Gas Constant

Gas Constant Definition

Let's start by looking at the definition for gas constant.

So, now that we know what it is, why do we need it? Well, the gas constant is a proportionality constant, meaning that it shows the extent of how two or more variables are related. More specifically, it tells us how temperature, pressure, volume, and Amount of Substance relate based on their units.

But, where did this constant come from? Did it pop out of thin air? Did someone just pick a number they liked? The truth is that this constant is derived from a whole slew of other constants, such as those from Boyle's law, Charles's law, and Avogadro's law. These laws (and a few others) were combined to form the ideal gas law, so it makes sense that the ideal gas constant is a combination of those laws' constants.

To be more specific, the gas constant is the molar equivalent of the Boltzmann constant (k_B) which is the combination of several constants, as shown below:

Fig.1-Relationship between the Boltzmann constant and the gas laws

The value of the Boltzmann constant is 1.380649 x 10^-23 J/K. Where J is "Joules" and K is "Kelvin".

Since the gas constant is the molar equivalent, that means that it also accounts for the amount of a substance.

To get the gas constant, we multiply the Avogadro constant (N_A) by the Boltzmann constant:

$$R=N_ak_B$$

$$R=(6.022x10^{23}mol^{-1})*(1.380649x10^{-23}\frac{J}{K}$$

$$R=8.314\frac{J}{molK}$$

As you will see later, the value of the gas constant changes based on its units. This constant is considered the "standard".

Some scientists say that the symbol R should be called the "Regnault constant" in honor of the French chemist Henri Victor Regnault, whose accurate experimental data were used to figure out the constant's early value. But no one seems to know why the letter R is used to stand for the constant.

Fig.2-Portrait of Henri Victor Regnault

The universal gas constant was probably found by Clausius's student A.F. Horstmann in 1873 and by Dmitri Mendeleev on September 12, 1874. Using his extensive measurements of the properties of gases, Mendeleev also calculated it with high precision, within 0.3% of its modern value.

Universal Gas Constant

As I mentioned earlier, the value for the standard or "universal" gas constant is 8.314 J/mol·K. To expand this out further, it is 8.3144598 J/mol·K.

The reason it is "universal" is that it is applicable to all ideal gases!

Gas Constant Value

While the previous value is considered the standard, there are several other values of the gas constant depending on the units used.

Let's look back at the ideal gas law to see what I mean:

$$PV=nRT$$

Pressure, for example, can be in units of atmospheres (atm), mmHg, Torr, bar, or Pascals (Pa). That's a lot of different units for just one variable! As you can imagine, that means there are a lot of different values of the gas constant.

While working with the ideal gas law, you are probably going to use this value:

0.08205 Latm/molK

This is because the above units are either the or one of the standard unit(s) for each individual variable.

Below is a table of some commons values of the gas constant.

As you can see, there are several values of the gas constant, but there aren't all different. Remember that the gas constant is a proportionality constant, so different units "relate" to each other in different ways.

Gas Constant for Air

The universal gas constant is applicable to all gases, but sometimes we want to be a bit more specific, which is where the specific gas constant comes in.

Air is a mixture of gases, so "M" would be the molar mass of the entire mixture. When we refer to the gas constant for air, we are referring to the gas constant for dry air. Air contains water vapor, and the amount of water vapor can fluctuate a lot, which is why we tend to ignore it.When using the mean molar mass of dry air (28.964917 g/mol), the R_specific of dry air is 287.05 J/kg·K.