Concept:When dealing with identical masses of different elements, the substance with the largest molar mass will inherently contain the fewest number of moles, and consequently, the fewest number of atoms.
Formula:$$ n = \frac{m}{M} $$
Solution:- Because all substances are diatomic (\( \text{N}_2, \text{H}_2, \text{O}_2 \)), their atomicity is identical (2 atoms per molecule). Therefore, we just need to compare their moles.
- Moles of \( \text{H}_2 = 10 / 2 = 5 \text{ moles} \).
- Moles of \( \text{N}_2 = 10 / 28 \approx 0.35 \text{ moles} \).
- Moles of \( \text{O}_2 = 10 / 32 \approx 0.31 \text{ moles} \).
- Since Oxygen (\( \text{O}_2 \)) has the heaviest molar mass, a 10g sample of it contains the lowest number of moles (0.31), and thus the least number of atoms.
Why other options are incorrect:- \( \text{H}_2 \): Because it is incredibly light (2 g/mol), 10 grams of hydrogen contains a massive 5 moles (most atoms).
- \( \text{N}_2 \): It is lighter than oxygen (28 vs 32), meaning 10g of Nitrogen contains slightly more atoms than 10g of Oxygen.
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