Question

In general, gas equation, PV = nRT ; V is the volume of:

(A) n moles of a gas

(B) any amount of gas

(C) one mole of a gas

(D) one gram of a gas

Answer 1

Hint: An ideal gas is a gas that is composed of a set of randomly-moving point particles that interact only through elastic collisions. The ideal gas concept is useful because it obeys the ideal gas law that was a simplified equation of state. The ideal gas equation can be written as PV = nRT.

Complete step by step answer:

- Firstly, let’s see the Ideal Gas Equation-The Ideal gas law is the equation of the state of a hypothetical ideal gas. We can write the ideal gas equation as:

PV = nRT

Where,

- P is the pressure of the ideal gas.

- V is the volume of the ideal gas.

- n is the amount of ideal gas measured in terms of moles.

- R is the universal gas constant.

- T is the temperature

The product of Pressure & Volume of gas consists of a constant relation with the product of the Universal gas constant and the temperature.

 - Now let’s see the Derivation of the Ideal Gas Equation

Let us consider the pressure exerted by the gas as ‘p,’

The volume of the gas as – ‘v’

Temperature as – T

the number of moles of gas- n

Universal gas constant – R

According to Boyle’s Law,

The volume is inversely proportional to the pressure at constant n & T,

i.e. $P\propto \dfrac{1}{V}$

According to Charles’ Law,

When p & n are constant, the volume of a gas has a direct relation with the Temperature.

i.e. $V\propto T$

Now, According to Avogadro’s Law,

When p & T are constant, the volume of a gas has a direct relation with the number of moles of gas.

i.e. $V\propto n$

Now, by combining all the three equations, we have-

$V\propto \dfrac{nT}{P}$

or PV = nRT

So, the correct answer is “Option A”.

Additional Information:

- With the ideal gas law, we can use the relationship between the amounts of gases (in moles) and their volumes (in liters) to calculate the stoichiometry of reactions involving gases, if the pressure and temperature are known.

- There are many reactions that are carried out in the laboratory that involves the formation or reaction of a gas.

- We also know that industrially important reactions are carried out in the gas phase for various practical reasons. Gases are mixed readily, are easily heated or cooled, and can be transferred from one place to another in a manufacturing facility through various simple pumps.

Note: It is important to note here that volume, pressure, and temperature depend on the n moles of gas, where a mole is the number of atoms or molecules that are present in a sample of the element.