Universal Gas Constant (original) (raw)

Last Updated : 3 Jan, 2024

**Gas Constant or **Universal Gas Constant is a physical constant, represented by the letter R, and is expressed in terms of energy units per mole of temperature increment. The value of the gas constant is the same as that of the Boltzmann constant, but it is expressed as the pressure-volume product rather than the energy per particle increment of temperature. In this article, we will look into what is Universal gas constant, it's value and uses, etc.

Table of Content

• What is Universal Gas Constant?
• Value of Universal Gas Constant
• Unit of Universal Gas Constant
• Dimensional formula of Gas Constant
• Applications of Universal Gas Constant

What is Universal Gas Constant?

The Universal Gas Constant, also known as the molar gas constant, is a physical constant denoted by the symbol R. It is expressed in units of energy per temperature increment per amount of substance and is the molar equivalent to the Boltzmann constant.

The universal gas constant applies to all ideal gases and is used in the ideal gas law, which states that the pressure (P) times the volume (V) is equal to the number of moles (n) times the gas constant (R) times the temperature (T). It combines constants from Boyle's law, Charles's law, and Avogadro's number.

Universal Gas Constant Formula

The gas constant is a proportionality constant that relates the energy scale in physics to the temperature and is used to relate the gas's pressure, volume, temperature, and amount of substance. The ideal gas law, which incorporates the gas constant, is given by the equation

**PV = nRT

Where

• **P is pressure,
• **V is volume,
• **n is the amount of substance,
• **R is the gas constant, and
• **T is the temperature.

Value of Universal Gas Constant

The Universal Gas Constant is a fundamental physical constant used to formulate the ideal gas law. Its value is approximately

**8.314 J/mol·K

Unit of Universal Gas Constant

Si Unit of Universal Gas Constant is J/mol K (Joles per mole Kelvin), but other than this there are some more units for Universal Gas Constant that are listed as follows:

• Liters·atmospheres per mole per Kelvin (L·atm/mol·K)
• Cubic meters·Pascals per mole per Kelvin (m³·Pa/mol·K)
• Calories per mole per Kelvin (cal/mol·K)
• Ergs per mole per Kelvin (erg/mol·K)

Value of Universal Gas Constant in Different Units

Inverse uses of the gas constant can be found in many academic fields. It is expressed in multiple units as a result. Here is a list of some gas constant values in various units:

Value of Universal Gas Constant at ATM

The R constant for atm in the US Standard Atmosphere is provided as

**R is equal to 8.31432×103 N⋅m⋅kmol −1 ⋅K −1

Dimensional formula of Gas Constant

The dimensional formula of the gas constant can be derived from the ideal gas law, (PV = nRT), where (P) is pressure, (V) is volume, (n) is the amount of substance, (R) is the gas constant, and (T) is the temperature.

From the ideal gas law, the dimensional formula of the gas constant can be expressed as:

**R = PV/nT

The dimensional expression for R can be obtained by writing pressure as force per unit area, which allows us to:

**R = (F/A) x Vol/ amount x temp

Volume and area can be expressed as length: area = (length)2 and volume = (length)3.

Thus we get-

**R = (F/l 2 ) x (l) 3 / amount x temp = force x l/ amount x temp

Since force times length is work, we get:

**R = Work/ amount x temp

Thus, a gas constant can be interpreted as work per degree per mole.

Specific Gas Constant

The specific gas constant, denoted as (Rspecific), is the gas constant divided by the molar mass of the gas. It is expressed in units of energy per temperature increment per unit mass. The specific gas constant is commonly represented by the symbol (R) and is used to relate the properties of a particular gas to its molar mass. The specific gas constant is given by the equation:

**[ R specific = R/M ]

Where:

• **R is the Gas constant, and
• **M is the Molar mass of the gas.

The value of the specific gas constant depends on the particular gas and is used in various thermodynamic calculations and equations. Value of Specific Gas Constant for some of the most common gases are:

Applications of Universal Gas Constant

Some of its key applications include:

• **Thermodynamics: The gas constant is extensively used in thermodynamics to relate the energy scale to the temperature when one mole of particles at a defined temperature is considered. It appears in various fundamental equations, such as the ideal gas law and the Nernst equation.
• **Unit Conversion: The universal gas constant is employed in unit conversions related to energy, temperature, and amount of substance. It is expressed in different units such as joules per mole per kelvin (J/mol·K), amu·m2·s-2·K-1, L·bar·K-1·mol-1, m3·Pa·K-1·mol-1, L·Torr·K-1·mol-1, and kcal·K-1·mol-1

Solved Problems

**Problem 1: Which of the following is the ideal gas equation?

• **P+V=nRT
• **PV=n+R+T
• **PV=2nRT
• **PV=nRT

**Solution:

The ideal gas equation is given by the formula PV=nRT

**Problem 2: At constant temperature, in a given mass of an idea gas

**A) The ratio of pressure and volume always remains constant

**B) Volume always remains constant

**C) Pressure Always remains constant

**D) The product of pressure and volume always remains constant

**Solution:

According to Boyle's law

V ~ 1/P

⇒ V = Constant/P

⇒ VP = Constant

**Problem 3: If 20cm 3 | gas at 1 atm. is expanded to 50cm 3 at constant T, then what is the final pressure

**A) 20 x 1/50

**B) 50 x 1/20

**C) 1 x 1/20 x 50

**D) None of these

**Solution:

At constant

T, P1V1 = P2V2

⇒ 1 x 20 = P2 x 50

⇒ P2 = 20/50 x 1