Value of R in Atm - Value of Gas Constant, Formula, FAQs
The value of R is a fundamental concept in thermodynamics and plays an important role in the ideal gas equation $P V=n R T$. Understanding the value of R in $\mathbf{P V}=\mathbf{n R T}$ helps students solve problems related to gases efficiently. The value of R in calories is especially useful when energy is expressed in heat units. Similarly, the value of R in atm simplifies calculations when pressure is measured in atmospheres. The value of R in cal is commonly taken as approximately 1.98 $\mathrm{cal} \mathrm{mol}^{-1} \mathrm{~K}^{-1}$. Learning different forms of the value of R ensures accuracy in physics and chemistry numericals.
This Story also Contains
- Value of Gas constant R
- Gas Constant Formula
- Universal Gas Constant Derivation
- Different Units Of R
- Why Does the Value of Gas Constant $R$ Change with Units?
- Applications: Using the Value of Gas Constant $R$ in atm
- Summary
Value of Gas constant R
The universal gas constant $R$ is a fundamental constant used in thermodynamics and appears in the ideal gas equation:
$P V=n R T$
The value of the gas constant is:$R=8.314 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}$
This value is used when pressure is expressed in pascal (Pa), volume in cubic meter ( $\mathrm{m}^3$ ), and temperature in kelvin (K).
Also Read -Unit of Pressure
Also read -
Gas Constant Formula
The gas constant $R$ in the ideal gas law is expressed as,
$
\begin{aligned}
P V & =n R T \\
\mathrm{R} & =\frac{\mathrm{PV}}{\mathrm{nT}}
\end{aligned}
$
where,
- $P$ is the pressure of the gas
- $V$ is the volume
- $n$ is the number of moles
- $T$ is the temperature in Kelvin
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, $P \propto \frac{1}{V}$ ( $T$ and $n$ are constant)
Charle's law, $V \propto T$ ( $P$ and $n$ are constant)
Avogadro's law, $\mathrm{V} \propto \mathrm{n}$ ( $T$ and $P$ are constant)
Combining these laws,
$
\begin{aligned}
& V \propto \frac{n T}{P} \\
& V=R \frac{n T}{P}
\end{aligned}
$
We can deduce from the ideal gas statement
$P V=n R T$ .........(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:
$\mathrm{R}=\frac{\mathrm{PV}}{\mathrm{nT}} $.......(2)
This is the formula for the gas constant.
The unit of $R$ is given by, which is derived from equation (2).
$
\begin{aligned}
& \mathrm{R}=\frac{\left(\mathrm{N} / \mathrm{m}^2\right) \times\left(\mathrm{m}^3\right)}{(\mathrm{mol}) \times(\mathrm{K})} \\
& \mathrm{R}=\frac{\mathrm{Nm}}{\mathrm{~mol} \times \mathrm{K}}
\end{aligned}
$
(Newton-meter = Joule)
$\mathrm{R}=\frac{\mathrm{Joule}}{\mathrm{~mol} \times \mathrm{K}}$........(3)
- As a result, the gas constant R is measured in $\frac{\text { Joule }}{\mathrm{mol}-\mathrm{K}}$ or $\mathrm{JMol}^{-1} \mathrm{~K}^{-1}$
- 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
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.
$
\mathrm{R}=\frac{8.31}{4.184} \mathrm{CalMol}^{-1} \mathrm{~K}^{-1}
$
$
\mathrm{R}=1.97 \mathrm{CaIMol}^{-1} \mathrm{~K}^{-1}
$
Similarly, the gas constant R values can be expressed in a variety of units, as shown in the table below.
| Value of R | Units of R |
| 8.31 | J mol⁻¹K⁻¹ |
| 1.98 | Cal mol⁻¹ K⁻¹ |
| 8.31 | m³(Pa)mol⁻¹K⁻¹ |
| 0.0821 | L(atm) mol⁻¹K⁻¹ |
| 62.36 | L(torr) mol⁻¹K⁻¹ |
| 1.98 x 10⁻³ | kCal mol⁻¹K⁻¹ |
| 8.3144598 × 103 | amu.m2.s-2.K-1 |
| 8.3144598 × 10-2 | L.bar.K-1.mol-1 |
Why Does the Value of Gas Constant $R$ Change with Units?
The universal gas constant $R$ appears in the ideal gas equation:
$P V=n R T$
It is a proportionality constant that relates pressure, volume, temperature, and the amount of gas. The physical significance of $R$ remains the same in all cases. However, its numerical value depends on the units used for these physical quantities.
Pressure, volume, and energy can be expressed in different units such as pascal (Pa), atmosphere (atm), cubic meter $\left(\mathrm{m}^3\right)$, litre $(\mathrm{L})$, joule $(\mathrm{J})$, or calorie (cal). When these units are changed, the value of $R$ must also change to maintain the correctness of the equation.
For example, when pressure is taken in pascal and volume in cubic meter, $R=8.314 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}$. But when pressure is in atmosphere and volume in litre, $R=0.0821 \mathrm{~L} \mathrm{~atm} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}$.
Thus, the change in the numerical value of $R$ is only due to a change in units, while its physical meaning remains unchanged.
Applications: Using the Value of Gas Constant $R$ in atm
In many problems of chemistry and physics, pressure is conveniently expressed in atmosphere (atm) and volume in litre (L). In such cases, the value of the gas constant is taken as:
$R=0.0821 \mathrm{~L} \mathrm{~atm} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}$
This form of $R$ is widely used because it simplifies calculations without the need for unit conversion.
1. Ideal Gas Equation: The value of $R$ in atm is commonly used in the ideal gas equation $P V=n R T$ when pressure is given in atm and volume in litres. It helps in directly calculating unknown quantities such as pressure, volume, temperature, or number of moles.
2. Calculation of Molar Volume: At standard temperature and pressure (STP), where pressure is 1 atm and temperature is 273 K , this value of $R$ is used to calculate the molar volume of a gas, which is approximately 22.4 L .
3. Chemical Reactions Involving Gases: In chemical reactions where gases are involved, especially in stoichiometric calculations, using $R$ in atm makes it easier to relate volume and moles directly.
4. Thermodynamics Problems: In basic thermodynamics problems involving gaseous systems, this value of $R$ is preferred when working with laboratory-scale units like atm and litre.
Also, check-
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.
Also Read:
Frequently Asked Questions (FAQs)
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.
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,
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.
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.
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.
The value of R is R=8.314 J/K/mole
The S.I unit of gas constant is J mol⁻¹K⁻¹.
