To determine which sample contains the greatest number of oxygen atoms, we must calculate how many moles of each compound are present in a 100.0-g sample, and then calculate the number of oxygen atoms based on the formula of each compound.

Steps:

1. Calculate the molar mass of each compound.
2. Determine the number of moles of each compound in a 100.0-g sample.
3. Calculate the number of oxygen atoms in each sample by multiplying the number of moles by the number of oxygen atoms per molecule.

a. H₂O (Water)

• Molar mass of H₂O: $2(1.01) + 16.00 = 18.02 \, \text{g/mol}$
• Moles of H₂O in 100.0 g: $\frac{100.0}{18.02} = 5.55 \, \text{mol}$
• Oxygen atoms: $5.55 \, \text{mol} \times 1 \, \text{O} \, \text{atom per molecule} = 5.55 \, \text{mol O atoms}$

b. N₂O (Nitrous oxide)

• Molar mass of N₂O: $2(14.01) + 16.00 = 44.02 \, \text{g/mol}$
• Moles of N₂O in 100.0 g: $\frac{100.0}{44.02} = 2.27 \, \text{mol}$
• Oxygen atoms: $2.27 \, \text{mol} \times 1 \, \text{O} \, \text{atom per molecule} = 2.27 \, \text{mol O atoms}$

c. C₃H₆O₂ (Propane-1,2-diol)

• Molar mass of C₃H₆O₂: $3(12.01) + 6(1.01) + 2(16.00) = 74.08 \, \text{g/mol}$
• Moles of C₃H₆O₂ in 100.0 g: $\frac{100.0}{74.08} = 1.35 \, \text{mol}$
• Oxygen atoms: $1.35 \, \text{mol} \times 2 \, \text{O} \, \text{atoms per molecule} = 2.70 \, \text{mol O atoms}$

d. CO₂ (Carbon dioxide)

• Molar mass of CO₂: $12.01 + 2(16.00) = 44.01 \, \text{g/mol}$
• Moles of CO₂ in 100.0 g: $\frac{100.0}{44.01} = 2.27 \, \text{mol}$
• Oxygen atoms: $2.27 \, \text{mol} \times 2 \, \text{O} \, \text{atoms per molecule} = 4.54 \, \text{mol O atoms}$

e. Comparison

• H₂O: 5.55 mol O atoms
• N₂O: 2.27 mol O atoms
• C₃H₆O₂: 2.70 mol O atoms
• CO₂: 4.54 mol O atoms

Conclusion:

The sample that contains the greatest number of oxygen atoms is H₂O with 5.55 moles of oxygen atoms.

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Would you like any further details or clarification on this solution?

Here are 5 related questions for further exploration:

1. How do you calculate the number of atoms in a given mole of a substance?
2. What is Avogadro's number and how is it used in these calculations?
3. How would the calculation change if the sample size was different?
4. How do molecular structure and bonding affect the physical properties of these compounds?
5. Why does water contain the most oxygen atoms despite its low molar mass?

Tip: When calculating atoms in a compound, always consider the molecular formula and the number of each type of atom within that formula.