Question

Which has maximum number of molecules :-

• A. $7\,gm\,N_2$
• B. $ 2 \, gm \, H_2$
• C. $ 16 \, gm \, NO_2$
• D. $ 16 \, gm \, O_2$

Answer 1

The Correct Option is B

To determine which option has the maximum number of molecules, we need to calculate the number of moles for each gas and then compare the number of molecules. We will use Avogadro's number, which states that 1 mole of any substance contains \(6.022 \times 10^{23}\) molecules.

1. Calculate the number of moles for each gas using the formula: n = \frac{m}{M} where n is the number of moles, m is the mass of the gas, and M is the molar mass.
2. Determine the molar mass of each gas:
   • N_2: Molar mass = 28 g/mol
   • H_2: Molar mass = 2 g/mol
   • NO_2: Molar mass = 46 g/mol
   • O_2: Molar mass = 32 g/mol
3. Calculate the number of moles for each option:
   • \text{For } 7 \, \text{g} \, N_2: n = \frac{7}{28} = 0.25 \text{ moles}
   • \text{For } 2 \, \text{g} \, H_2: n = \frac{2}{2} = 1 \text{ mole}
   • \text{For } 16 \, \text{g} \, NO_2: n = \frac{16}{46} \approx 0.35 \text{ moles}
   • \text{For } 16 \, \text{g} \, O_2: n = \frac{16}{32} = 0.5 \text{ moles}
4. Now, compare the number of moles:
   • N_2 = 0.25 \text{ moles}
   • H_2 = 1 \text{ mole}
   • NO_2 \approx 0.35 \text{ moles}
   • O_2 = 0.5 \text{ moles}
5. H_2 has the maximum number of moles, hence, the maximum number of molecules.

The correct answer is 2 \, \text{gm} \, \text{H}_2, because it contributes the largest number of molecules.