Concept:Based on Avogadro's principle, if two different substance samples contain the exact same number of moles, they inherently contain the exact same number of molecules.
Formula:$$ \text{Moles} = \frac{\text{Mass}}{\text{Molar Mass}} $$
Solution:- First, determine the moles of the reference sample (\( \text{CO}_2 \)):
- Molar mass of \( \text{CO}_2 = 12 + 32 = 44 \text{ g/mol} \).
- Moles of \( \text{CO}_2 = 22 \text{ g} / 44 \text{ g/mol} = 0.5 \text{ moles} \).
- Now evaluate the correct option (Water):
- Molar mass of \( \text{H}_2\text{O} = 2 + 16 = 18 \text{ g/mol} \).
- Moles of \( \text{H}_2\text{O} = 9 \text{ g} / 18 \text{ g/mol} = 0.5 \text{ moles} \).
- Since both samples equal exactly 0.5 moles, they contain the same number of molecules.
Why other options are incorrect:- 2 g of \( \text{H}_2 \): Molar mass = 2. \( 2/2 = 1.0 \text{ mole} \).
- 32 g of \( \text{O}_2 \): Molar mass = 32. \( 32/32 = 1.0 \text{ mole} \).
- 71 g of \( \text{Cl}_2 \): Molar mass = 71. \( 71/71 = 1.0 \text{ mole} \).
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