Question

The characteristic equation of gases PV=nRT holds good for:
(A) Monoatomic gases
(B) Diatomic gas
(C) Real gases
(D) Ideal gases

Answer 1

Hint: The ideal gas law states that the product of the pressure and the volume of one gram molecule of an ideal gas is equal to the product of the absolute temperature of the gas, its moles and the universal gas constant. The ideal gas law is also known as general gas law.

Complete Step by step solution
Given that, PV=nRT
Here,
P=Pressure
V= Volume
n= Number of moles of the gas
R= Gas constant
T= Temperature
 Derivation:
According to Boyles’s law
 $ \Rightarrow \text{V}\propto \dfrac{\text{1}}{\text{P}} $ ………… (1)
Now, According to Charles’ law
 $ \Rightarrow \text{V}\propto \text{T } $ ………… (2)
Comparing (1) and (2), we have
 $ \Rightarrow \text{V}\propto \dfrac{\text{T}}{\text{P}} $
 $ \Rightarrow $ PV=nRT
Here, R is the gas constant.
Now, for n moles of gas
 $ \Rightarrow $ PV=nRT
This is an ideal or perfect gas equation. Thus, it holds good for ideal gases.
Therefore, option-D is correct.

Additional Information
For real gas, we make two changes in the ideal gas equation. First, adding constant to the pressure and second subtracting another constant from volume. Hence, the ideal gas equation becomes,
 $ \Rightarrow \left( \text{P}+\text{a}{{\text{n}}^{2}} \right)\left( \text{V}-\text{nb} \right) $
Here,
a=constant for the attraction between molecules in the given gas.
b= is the volume, those molecules take up inside the container.

Note
 Boyle’s law states that at constant temperature, the pressure of a given quantity of gas varies inversely with its volume. Further, Charles' law states that at constant pressure, the temperature is directly proportional to the volume of the dry gas. In ideal gases, molecules do not interact with each other.