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# Gas Constant

Gases are all around us. The air we breathe is a combination of different gases, such as nitrogen (~78%) and oxygen (~21%). In chemistry, there are a few laws which dictate how an ideal gas behaves, which are combined into the Ideal Gas Law. In order for this law to work, however, there was a gas constant (R) added to this equation.

So, what's the point of it? Why do we need this constant? Continue reading to find out more about gas constant!

• First, we will define what the gas constant is and where it is derived from
• Next, we will learn what the universal gas constant is
• Thereafter, we will look at some different values for the gas constant
• Lastly, we will learn about the gas constant for air and learn about the concept of the specific gas constant

## Gas Constant Definition

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

The gas constant (R) (also called the ideal gas constant) is a physical constant that appears in the Ideal Gas Law.

The ideal gas law is an equation showing the behaviors of an ideal gas. The equation is:

$$PV=nRT$$

Where P is pressure, V is volume, n is the number of moles, R is the gas constant, and T is temperature

An ideal gas is an estimation of how real gases behave. Ideal gas particles have the following properties:

• Are in constant motion
• Have negligible mass
• Have negligible volume
• Have no interactions (attraction/repulsion) between particles

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 (kB) 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".

Joules are units of energy and Kelvin is a unit of temperature. Therefore, the Boltzmann constant relates a gas particle's energy to its temperature

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 (NA) by the Boltzmann constant:

Avogadro's constant is 6.022x1023 mol-1, and relates the number of particles to the amount of a substance.

$$R=N_ak_B$$

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

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

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.

Did you know?!

• Jan Baptist van Helmont, a Flemish chemist who lived in the 1600s, came up with the word "gas."
• They say Van Helmont made up the word "gas" from the words "gahst" and "geist," which mean "ghost" and "spirit," respectively.
• The physicist Michael Faraday came up with rubber balloons as a way to store gases for experiments.

## 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.

Table 1-Different Values of the Gas Constant
Gas constant ValueUnits
0.08205Latm/molK
8.314J/molK
62.36LTorr/molK
8.314LPa/molK
62.36mmHgL/molK
8.205x10-5m3atm/molK

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.

The specific gas constant relates the universal gas constant and the molar mass of a gas (or mixture of gases).

The formula is:

$$R_{specific}=\frac{R}{M}$$

Where R is the universal gas constant and M is the molar mass of the gas(es)

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 Rspecific of dry air is 287.05 J/kg·K.

## Gas Constant - Key takeaways

• The gas constant (R) (also called the ideal gas constant) is a physical constant that appears in the ideal gas law.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.
• It is also called the ideal gas constant, the molar gas constant, and the universal gas constant.
• The value of the gas constant is the same as the Boltzmann constant, but it is written as the product of pressure and volume instead of energy per temperature change per particle.
• The SI value of the molar gas constant is exactly 8.31446261815324 J.K-1mol-1
• 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.
• The universal gas constant was probably found by Clausius's student A.F. Horstmann in 1873 and by Dmitri Mendeleev on September 12, 1874.
• The specific gas constant is the ratio of the molar gas constant (R) to the molar mass (M) of the gas mixture.

## References

1. Fig.1-Relationship between the Boltzmann constant and the gas laws by Cmglee on Wikimedia Commons (https://commons.wikimedia.org/wiki/User:Cmglee) licensed by CC BY-SA 3.0 (https://creativecommons.org/licenses/by-sa/4.0/)

#### Flashcards in Gas Constant 6

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What do you mean by gas constant?

The gas constant (R) (also called the ideal gas constant) is a physical constant that appears in the ideal gas law. 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.

How do you calculate the gas constant?

The gas constant is the product of the Boltzmann constant and the Avogadro constant

What is the gas constant unit?

The standard units for the gas constant are J/molK

Does air have a gas constant?

The specific gas constant of dry air is 287.05 J/kgK

Why is the universal gas constant R?

The origins of the naming of the constant are unknown.

Some scientists saw 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.

## Test your knowledge with multiple choice flashcards

What is the formula for the ideal gas law?

The gas constant is the molar equivalent of what constant

What is the standard value/units of the gas constant?

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