Which has the maximum number of molecules among the following?

Options

A. `8 g H_(2)`
B. `64 g SO_(4)`
C. `44 g CO_(2)`
D. `48 g O_(3)`

Answer

To determine which substance has the maximum number of molecules among the given options, we will calculate the number of moles for each substance and then convert that to the number of molecules using Avogadro's number (6.022 x 10²³ molecules/mole).

### Step-by-Step Solution:

1. **Calculate the number of moles of H₂O (Water)**:
- Given mass = 8 grams
- Molar mass of H₂O = 2 (H) + 16 (O) = 18 g/mol
- Number of moles = mass / molar mass = 8 g / 18 g/mol = 0.444 moles
- Number of molecules = moles × Avogadro's number = 0.444 moles × 6.022 x 10²³ molecules/mole = 2.67 x 10²³ molecules

2. **Calculate the number of moles of SO₄ (Sulfur Tetraoxide)**:
- Given mass = 64 grams
- Molar mass of SO₄ = 32 (S) + 4 × 16 (O) = 32 + 64 = 96 g/mol
- Number of moles = mass / molar mass = 64 g / 96 g/mol = 0.667 moles
- Number of molecules = moles × Avogadro's number = 0.667 moles × 6.022 x 10²³ molecules/mole = 4.01 x 10²³ molecules

3. **Calculate the number of moles of CO₂ (Carbon Dioxide)**:
- Given mass = 44 grams
- Molar mass of CO₂ = 12 (C) + 2 × 16 (O) = 12 + 32 = 44 g/mol
- Number of moles = mass / molar mass = 44 g / 44 g/mol = 1 mole
- Number of molecules = moles × Avogadro's number = 1 mole × 6.022 x 10²³ molecules/mole = 6.022 x 10²³ molecules

4. **Calculate the number of moles of O₃ (Ozone)**:
- Given mass = 48 grams
- Molar mass of O₃ = 3 × 16 (O) = 48 g/mol
- Number of moles = mass / molar mass = 48 g / 48 g/mol = 1 mole
- Number of molecules = moles × Avogadro's number = 1 mole × 6.022 x 10²³ molecules/mole = 6.022 x 10²³ molecules

### Summary of Molecule Counts:
- H₂O: 2.67 x 10²³ molecules
- SO₄: 4.01 x 10²³ molecules
- CO₂: 6.022 x 10²³ molecules
- O₃: 6.022 x 10²³ molecules

### Conclusion:
Among the given options, H₂O has the maximum number of molecules, which is approximately 2.67 x 10²³ molecules.

### Final Answer:
The substance with the maximum number of molecules is **H₂O (Water)**.

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