Dimensional formula of Universal Gas Constant

Gases possess intrinsic and exciting properties, making them valuable to study physics. Unlike other matters, gases do not have any specific shape or volume. They are capable of filling up any space they are given. This property of gases where they can fill up any space available is due to their molecules’ capability to rush. This mostly happens because the intermolecular forces between the two adjacent gas molecules are feeble.

All these properties of gases led to the discovery of multiple aspects associated with its activities like the kinetic theory, the universal gas constant and a lot more. We will discuss all of that and universal gas’s constant importance in detail further.

What are gases?

Gases are defined as a state of matter devoid of any specific shape, size or volume. They possess a lower density than solids and liquids as well. Gases also possess unique properties, which makes them an exciting matter to study.

Compressibility of gases

The intermolecular spaces between the molecules of gases are massive. Still, this intermolecular space is reduced when pressure is exerted on gases, bringing the gas molecules closer. This effectively reduces the gas volume, called the compressibility of gases.

Temperature also affects the volume of gases; the decreasing temperature will decrease the volume of gases. When the temperature is reduced, the amount of energy that works in the particles is also reduced—leading to the Diminished in the movement of gas molecules, thereby reducing their volume.

Expansion of gases

Temperature and pressure affect the expansion capability of gases as well. When pressure is exerted on gases, contraction happens, and the gas contracts. In contrast, the gas also expands when the pressure is pulled away. When temperature increases, the gas molecules gain energy to rush, thereby increasing their volume. This happens because the intermolecular attraction between the gas molecules decreases, and gases run through space.

Diffusion of gases

The effortless diffusion capability of gases facilitates the homogeneous mixing of two gases. When two gases are mixed, they quickly enter into the intermolecular distances of another gas. As gases possess big intermolecular spaces; 

The density of gases

As gases possess large volumes due to the massive intermolecular spaces, this is also why they have very low densities.

Pressure exertion capability of gases

Gases are the only matter which can exert pressure in every direction. When gases are stored in a closed container, they exert pressure on the inner walls of the container. This happens because of the rapid movement of the molecules. In comparison, solids and liquids cannot do the same.

Gas laws

Even though all gases are not chemically the same in their properties, they all obey gas laws. The gas laws are developed by several scientists depending on pressure, temperature, volume, and amount. These laws establish a connection between the several properties of the gases like pressure, volume etc.

Boyle’s Law- according to this Law, the pressure and volume of a gas are inversely proportional to each other when the temperature and quantity of the gas are kept constant. 

Charles’s Law- according to this Law, for a constant volume, the pressure of a specific mass of gas will vary directly with the temperature change.

Avogadro’s Law- According to this Law, under specific temperature and pressure conditions, the same volumes of various gases possess an equal number of molecules. The value of Avogadro’s number is 6.02214076 × 1023.

Gay-Lussac’s Law- According to this Law, the pressure put by a gas of a specific mass to a particular volume varies directly with the temperature maintained. 

Ideal gas law- According to this Law, the pressure, temperature, and volume are interconnected by the following relationship; pV=nRT (p= pressure, v= volume, n= number of moles of gas R= gas law constant and T= absolute temperature).

The universal gas equation and universal gas constant

The universal gas equation, in simple words, can be defined as the amalgamation of all the gas laws mentioned above. The properties of gases like pressure, volume and temperature are all interrelated. Robert Boyle first studied this. According to Boyle’s Law, PV = constant.

According to Charles law, V/T= constant.

When these two laws are combined, PV/T = constant.

The constant in this Law is stated as the universal gas constant designated as R, which is stable = nR, where n is the number of moles of gas.

So, if we combine Boyle’s Law, Charles’s Law and Avogadro’s Law, we can derive the universal gas equation, which is 

pV=nRT. Here R is the universal gas constant.

Derivation: 

V=nRT/P

We can also say PV=nRT.

R= PV (nT)-1     ______A

P= pressure, V= volume, n= number of moles, T= absolute temperature, and R= universal gas constant.

According to the dimensional formula of volume, V= [M0 L3 T0]_____ 1

The dimensional formula of temperature is [M0 L0 T0 K1]_____2

 We know, pressure = force x (area)-1

Then, Mass × acceleration × [Area]-1 = [M] × [L1 T-2] × [L2]-1

So the dimensional formula of pressure is [M1 L-1 T-2]_____3

Now by putting 1, 2 and 3 in equation A, we get,

R= [M1 L-1 T-2] × [M0 L3 T0] × [M0 L0 T0 K1]-1 = [M1 L2 T-2 K-1].

 So the dimensional formula of a universal gas constant is [M1 L2 T-2 K-1].

Dimensional formula of universal gas constant:

R= [M1 L2 T–2 K–1].

The value of R is 0.0821 litre/ k mol.

Conclusion

The universal gas constant importance is essential in understanding the integral aspects of gases. It portrays the essential properties a gas possesses and the measuring properties of the gas as well. The gas laws govern major relationships between gases and other properties like volume, pressure etc. hence it is extremely important to understand them before studying the universal gas constant.

Apart from that, to get a clear idea about the topic, you can also study the universal gas constant notes.