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 can follow these steps:

### Step 1: Determine the molar mass of sucrose (C12H22O11)
- The molar mass of sucrose can be calculated as follows:
- Carbon (C): 12 atoms × 12 g/mol = 144 g/mol
- Hydrogen (H): 22 atoms × 1 g/mol = 22 g/mol
- Oxygen (O): 11 atoms × 16 g/mol = 176 g/mol
- Total 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
- Moles of sucrose = mass / molar mass = 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 oxygen atoms.
- Therefore, the number of oxygen atoms in 0.01 moles of sucrose:
- Number of oxygen atoms = 0.01 moles × 11 oxygen atoms/mole × Avogadro's number (6.022 × 10^23 atoms/mole)
- Number of oxygen atoms in sucrose = 0.01 × 11 × 6.022 × 10^23 = **6.68 × 10^22 oxygen atoms**

### Step 4: Determine the number of moles of water (H2O)
- Given mass of water = 18 g
- Molar mass of water = 18 g/mol
- Moles of water = mass / molar mass = 18 g / 18 g/mol = **1 mole**

### Step 5: Calculate the number of oxygen atoms in water
- Each mole of water contains 1 oxygen atom.
- Therefore, the number of oxygen atoms in 1 mole of water:
- Number of oxygen atoms = 1 mole × 6.022 × 10^23 atoms/mole = **6.022 × 10^23 oxygen 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 = 6.68 × 10^22 + 6.022 × 10^23
- Total number of oxygen atoms = 6.68 × 10^22 + 60.22 × 10^22 = **6.69 × 10^23 oxygen atoms**

### Final Answer
The total number of oxygen atoms in the solution is approximately **6.69 × 10^23**.

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