abide by the kinetic-molecular theory.

One of the most important equations involving the gas constant is the Ideal gas law, which states:

$
P V=n R T
$
Where:
$P$ is the pressure of the gas (in atmospheres or Pascals)
$V$ is the volume of the gas (in liters or cubic meters)
$n$ is the number of moles of gas
$R$ is the gas constant
$T$ is the temperature of the gas (in Kelvin)

Applications of the Gas Constant

Thermodynamics: In thermodynamic processes, R is used in calculating entropies and the Gibbs free energy.

Physical Chemistry: It is used in determining gas behavior in reactions and characteristics such as equilibrium constant and coefficient, as well as reaction rate.

Boltzmann's Distribution: It is useful in understanding ways energy might be spread out in systems at equilibrium, at different temperatures, and in the use of statistical mechanics.