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

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

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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

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 $\mathrm{R}=8.314 \mathrm{~J} / \mathrm{K} / \mathrm{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, $P \propto \frac{1}{V}$ ( $T$ 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:

$\mathrm{R}=\frac{\mathrm{PV}}{\mathrm{nT}} \ldots \ldots \ldots$.......(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 $\mathrm{\$\backslash mathrm\{R\}=8.31\; \backslash mathrm\{JMol\}^\{-1\}\; \backslash mathrm\{~K\}^\{-1\}\$}$

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.

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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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