## Value of R In Atm - Detailed Explanation

R also called the gas constant is one of the important constants in a lot of subjects. They also tend to provide solutions to the work that is done by the gas in various units. The value of R that is being used will entirely depend on the units that are asked in the questions. Once you analyze the units you will be able to find the right value for the question. Vedantu also provides information regarding the Value of R In Atm - Detailed Explanations, Examples, Units, and FAQs for students who would like to learn more regarding the same.

The gas constant or ideal gas constant or molar constant is an important physical constant used in most of the fundamental equations of thermodynamics, kinetic theory of gasses, etc., and is denoted by the letter “R”. In Physics, the ideal gas constant R is defined as -Work done by the gas (or on the gas) per unit mole per unit temperature change. Though the ideal gas constant R is a constant value it can be expressed in various unit systems.

### Value of Gas Constant

From the ideal gas expression we have,

PV = nRT…….(1)

Where,

P - Pressure of the ideal gas

V - Volume of the ideal gas

n - Number of moles

R - The universal gas constant

T - Temperature

On rearranging the above equation for R we get,

R = PV/nT …….(2)

This is the gas constant formula.

From equation (2) the unit of gas constant R is given by,

⇒ R = (N/m²) x (m³)/(mol) x (K)

⇒ R = N m/mol x K

⇒ R = joule/mol x K (∵ Newton-meter = Joule)

Therefore, the unit of gas constant R is Joule/mol-K or J mol\[^{-1}\]K\[^{-1}\].

The value of R at atm i.e., at STP (standard temperature and pressure) is calculated as follows.

At STP, for 1 mole of gas (n=1mol), the value of temperature is 273K, pressure is 1.01 x 10\[^{5}\] N/m\[^{2}\] , and volume is 22.4 x 10\[^{-3}\]m\[^{3}\].

Substituting these values in equation (2) and simplifying, we get the value of the gas constant,

R = 8.31 J mol\[^{-1}\] K\[^{-1}\]

Therefore, the value of R is J mol\[^{-1}\] K\[^{-1}\].

### Value of R:

The value of R can be expressed in various unit systems according to the need for calculation. For example, if you want to use the value of the gas constant in calories then, we know that 4.184 joules are equal to 1 calorie, then the value of R is,

R = 8.31/4.184 Cal mol\[^{-1}\] K\[^{-1}\] = 1.98 Cal mol\[^{-1}\] K\[^{-1}\]

### Examples:

1: Calculate the Value of R in ergs mol⁻¹K⁻¹.

Ans: We know that value of R = 8.31 J mol⁻¹K⁻¹,

Now, substituting 1J = 10⁷ergs

R = 8.31 x 10⁷ergs mol⁻¹K⁻¹.

Therefore, the value of R in the CGS system.

2: Calculate the Value of R in L(atm) mol⁻¹K⁻¹.

Ans: From ideal gas equation we know that,

⇒ R = PV/nT

For n=1mol at STP, P=1atm, T=273K, and V=22.4L

Substituting the above values in equation of R,

⇒ R = 1atm x 22.4 L/1mol x 243 K

⇒ R = 0.0821 L(atm) mol⁻¹K⁻¹ is the required answer.

### Did you Know?

The value of R will be changing as the pressure and volume of the system is varied. Choose the appropriate value of R depending upon which measuring system is being referred to.

The ideal condition is used to arrive at the value of R at different conditions.

## FAQs on Value of R in Atm

**1. What is the Relation Between Joule and Calorie?**

1 calorie = 4.184 joules.

**2. What is the Value of 1 Torr?**

Torr is a unit of atmospheric pressure, and is equal to a pressure below a 1mm column of Hg.

**3. What is the Relation Between Joule and Torr?**

1L torr = 0.13332J

**4. What is the gas constant?**

The gas constant denoted by R is defined as the work that is done by the gas or on the gas per unit mole per unit change in temperature. The gas constant is also commonly called the ideal gas constant or the universal gas constant or the molar constant. It is an important physical and chemical constant that is used in a variety of problems to solve them. Even though it may be a constant it has various values depending on the units that are present.

**5. What is the value of R?**

The value of R is expressed in a variety of unit systems and it completely depends on the way the calculation is performed. For example, if the gas constant is to be used in terms of calories then the value of the gas constant can be given as:

R = 8.314 / 4.184 Cal mol K

Here 4.184 joules will be equal to 1 calorie and hence this value is used to divide with the gas constant. Similarly with the various values being divided the various values of R can be obtained.

**6. What is the value of R in different systems and units?**

Values of R vary with vary units being used and can be provided as follows:

It is seen that generally according to the ideal gas equation

R = PV / nT

where P indicates pressure,

V indicates volume,

n indicates a number of moles of gas, and

T indicates temperature.

At STP the values of pressure become 1 atm and temperature becomes 273 Kelvin or zero degree Celsius.

N will be taken as one and the volume of gas will be 22.4 liters.

By using these values when R is calculated it comes around R = 0.0821-litre atm/mol K.

In the CGS system the n and T will remain the same which means that there is no unit change while P which is equal to 1 atm will become 101325 X 105 and V will become 22400 ml.

After the calculation, the value of R becomes 8.314 X 107 erg / Mol. K.

In the MKS system P will be equal to 101325 newtons per meter square and V is equal to 22.4 X 10-3 m3 and hence the value of R is 8.314 J/ Mol. K.

**7. How to decide whether to use 0.0821 or 8.314 for R?**

R = 8.314 Joule /mol.

K is the value that is obtained in SI units.

This value can also be written as R = 0.0821 atm-liter / mol. K or R = 1.9872 Cal / mol. K.

The value of R will depend on the value of other variables such as the ideal gas equation which is given by PV = nRT.

If the values of P is in atm,

V is in liters,

T is in Kelvin then

R will be equal to 0.0821 atm-liter / mol K.

If the pressure is provided in Pascal and volume is in cubic meters while the temperature is in Kelvin then the value of R will be 8.314 J / mol. K

**8. How to remember the formula and values that are related to the gas constant?**

The formula and values of the gas constant are something that is a long list and might become hard to remember for some students. In such cases, you can refer to the Vedantu Physics formula list where all the formulae and values will be provided in the same list. This will also allow you to practice them right before the exam and hence keep the values fresh in your mind. You can also check out some other detailed information R through Vedantu as well which might be important in both Physics and Chemistry.