3.42 g of sucrose are dissolved in 18g of water in a beaker. The number of oxygen atoms in the solution are

Options

A. `6.68 xx 10^(23)`
B. `6.09 xx 10^(22)`
C. `6.022 xx 10^(23)`
D. `6.022 xx 10^(21)`

Explanation

To find the number of oxygen atoms in a solution of sucrose and water, we will follow these steps:

### Step 1: Calculate the molar mass of sucrose (C₁₂H₂₂O₁₁)
- The atomic masses are approximately:
- Carbon (C) = 12 g/mol
- Hydrogen (H) = 1 g/mol
- Oxygen (O) = 16 g/mol

Using the formula for sucrose:
- Molar mass of sucrose = (12 × 12) + (22 × 1) + (11 × 16)
- Molar mass of sucrose = 144 + 22 + 176 = 342 g/mol

### Step 2: Calculate the number of moles of sucrose
- Given mass of sucrose = 3.42 g
- Number of moles of sucrose = mass / molar mass
- Number of moles of sucrose = 3.42 g / 342 g/mol = 0.01 moles

### Step 3: Calculate the number of oxygen atoms in sucrose
- Each mole of sucrose contains 11 moles of oxygen atoms.
- Therefore, the number of moles of oxygen in 0.01 moles of sucrose = 0.01 moles × 11 = 0.11 moles of oxygen.
- Using Avogadro's number (6.022 × 10²³), the number of oxygen atoms = 0.11 moles × 6.022 × 10²³ atoms/mole = 6.626 × 10²² atoms.

### Step 4: Calculate the number of oxygen atoms in water (H₂O)
- Molar mass of water = (2 × 1) + (1 × 16) = 18 g/mol
- Given mass of water = 18 g
- Number of moles of water = mass / molar mass
- Number of moles of water = 18 g / 18 g/mol = 1 mole

### Step 5: Calculate the number of oxygen atoms in water
- Each mole of water contains 1 mole of oxygen atoms.
- Therefore, the number of moles of oxygen in 1 mole of water = 1 mole.
- The number of oxygen atoms = 1 mole × 6.022 × 10²³ atoms/mole = 6.022 × 10²³ atoms.

### Step 6: Calculate the total number of oxygen atoms in the solution
- Total number of oxygen atoms = oxygen atoms from sucrose + oxygen atoms from water
- Total number of oxygen atoms = 6.626 × 10²² + 6.022 × 10²³
- To add these, we convert 6.626 × 10²² to the same power of ten:
- 6.626 × 10²² = 0.6626 × 10²³
- Now, adding them:
- Total = 0.6626 × 10²³ + 6.022 × 10²³ = 6.6846 × 10²³

### Final Answer:
The total number of oxygen atoms in the solution is approximately **6.6846 × 10²³**.

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