3.28 g of a sample of pure copper when heated in presence of oxygen of some time forms black copper oxide `(CuO)` which weighs 3.92 g. What approximate percent of copper remains unoxidized?

Options

A. `4.6%`
B. `5.6%`
C. `6.6%`
D. `7.6%`

Explanation

To determine the approximate percent of copper that remains unoxidized after the reaction, we can follow these steps:

### Step 1: Determine the mass of copper that has reacted.
We start with the total mass of the copper sample and the mass of the copper oxide formed.

- Mass of pure copper = 3.28 g
- Mass of copper oxide (CuO) formed = 3.92 g

### Step 2: Calculate the mass of oxygen that has reacted.
The mass of oxygen that has reacted can be calculated by subtracting the mass of copper from the mass of copper oxide.

\[ \text{Mass of oxygen} = \text{Mass of CuO} - \text{Mass of Cu} \]
\[ \text{Mass of oxygen} = 3.92 \, \text{g} - 3.28 \, \text{g} = 0.64 \, \text{g} \]

### Step 3: Calculate the moles of copper and oxygen.
Next, we convert the masses of copper and oxygen to moles using their molar masses.

- Molar mass of copper (Cu) = 63.5 g/mol
- Molar mass of oxygen (O) = 16.0 g/mol

Calculating moles of copper:
\[ \text{Moles of Cu} = \frac{\text{Mass of Cu}}{\text{Molar mass of Cu}} = \frac{3.28 \, \text{g}}{63.5 \, \text{g/mol}} \approx 0.0517 \, \text{mol} \]

Calculating moles of oxygen:
\[ \text{Moles of O} = \frac{\text{Mass of O}}{\text{Molar mass of O}} = \frac{0.64 \, \text{g}}{16.0 \, \text{g/mol}} = 0.04 \, \text{mol} \]

### Step 4: Determine the moles of copper that have reacted.
In the formation of copper oxide (CuO), one mole of copper reacts with one mole of oxygen. Thus, the moles of copper that reacted will be equal to the moles of oxygen that reacted.

\[ \text{Moles of Cu reacted} = \text{Moles of O} = 0.04 \, \text{mol} \]

### Step 5: Calculate the mass of copper that has reacted.
Now, we can calculate the mass of copper that has reacted using the moles of copper that reacted.

\[ \text{Mass of Cu reacted} = \text{Moles of Cu reacted} \times \text{Molar mass of Cu} = 0.04 \, \text{mol} \times 63.5 \, \text{g/mol} = 2.54 \, \text{g} \]

### Step 6: Calculate the mass of unoxidized copper.
Now we can find the mass of copper that remains unoxidized.

\[ \text{Mass of unoxidized Cu} = \text{Initial mass of Cu} - \text{Mass of Cu reacted} \]
\[ \text{Mass of unoxidized Cu} = 3.28 \, \text{g} - 2.54 \, \text{g} = 0.74 \, \text{g} \]

### Step 7: Calculate the percentage of unoxidized copper.
Finally, we can calculate the percentage of copper that remains unoxidized.

\[ \text{Percentage of unoxidized Cu} = \left( \frac{\text{Mass of unoxidized Cu}}{\text{Initial mass of Cu}} \right) \times 100 \]
\[ \text{Percentage of unoxidized Cu} = \left( \frac{0.74 \, \text{g}}{3.28 \, \text{g}} \right) \times 100 \approx 22.56\% \]

### Final Answer:
The approximate percent of copper that remains unoxidized is **22.56%**.