The volume of 10 g of gas X is 5.6 litre at NTP. What is the molecular weight of X?

The correct answer is 40.

Key Points

• Avagadro's law:
  • "Equal volumes of all gases at the same temperature and pressure should contain an equal number of molecules".
• Law means that as long as the temperature and pressure remain constant, the volume depends upon the number of molecules of the gas or in other words amount of the gas.
• E.g: If 1 liter of H2 contains x molecules, then 1 liter of O2/Cl2/ any other gas will contain equal molecules, under similar conditions of temperature and pressure.
• Avogadro made a distinction between atoms and molecules.
• Since the volume of a gas is directly proportional to the number of moles; one mole of each gas at normal temperature and pressure (NTP) will have the same volume.
• i.e., one mole= Avagodro number of molecules (6.022 ×1023 molecules)
• Hence, at NTP, 22.4 L of H2/O2/Cl2/ any other gas contains 1 mole of the substance or NA molecules (Avagadro no: of molecules). 
• Mathematically, Avagadro's law is given by:

\(W \propto V\)       

⇒ \({\text{W = K V}}\)

⇒ \(\frac{{{W_1}}}{{{V_1}}} = \frac{{{W_2}}}{{{V_2}}}\)

Vapour Pressure:

• It is the ratio of the mass of one molecule of a substance vapour to the mass of hydrogen.
• Vapour density is related to the Molecular mass of a substance by the equation:
  • Molecular mass = 2 × Vapour density

Calculation:

Given:

• Mass of the substance = 10g
• Temperature = 298K
• Pressure = 1 atm
• Volume = 5.6 L

1-mole gas occupies 22.4 L of volume at NTP.

\(\frac{{{W_1}}}{{{V_1}}} = \frac{{{W_2}}}{{{V_2}}}\)

\(\frac{{{10}}}{{{5.6}}} = \frac{{{W_2}}}{{{22.4}}}\)

W2 = 40 

Molecular mass = 40g