Question

What is Avogadro’s law?
A) \[\dfrac{{{V_2}}}{{{V_1}}} = \dfrac{{{T_2}}}{{{T_1}}}\]
B) \[\dfrac{{{V_1}}}{{{n_1}}} = \dfrac{{{V_2}}}{{{n_2}}}\]
C) \[{P_1}{V_1} = {P_2}{V_2}\]
D) None of these

Answer 1

Hint: We have to remember that ideal gas molecules do not attract each other. The value of \[R\] = 8.314 \[J/Kmol\]
We can write the ideal gas equation as \[PV = nRT\]
Where P-pressure of the gas
V-volume
R-gas constant
n-number of moles
T-Temperature

Complete step by step answer:
We will look at this question by understanding this law:
Avogadro’s law states that the gases at same pressure and temperature at equal volumes will have the same number of molecules.
Ideal gas equation states that:
\[PV = nRT\], which states that pressure and volume is directly proportional temperature and number of moles.
Considering an example of Hydrogen and nitrogen gas having equal numbers of moles at same pressure and temperature with equal volumes is observed to show an ideal behavior.
Avogadro’s law can be written as
\[V \propto n{\mkern 1mu} \]
\[V = kn\]
Where, \[V\] is the volume of a gas
\[n\]=no. of moles
\[k\]= constant at given temperature and pressure
Thus this law can be narrated as at same temperature and pressure, equal volume of gases contains equal number of moles.
\[\dfrac{{{V_1}}}{{{n_1}}} = \dfrac{{{V_2}}}{{{n_2}}}\]
Where \[{V_1}\]=volume of gas 1
\[{V_2}\]=volume of gas 2
\[{n_1}\]=no. of moles of molecule1
\[{n_2}\]=no. of moles of molecule2
Option A) this is an incorrect option as \[\dfrac{{{V_2}}}{{{V_1}}} = \dfrac{{{T_2}}}{{{T_1}}}\] this represents Charles law.
Option B) this is a correct option as explained above \[\dfrac{{{V_1}}}{{{n_1}}} = \dfrac{{{V_2}}}{{{n_2}}}\] this is Avogadro’s law as explained above.
Option C) this is an incorrect option as \[{P_1}{V_1} = {P_2}{V_2}\] this equation represents Boyle’s law.
Option D) this is an incorrect option as we got option B as a correct option.

Hence, the correct answer is, ‘Option D’.

Note: We have to remember that Boyle's law states that Pressure is inversely proportional to Volume and Charles’s law states that Temperature is directly proportional to volume.