Which one of the following has different number of molecules ? (All ar

Which one of the following has different number of molecules ? (All are kept at normal temperature and pressure)

3 gram of Hydrogen
48 gram of Oxygen
42 gram of Nitrogen
2 gram of Carbon
This question was previously asked in
UPSC NDA-2 – 2016
To determine which option has a different number of molecules, we need to calculate the number of moles for each substance. The number of molecules is directly proportional to the number of moles (Avogadro’s law states that equal volumes of gases at the same temperature and pressure contain equal numbers of molecules; here we are comparing masses).
– A) 3 gram of Hydrogen (H₂): Molar mass ≈ 2 g/mol. Moles = 3 g / 2 g/mol = 1.5 moles.
– B) 48 gram of Oxygen (O₂): Molar mass ≈ 32 g/mol. Moles = 48 g / 32 g/mol = 1.5 moles.
– C) 42 gram of Nitrogen (N₂): Molar mass ≈ 28 g/mol. Moles = 42 g / 28 g/mol = 1.5 moles.
– D) 2 gram of Carbon (C): Molar mass ≈ 12 g/mol. Moles = 2 g / 12 g/mol = 1/6 moles ≈ 0.167 moles.
Options A, B, and C all contain 1.5 moles (and thus the same number of molecules). Option D contains a significantly different number of moles (and thus atoms, as carbon exists as atoms in its elemental solid form).
– The number of molecules in a given mass of a substance is proportional to the number of moles, which is calculated as Mass / Molar Mass.
– Avogadro’s number (approximately 6.022 x 10²³) represents the number of particles (atoms, molecules, etc.) in one mole of a substance.
The condition “All are kept at normal temperature and pressure” (NTP) is relevant for comparing volumes of gases using Avogadro’s law, but here we are comparing masses and thus the number of moles/molecules directly using molar masses. Note that elemental carbon is a solid at NTP, while hydrogen, oxygen, and nitrogen are gases (diatomic molecules H₂, O₂, N₂). The question phrasing “number of molecules” for carbon is slightly imprecise as solid carbon consists of atoms in a lattice, but the underlying principle is comparing the amount of substance (moles).
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