# What does the Constant R in the Ideal Gas Law mean?

Jan 20, 2016

Regnault constant, or Universal Gas Constant.

#### Explanation:

Gas constant, R, is named after the French chemist Henri Victor Regnault. It is also called the Universal Gas Constant.

Gas constant is equivalent to Boltzmann constant ${k}_{B}$ multiplied by Avogadro's number ${N}_{A} = 6.0221413 \times {10}^{23}$ ${\text{things"cdot"mol}}^{- 1}$, expressed in terms of energy.

There are many values of R depending on the units used.

Here are some examples:

"8.314 J"cdot"K"^[-1]"mol"^[−1]
$8.314 \times {10}^{7}$ "erg"cdot"K"^[−1]"mol"^[−1]
8.314xx10^[−3] "amu" cdot["km"^2]/"s"^2"K"^[−1]
$8.314$ "L"cdot"kPa"cdot"K"^[−1]"mol"^[−1]
8.314xx10^[−5] "m"^3 "bar"cdot"K"^[−1]"mol"^[−1]
8.314xx10^[−2] $\text{L" "bar"cdot"K"^[−1] "mol"^[−1]}$
$62.36$ "L"cdot"Torr"cdot"K"^[−1]"mol"^[−1]
$0.08206$ "L"cdot"atm"cdot"K"^[−1]"mol"^[−1]

Jan 20, 2016

R can be viewed as a scaling factor for molar energy of ideal gas law. For ideal gas law, energy can be viewed as increasing linearly with temperature. $E = \alpha T$
Through derivation. it was shown that for one-dimension, $E = \frac{1}{2} R T$ while for 3 dimension $E = \frac{3}{2} R T$
The above is for 1 mole of ideal gas. For 1 molecule of gas, we know that $R = {N}_{A} k$
So 1 molecule of ideal gas moving in 3 dimension is $E = \frac{3}{2} k T$
You can equate the kinetic energy of the molecule $E = \frac{1}{2} m {v}^{2}$ to previous equation and get
$E = \frac{3}{2} k T = \frac{1}{2} m {v}^{2}$