Question

What is R in the mathematical expression of the ideal gas law?

Answer 1

Hint : The gas laws comprise of the five primary laws namely (i) Charles' Law, (ii) Boyle's Law, (iii) Avogadro's Law, (iv) Gay-Lussac Law and (v) Combined Gas Law. These five gas laws invented the relationship between temperature, pressure, volume and the amount of gas.

Complete Step By Step Answer:
The ideal gas equation refers to the equation of a state of hypothetical ideal gas. In the question, we have been asked about ‘R’ in ideal gas law expression. So first of all, let us see the expression of ideal gas law:
$PV = nRT$ where $P$ is pressure, $V$ is volume, $n$ is amount of substance, $R$ is ideal gas constant and $T$ is temperature.
Let us now discuss the unit for each of these terms used in ideal gas equation one by one:
$P$ - The most common units to express pressure include $atm,{\text{ }}mm{\text{ }}Hg,{\text{ }}torr,{\text{ }}Pa,{\text{ }}kPa,{\text{ }}bar$
$V$ - The most common units to express volume include $L,{\text{ }}{m^3},{\text{ }}c{m^3},{\text{ }}d{m^3}$
$n$ - It is actually the number of moles, thus units are $mol$
$T$ - The most common units to express temperature include $^oC,{\text{ }}K{,^o}F\;$
$R$ - The ideal gas constant can be actually expressed in multiple units, depending upon what it has been used for $P$ , $V$ and $T$ . The possible values as well as units of $R$ are listed below. $R$ can be expressed as follows:
$R = \dfrac{{PV}}{{nT}}$
The most widely employed expression for $R$ is when $V$ is given in litres ( $L$ ), $P$ is given in atmosphere ( $atm$ ), and $T$ is given in Kelvin ( $K$ ) so $R$ can be expressed as:
$R = 0.0821\dfrac{{L.atm}}{{mol.K}}$
The other widely employed expression for $R$ is when $V$ is given in litres ( ${m^3}$ ), $P$ is given in atmosphere ( $Pa$ ) which results into Joules ( $J$ ) when multiplied and $T$ is given in Kelvin ( $K$ ) so $R$ can be expressed as:
$R = 8.314\dfrac{J}{{mol.K}}$

Note :
You must always make sure regarding the units being employed for $R$ that must match the units of $P$ , $V$ , $n$ and $T$ . Keep in mind that real gases are non-ideal which do not follow the ideal gas law exactly. For real gases, two changes have been incorporated like (i) a constant has been added to the pressure (P) and (ii) a different constant has been subtracted from the volume (V). Thus, the new equation for real gas law is: $(P + a{n^2}) \times (V - nb) = nRT$ .