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 universal gas constant, R?
The universal gas constant, denoted by the symbol R, is a fundamental physical constant that appears in the ideal gas law (PV = nRT). It represents the work done by one mole of an ideal gas when its temperature increases by one Kelvin. Because it links energy, temperature, and the amount of substance, it is crucial in physics and chemistry, particularly in thermodynamics and the kinetic theory of gases.
2. What is the value of R in L atm mol⁻¹ K⁻¹?
The value of the gas constant R, when pressure is measured in atmospheres (atm) and volume in litres (L), is 0.0821 L atm mol⁻¹ K⁻¹. This value is commonly used in chemistry problems where experimental conditions are given in these units, especially when dealing with gas volumes at Standard Temperature and Pressure (STP).
3. What is the standard SI value of R in Joules per mole Kelvin?
In the International System of Units (SI), the value of the universal gas constant R is 8.314 J mol⁻¹ K⁻¹. This value is used when pressure is in Pascals (N/m²), volume is in cubic metres (m³), temperature is in Kelvin (K), and the amount of substance is in moles (mol). It is the most common value used in physics calculations.
4. How is the value of R calculated in calories per mole Kelvin?
To express the gas constant R in calories, you must convert its SI value from Joules. Given the conversion factor 1 calorie = 4.184 Joules, you can calculate the value as follows:
R = 8.314 J mol⁻¹ K⁻¹ / 4.184 J/cal
This results in R ≈ 1.987 cal mol⁻¹ K⁻¹. This value is often used in thermochemistry problems.
5. How do I decide whether to use R = 0.0821 or R = 8.314 in a problem?
The choice between using R = 0.0821 and R = 8.314 depends entirely on the units used for pressure and volume in the given problem. You should always check the units of the other variables to ensure they are consistent. Use the following guide:
- Use R = 0.0821 L atm mol⁻¹ K⁻¹ when pressure is given in atmospheres (atm) and volume is in litres (L).
- Use R = 8.314 J mol⁻¹ K⁻¹ when pressure is given in Pascals (Pa) or Newtons per square meter (N/m²) and volume is in cubic meters (m³). This is the standard for SI unit calculations.
6. How is the value R = 0.0821 L atm mol⁻¹ K⁻¹ derived from the ideal gas law?
The value of R can be derived using the ideal gas equation, R = PV/nT, under Standard Temperature and Pressure (STP) conditions. At STP, one mole of an ideal gas has the following properties:
- Pressure (P) = 1 atm
- Volume (V) = 22.4 L
- Number of moles (n) = 1 mol
- Temperature (T) = 273.15 K
Substituting these values into the equation: R = (1 atm × 22.4 L) / (1 mol × 273.15 K) ≈ 0.0821 L atm mol⁻¹ K⁻¹.
7. Why is R called the 'universal' gas constant if its numerical value changes with different units?
R is called the 'universal' gas constant because it represents the same underlying physical relationship for any ideal gas, regardless of its chemical identity. The numerical value of R changes only because we express it in different systems of units (like L-atm vs. SI units). The constant itself—the amount of energy per mole per Kelvin—remains the same. This is similar to how a distance of '1 mile' and '1.61 kilometers' represent the exact same length, just with different numerical values and units.
8. What are the values of R when using other common pressure units like bar or Pascal?
The value of R adapts to different pressure units. Besides atm and Pascals, another common unit is the bar. The corresponding values for R are:
- When pressure is in Pascals (Pa) and volume in m³, R = 8.314 J mol⁻¹ K⁻¹.
- When pressure is in bar and volume is in L, R = 0.08314 L bar mol⁻¹ K⁻¹. This value is very close to the one for atm because 1 bar is almost equal to 1 atm (1 bar = 0.987 atm).
Choosing the correct value of R is essential for accurate calculations in thermodynamics problems.
