Ideal gas constant (R), what is it, where to use R = 0.08206?

The decimal number 0.08206 represents the ideal gas constant, also known as the Universal gas constant or molar gas constant in L.atm/ (mol. K).

What is R?  

R denotes the chemical behavior of a gas under ideal temperature and pressure conditions, i.e., 293.15 K and 1 atm, respectively. R determines the kinetic energy occupied by an ideal gas.

Three different gas laws are combined into the ideal gas equation, i.e., PV= nRT. In the ideal gas equation, the value of R stays constant.

In this article, you will learn everything there is to know about the ideal gas constant (R), including what it is and how to use it, through plenty of examples.

Hence, wait no more; dive into the article and continue reading! 

What does PV = nRT represent?

In the ideal gas equation, PV = nRT:

• P = pressure of the gas, measured in atmospheres (atm) or Pascals (Pa) where 1 atm = 1.01325 x 10⁵
• V = Volume occupied by the gas in meter cubic (m³) or litres (L) where 1 m³ = 1000 L
• n = number of moles of gas in mol (moles = mass/molar mass of the gas)
• R = molar gas constant or ideal gas constant
• T = temperature, measured in Kelvins (K) where 1 K = 1 °C + 273.15

What are ideal conditions?

Under ideal conditions,

• P = 1 atm or 1.01325 x 10⁵ Pa
• V = 0.0224 m³ or 4 L
• n = 1 mole
• T= 273 K
• R = 0.08206 L.atm/ (mol. K).

Units of R = 0.08206

You must note that R = 0.08206 if the pressure is measured in atm while the volume of gas is given in liters.

Therefore, the units of R = 0.08026 are L.atm/ (mol. K).

In contrast, if the volume of the ideal gas is given in m³ while its pressure is measured in Pa, in that case, the value of R becomes:

⇒ PV = nRT

∴ R = 8.314 Pa.m³/mol.K

Thus, the value of the ideal gas constant R = 8.314 in Pa.m³/ (mol. K).

8.314 is the value of the ideal gas constant in SI units, therefore; it is usually preferred over 0.08206.  

A gas deviates from ideal behavior if the value of temperature, pressure, volume or concentration changes.

 In order to calculate any unknown value using PV = nRT, we need to plug in all the given variables along with the fixed value of R, i.e., 0.08206.

Either of the numerical values (0.08206 or 8.314) can be used, predominantly depending upon the units in which temperature, pressure, and volume are given.

Now let us see the examples given below so that you can learn to use R and find unknown values from the ideal gas equation.

But in the first example, let’s find out where R comes from.

For example, under ideal conditions, i.e., a standard temperature (273 K) and pressure (1 atm), 1 mole of a gas occupies 22.4 L volume. Using this information calculate the value of R in L.atm/ (mol. K). 

We know that the ideal gas equation is PV = nRT.

Making R the subject of the formula and plugging in all the known values, we can easily find R, as shown below.

∴ R = 0.08206 L.atm/ (mol.K)

Result: The above calculation confirms that the value of R = 0.08206 L.atm/ (mol. K) under ideal conditions.

Another example is– A 2 molar sample of gas in a container that occupies a volume of 5 liters. The pressure of the gas is 3 atmospheres. Use the value of R to find the temperature of the gas in Kelvins (K).

⇒ PV = nRT

In this example, the value of T is unknown, so we make T the subject of the formula as follows:

⇒ T = PV/NR

As per the question statement, P = 3 atm, V = 5 L, n = 2 mol.

So we can substitute the above values and the value of R = 0.08206 (as pressure is given in atm while volume in L) to find the unknown value of T.

∴ T = (3 × 5) / (2 × 0.08206)

∴ T = 91.4 K

Result: The temperature of the gas in the container is 91. 4 K.

More examples involving ideal gas constant (R = 0.08206)

A gas exerts a pressure of 5 Pascals at a temperature of 300 K. The number of moles of gas is 3. Take R= 0.08206 to determine the volume occupied by the gas in liters.

⇒ PV = nRT As per the question statement, P = 5 Pa, T = 300 K, n = 3 and R = 0.08206 L.atm/(mol.K) In order to find the unknown V in m3 we need to convert pressure into atm, as follows: Result: The gas occupies a volume of 1.50 x 106 L.

Find the pressure exerted by a gas that occupies a volume of 2 liters at a temperature of 25°C if the number of moles of gas is 0.5. Hint: Don’t forget to use R= 0.08206 L.atm/(mol.K)

⇒ PV = nRT As per the question statement, V = 2 L, T =  25°C, n = 0.5 and R = 0.08206 L.atm/(mol.K) It is important to note that consistency in units is very important while solving questions using the ideal gas equation. As R = 0.08206 L.atm/(mol. K) therefore, we need to convert the given temperature from degree Celsius to Kelvin, as shown below: ⇒ 1 K = 1 °C + 273.15 ∴ 25°C = 25 + 273.15 = 298.15 K Now make P the subject of the formula from the ideal gas equation and substitute all the known variables: ∴ P = 6.12 atm Result: The pressure exerted by the gas in the container is 6.12 atm.

FAQ

What is (R = 0.08206)?

R represents the ideal gas constant, also known as the Universal constant in the ideal gas equation, i.e., PV = nRT. R denotes a fixed numerical value, i.e., 0.08206 L.atm/ (mol. K) or 8.314 m3.Pa/ (mol. K).

What is the ideal gas equation?

PV = nRT represents the ideal gas equation, also known as the equation of state. It represents the chemical behavior of 1 mol gas under ideal conditions of temperature (273 K), pressure (1 atm), and volume (22.4 L).

Which gas laws are used to derive the ideal gas constant (R = 0.08206)?

The ideal gas constant (R) is derived from a combination of: Boyle’s law: The pressure exerted by an ideal gas is inversely proportional to its volume (P ∝  1/V). Charles’ law: The volume occupied by a gas is directly proportional to the temperature (V ∝ T). Avogadro’s law: Under the same temperature and pressure conditions, equal volumes of different gases contain the same number of molecules.