Value of R in Atm - Value of Gas Constant, Formula, FAQs

Value of R in Atm - Value of Gas Constant, Formula, FAQs

Edited By Vishal kumar | Updated on Jul 02, 2025 04:40 PM IST

The gas constant, also known as the ideal gas constant or the molar constant, is an important physical constant that is denoted by the letter "R" and is utilized in most of the fundamental equations of thermodynamics, kinetic theory of gases, and so on. The ideal gas constant R is defined in physics as -Work done by the gas (or on the gas) per unit mole per unit temperature change. Boyle's law, Charles' law, Avogadro's law, and Gay-law Lussac's are all used to create the constant. The ideal gas law, the Arrhenius equation, and the Nernst equation all contain it as a physical constant.

This Story also Contains
  1. What is the meaning of R
  2. Gas Constant Formula
  3. Gas Constant Value
  4. Universal Gas Constant Derivation
  5. Different Units Of R
  6. Summary
Value of R in Atm - Value of Gas Constant, Formula, FAQs
Value of R in Atm - Value of Gas Constant, Formula, FAQs

The gas constant is a constant proportionality in physics that links the energy scale to the temperature scale and the measurement of the quantities of the substance. As a result, prior decisions and accidents in the definition of energy, temperature, and material amount eventually decide the value of the gas constant. The Boltzmann constant and the Avogadro constant, which separately connect energy to temperature and particle count to substance amount, were also determined.

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What is the meaning of R

The gas constant is defined in physics as the product of pressure and volume. R is an abbreviation for energy per temperature increase per mole. Value of R in atm is a constant. However, the value of the gas constant can be stated in a variety of units. R is also known as the ideal gas constant, the universal gas constant, and the molar constant.

As the pressure and volume of the system are changed, the value of R will change. Depending on the measuring system is being used, choose the appropriate R value.

The ideal condition is used to determine the R-value under various scenarios.

Also Read -Unit of Pressure

Gas Constant Formula

The gas constant R in the ideal gas law is expressed as,

PV=nRT

R=PVnT

where,

  • P is the pressure of the gas
  • V is the volume
  • n is the number of moles
  • T is the temperature i n kelvin
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Gas Constant Value

Universal gas constant R, which is a physical constant measured in units of energy per temperature increment per mole. The ideal gas constant, molar gas constant, and universal gas constant are all interchangeable names. The gas constant is identical to the Boltzmann constant; however, it is expressed as the pressure-volume product rather than energy per temperature increment per particle.

The value of R is R=8.314 J/K/mole

Universal Gas Constant Derivation

The combination of Boyle's law, Charle's law and Avogadro's law gives the ideal gas equation.It is a relation between four variables and describes any state of gas. It is also called the equation of state.

Boyle's law, P1V (T and n are constant)

Charle's law, VT (P and n are constant)

Avogadro's law, Vn (T and P are constant)

Combining these laws,

VnTP

V=RnTP

We can deduce from the ideal gas statement

PV=nRT…….(1)

Where,

P is the ideal gas's pressure.

V is the ideal gas's volume.

n is the number of moles.

The universal gas constant R.

T is the temperature

We get by rearranging the previous equation for R:

R=PVnT………(2)

This is the formula for the gas constant.

The unit of R is given by, which is derived from equation (2).

R=(N/m2)×(m3)(mol)×(K)

R=Nmmol×K

(Newton-meter = Joule)

R=Joulemol×K

As a result, the gas constant R is measured in JoulemolK or JMol1 K1

  • The following formula is used to find the value of R at standard temperature and pressure).

Temperature is 273K, pressure is1.01105N/m2, and volume is 22.410-3m3 at STP for 1 mole of gas (n=1mol).

We find the gas constant value R by substituting these numbers in equation (2) and simplifying.

As a result, the value is R=8.31 JMol1 K1

Related Topic:

Different Units Of R

R value can be stated in a variety of unit systems depending on the necessity for calculation. We know, for instance, that 1 calorie = 4184 joules when you use the gas constant R-value in calories, and then the value of R is.

R=8.314.184CalMol1 K1

R=1.97CalMol1 K1

Similarly, the gas constant R values can be expressed in a variety of units, as shown in the table below.

Value of RUnits of R
8.31J mol⁻¹K⁻¹
1.98Cal mol⁻¹ K⁻¹
8.31m³(Pa)mol⁻¹K⁻¹
0.0821L(atm) mol⁻¹K⁻¹
62.36L(torr) mol⁻¹K⁻¹
1.98 x 10⁻³kCal mol⁻¹K⁻¹
8.3144598 × 103amu.m2.s-2.K-1
8.3144598 × 10-2L.bar.K-1.mol-1

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Summary

The gas constant R is an essential parameter in thermodynamics and physical chemistry. It helps in facilitating the understanding and calculation of gas behaviours. In this article, we learnt about the definition of the gas constant, R-value and its different units. Its values vary based on units. The gas constant R is a crucial constant in thermodynamics and ideal gas equation.

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Frequently Asked Questions (FAQs)

1. Determine R value in L(atm) Mol-1K-1.

We know from the ideal gas equation that,


R=PV/nT


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


By substituting the above values into the R equation,


R = 1 atm x 22.4 L/1 mol x 243 K


The required answer isR = 0.0821 L(atm) Mol-1K-1.

2. What are the various R values?

The value of the gas constant 'R' is determined by the pressure, volume, and temperature units used.

R = 0.0821 litre.atm/mol-K, 

R = 8.3145 J/mol-K, 

R = 8.2057 m3atm/mol-K, 

R = 62.3637 L-Torr/mol-K, 

3. In PV nRT, what is R?

 PV=nRT, where n is the number of moles and the universal gas constant R is the ideal gas law. The value of R varies depending on the units used, but it is commonly expressed as R = 8.314 J/mol-K in S.I. units. As a result, the gas constant R value is equated to 287 J/kg-K can be used for air.

4. What's STP's R value?

The value of R is computed accordingly at atm i.e. at STP (standard temp and pressure). At STP, the temperature value is 273K, for 1 mole of gas (n=1 mol), the pressures are1.01105.

5. What is the universal gas constant R value?

The dimensions are energy per degree per mole of the universal gas constant R. The value of R is 8.314598 joules of kelvin (K) a mole in the meter-kilogram-second system.

6. What is the value of R?

The value of R is R=8.314 J/K/mole

7. Why is R called the universal gas constant?

The R is called the universal gas constant because the value of R is the same for all the gases irrespective of their nature.

8. Why is R called the universal gas constant?
R is called the universal gas constant because it applies universally to all ideal gases, regardless of their chemical composition or molecular structure. It's a fundamental constant in the study of gas behavior.
9. What is the S.I unit of gas constant?

The S.I unit of gas constant is J mol⁻¹K⁻¹.

10. How does the value of R change if we use different units?
The numerical value of R changes depending on the units used, but its physical meaning remains the same. For example, R = 8.314 J/(mol⋅K) in SI units, while R = 0.08206 atm⋅L/(mol⋅K) when using atmospheres and liters.
11. Why do we need different values of R for different unit systems?
Different values of R are needed for different unit systems to ensure consistency in calculations. The physical meaning of R remains the same, but its numerical value changes to accommodate different units of pressure, volume, and temperature.
12. How does the value of R in atm⋅L/(mol⋅K) compare to its value in SI units?
The value of R in atm⋅L/(mol⋅K) is 0.08206, while in SI units (J/(mol⋅K)) it's 8.314. The difference is due to the conversion between atmospheres and pascals, and liters and cubic meters.
13. Can R be used for calculations involving real gases?
While R is defined for ideal gases, it can be used for real gases in many practical situations. For more accurate results with real gases, especially at high pressures or low temperatures, additional correction factors or more complex equations of state are needed.
14. What happens to the value of R at extremely high temperatures or pressures?
The value of R itself doesn't change with temperature or pressure. However, at extreme conditions, gases may deviate from ideal behavior, making calculations using R less accurate without additional corrections.
15. How does R appear in the ideal gas law equation?
In the ideal gas law equation PV = nRT, R serves as the proportionality constant that relates pressure (P), volume (V), number of moles (n), and temperature (T) for an ideal gas.
16. How does R relate to the average kinetic energy of gas molecules?
The average kinetic energy of gas molecules is directly proportional to temperature, with R serving as part of the proportionality constant. Specifically, average kinetic energy = (3/2)RT per mole of gas.
17. How does the gas constant R appear in the van der Waals equation?
In the van der Waals equation, (P + an²/V²)(V - nb) = nRT, R appears in the same way as in the ideal gas law. The equation includes additional terms 'a' and 'b' to account for molecular interactions and volume.
18. How does R help in understanding the concept of absolute zero?
R helps in understanding absolute zero through the ideal gas law. As temperature approaches absolute zero, the volume or pressure of an ideal gas would theoretically approach zero, maintaining the relationship PV = nRT.
19. Can R be used to calculate the density of a gas?
Yes, R can be used to calculate gas density. By rearranging the ideal gas law, density (ρ) can be expressed as ρ = PM/(RT), where M is the molar mass of the gas.
20. What is the value of R in atm⋅L/(mol⋅K)?
The value of R (gas constant) in atm⋅L/(mol⋅K) is 0.08206. This value is commonly used in gas law calculations when pressure is expressed in atmospheres and volume in liters.
21. What's the significance of R in calculating molar volume?
R is crucial in calculating molar volume because it relates the volume occupied by one mole of an ideal gas to its temperature and pressure. At STP, the molar volume of an ideal gas is about 22.4 L, which can be derived using R.
22. Can R be used in calculations involving mixtures of gases?
Yes, R can be used for mixtures of gases. In ideal gas mixtures, each component behaves independently, and the total pressure is the sum of partial pressures. R applies to each component and the mixture as a whole.
23. How is R used in calculating the heat capacity of gases?
R is used in calculating the heat capacity of gases. For an ideal monatomic gas, the molar heat capacity at constant volume (Cv) is (3/2)R, and at constant pressure (Cp) is (5/2)R. These relationships stem from the kinetic theory of gases.
24. Can R be used to determine the molecular mass of an unknown gas?
Yes, R can be used to determine the molecular mass of an unknown gas. By measuring the pressure, volume, and temperature of a known amount of gas, you can use the ideal gas law (PV = nRT) to calculate the number of moles, and thus the molecular mass.
25. Why is the gas constant R important in kinetic theory?
The gas constant R is crucial in kinetic theory because it relates the average kinetic energy of gas molecules to their temperature. It appears in many gas laws and equations, helping us understand the behavior of gases under different conditions.
26. How is R related to Boltzmann's constant?
R is related to Boltzmann's constant (k) by the equation R = NA * k, where NA is Avogadro's number. This relationship connects the macroscopic gas constant to the microscopic Boltzmann constant.
27. How was the value of R originally determined?
The value of R was originally determined through careful experimental measurements of gas behavior under various conditions. Scientists like Avogadro and Gay-Lussac contributed to its discovery through their work on gas laws.
28. Can the gas constant R be used for all gases?
Yes, the gas constant R is universal and applies to all ideal gases. It's the same value regardless of the type of gas, which is why it's called the universal gas constant.
29. How does R relate to the concept of equipartition of energy?
R is related to the equipartition of energy principle through the relationship with temperature. Each degree of freedom of a molecule contributes (1/2)RT of energy per mole, where R acts as a scaling factor.
30. Why doesn't the value of R depend on the type of gas?
R doesn't depend on the type of gas because it's a universal constant that relates the macroscopic properties of gases to their molecular behavior. The ideal gas law assumes all gases behave identically at the molecular level, hence a universal constant.
31. Why is R important in understanding gas diffusion?
R is important in understanding gas diffusion because it relates to the kinetic energy and thus the speed of gas molecules. The diffusion rate depends on the root mean square speed of molecules, which is proportional to √(RT/M).
32. How does R help in calculating the pressure exerted by a gas?
R helps in calculating gas pressure through the ideal gas law. Rearranging PV = nRT, we get P = nRT/V, showing how pressure depends on temperature, amount of gas, and volume, with R as the proportionality constant.
33. How does R relate to the mean free path of gas molecules?
R is indirectly related to the mean free path of gas molecules through its connection to temperature and molecular speed. The mean free path is inversely proportional to pressure and directly proportional to temperature, where R plays a role.
34. How does R appear in the equation for effusion rate?
R appears in the equation for effusion rate through its relationship with temperature. The effusion rate is proportional to √(T/M), where T is temperature and M is molar mass. R is implicit in the temperature term.
35. How does R relate to the speed of sound in a gas?
R is involved in calculating the speed of sound in a gas. The speed of sound (v) in an ideal gas is given by v = √(γRT/M), where γ is the heat capacity ratio and M is the molar mass of the gas.
36. Why is it important to specify the units when giving the value of R?
Specifying the units for R is crucial because its numerical value changes with different unit systems. Without proper units, calculations can lead to significant errors, as the value of R spans several orders of magnitude across different unit systems.
37. How does R appear in the Maxwell-Boltzmann distribution?
R appears in the Maxwell-Boltzmann distribution through the relationship with Boltzmann's constant (k = R/NA). This distribution describes the probability of a molecule having a certain speed at a given temperature.
38. Can R be used to calculate the work done by an expanding gas?
Yes, R can be used in calculations involving work done by an expanding gas. For an isothermal expansion of an ideal gas, the work done is W = nRT ln(V2/V1), where R plays a key role.
39. Can R be used to predict deviations from ideal gas behavior?
While R itself doesn't predict deviations from ideal gas behavior, comparing experimental results to calculations using R in the ideal gas law can reveal these deviations. Significant discrepancies indicate non-ideal behavior.
40. Why is R important in understanding gas compression processes?
R is crucial in understanding gas compression processes because it relates pressure, volume, and temperature changes. In adiabatic compression, for example, the relationship PV^γ = constant involves R implicitly through the heat capacity ratio γ.
41. How does R appear in the equation for gas viscosity?
R appears in gas viscosity equations through its relationship with temperature. Gas viscosity is proportional to √(MT), where M is molar mass and T is temperature. R is implicit in the temperature dependence of viscosity.
42. Can R be used to calculate the speed of gas molecules?
Yes, R is used to calculate the root mean square speed of gas molecules. The equation vrms = √(3RT/M) directly involves R, relating molecular speed to temperature and molar mass.
43. How does R help in understanding the concept of partial pressure?
R helps in understanding partial pressure through Dalton's law of partial pressures. For a mixture of ideal gases, each gas exerts a partial pressure as if it were alone, and the total pressure is the sum of these. R applies to each gas independently.
44. Why is R important in calculating the compressibility factor of gases?
R is important in calculating the compressibility factor (Z) of gases. Z is defined as PV/nRT, where R is crucial. Deviations of Z from 1 indicate non-ideal behavior of real gases.
45. How does R appear in the Clausius-Clapeyron equation?
R appears explicitly in the Clausius-Clapeyron equation, which describes the relationship between vapor pressure and temperature: ln(P2/P1) = (ΔHvap/R)(1/T1 - 1/T2), where ΔHvap is the enthalpy of vaporization.
46. Can R be used to calculate the critical temperature of a gas?
While R itself doesn't directly determine the critical temperature, it's involved in calculations related to critical points. The critical temperature is often expressed in terms of other parameters that involve R in their definitions.
47. How does R help in understanding the Joule-Thomson effect?
R is involved in understanding the Joule-Thomson effect through its role in the ideal gas law and equations of state. The effect describes temperature changes in a gas undergoing expansion, where deviations from ideal behavior are important.
48. Why is R important in calculating the work done in a cyclic process?
R is important in calculating work in cyclic processes because it relates pressure, volume, and temperature changes. In processes like the Carnot cycle, R is crucial for determining the work done and efficiency of the cycle.
49. How does R relate to the concept of fugacity in real gases?
R is involved in the concept of fugacity, which is used to describe the effective pressure of a real gas. Fugacity is often expressed as f = φP, where φ is the fugacity coefficient, which depends on how the real gas deviates from ideal behavior described by R.
50. Can R be used to calculate the change in internal energy of a gas?
Yes, R can be used to calculate changes in internal energy of an ideal gas. For a monatomic ideal gas, the change in internal energy ΔU = (3/2)nRΔT, directly involving R in the calculation.
51. How does R appear in the van 't Hoff equation?
R appears explicitly in the van 't Hoff equation, which relates the change in equilibrium constant with temperature: d(ln K)/dT = ΔH°/RT², where K is the equilibrium constant and ΔH° is the standard enthalpy change of the reaction.
52. Why is R important in understanding gas solubility?
R is important in understanding gas solubility through Henry's law, which states that the amount of dissolved gas is proportional to its partial pressure above the liquid. The proportionality constant often involves R in its temperature dependence.
53. How does R help in calculating the efficiency of heat engines?
R helps in calculating heat engine efficiency by its role in determining the work done and heat transferred in thermodynamic cycles. For example, in the Carnot cycle, efficiency depends on temperature ratios, where R is implicitly involved.
54. Can R be used to predict the behavior of gases at very low temperatures?
While R is defined for ideal gases, it can be used as a starting point for understanding gas behavior at low temperatures. However, at very low temperatures, quantum effects become significant, and deviations from classical behavior described by R occur.
55. How does R relate to the concept of degrees of freedom in molecular motion?
R is related to degrees of freedom through the equipartition theorem. Each degree of freedom contributes (1/2)R to the molar heat capacity of a gas, linking R directly to the molecular structure and motion.
56. Why is R important in understanding gas adsorption processes?
R is important in gas adsorption processes because it's involved in describing the gas phase behavior. Adsorption isotherms often involve pressure and temperature terms, where R plays a role in relating these variables to molecular behavior.
57. How does R appear in the Sackur-Tetrode equation for entropy?
R appears explicitly in the Sackur-Tetrode equation, which gives the entropy of an ideal monatomic gas: S = nR[ln(V/n) + (3/2)ln(T) + constant]. This equation connects microscopic properties to macroscopic entropy.
58. Can R be used to understand the behavior of supercritical fluids?
While R is primarily used for ideal gases, it serves as a starting point for understanding supercritical fluids. The behavior of supercritical fluids deviates significantly from ideal gas law, but R is still involved in equations describing their properties, often with additional correction terms.

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