Question

How can I calculate the gas law constant?

Answer 1

Hint: The gas constant also known as molar gas constant is denoted by the symbol $R.$ It is equivalent to Boltzmann constant, but expressed in units of energy per temperature increment per mole.

Complete step by step answer:
The gas constant is the constant of proportionality that refutes the energy scale in physics to the temperature being considered.
The gas constant $R$ is defined as the Avogadro constant ${N_A}$ multiplied by the Boltzmann constant $\left( {{K_8}\& K} \right)$
$R = {N_A}.K$
${N_A}\& K$ are defined with exact numerical values when expressed in SI units. The values of gas constant is exactly defined as $8.814462J{K^{ - 1}}mo{l^{ - 1}}$
The Boltzmann constant $\left( K \right)$ is the proportionality factor that relates the arranged relative kinetic energy of particles in a gas with the thermodynamics temperature of gas. Boltzmann constant is $1.380649 \times {10^{ - 12}}{\text{ J/K}}$
Avogadro constant $\left( {{N_A}} \right)$ is the proportionality factor that relates the number of constituent particles in a sample with the amount of substance in the sample.
${N_A} = 6.022 \times {10^{23}}{\text{ mo}}{{\text{l}}^{ - 1}}$
Therefore as we know $R = {N_A}.K$
$R = 6.022 \times {10^{23}} \times 1.380649 \times {10^{ - 23}}$
$R = 8.314462{\text{ J/K mol}}{\text{.}}$
The gas constant occurs in the ideal gas law, as follow:
$PV = nRT$
Where, $P$ is the absolute pressure (Pascal’s), $V$ is the volume of gas $({m^3})$, $n$ is the amount of gas (moles), $T$ is the thermodynamics temperature $(K)$, $R$ is the gas constant. The gas constant is expressed in the physical units as molar entropy and molar heat capacity.
It terms of Boltzmann constant we can generative the gases law as,
$PV = n{N_A}{K_B}T$
$R = {N_A}{K_B}$

Additional Information:
The state of an amount of gas is determined by its pressure, volume and temperature. The modern form of the equation relates these simply in two main forms. Specific gas constant of a gas or a mixture of gases $\left( {{R_{specific}}} \right)$ is given by the molar gas constant divided by the molar mass of the gas mixture.
${R_{specific}} = \dfrac{R}{M}$
Mayer’s relation relates the specific gas constant to the specific heats for a calorically perfect and a thermally perfect gas.
${R_{specific}} = {C_P} - {C_V}$
Where ${C_P}$ is the specific heat for constant pressure and ${C_V}$ is specific heat for constant volume. The ideal gas law can also be derived from first principles using the kinetics theory of gases, in which the molecules, or atoms of gases are point masses processing mass but no volume and undergo only elastic collision with each other and kinetic energy are conserved.

Note: The equation of state given here $\left( {PV = nRT} \right)$ applies to an ideal gas or an approximation to a real gas that behaves sufficiently like an ideal gas. Since the ideal gas neglects both the molecular size and intermolecular attraction it is most accurate for monatomic gases at high temperature and low pressures.
For a d-dimensional system the ideal gas pressure is
${P^{\left( d \right)}} = \dfrac{{N{K_8}T}}{{{L^d}}}$
Where ${L^d}$ is the volume of the d-dimensional domain in which the gas exists. Note that the dimensions of the pressure changes with dimensionality. The empirical law that led to the derivation of the ideal gas law was discovered with experiments that changed only two state variables of the gas that kept every other one constant.