A sample of impure cuprous oxide contains 66.67% copper, by ,mass. What is the percentage of pure `Cu_2`O in the sample? (Cu=63.5)

Options

A. 75%
B. 70%
C. 80%
D. 15%

Explanation

To solve the problem of finding the percentage of pure cuprous oxide (Cu₂O) in a sample that contains 66.67% copper by mass, we can follow these steps:

### Step 1: Determine the mass of copper in the sample
Assuming we have a 100 g sample of the impure cuprous oxide, the mass of copper in the sample can be calculated as follows:
\[ \text{Mass of Cu} = 66.67\% \text{ of } 100 \text{ g} = 66.67 \text{ g} \]

### Step 2: Calculate the moles of copper
Using the atomic mass of copper (Cu = 63.5 g/mol), we can calculate the number of moles of copper in the sample:
\[ \text{Moles of Cu} = \frac{\text{Mass of Cu}}{\text{Molar mass of Cu}} = \frac{66.67 \text{ g}}{63.5 \text{ g/mol}} \approx 1.05 \text{ moles} \]

### Step 3: Determine the moles of oxygen in Cu₂O
In cuprous oxide (Cu₂O), the ratio of copper to oxygen is 2:1. Therefore, for every 2 moles of copper, there is 1 mole of oxygen. Thus, the moles of oxygen can be calculated as:
\[ \text{Moles of O} = \frac{1.05 \text{ moles Cu}}{2} = 0.525 \text{ moles O} \]

### Step 4: Calculate the mass of oxygen
Now, we can calculate the mass of oxygen using its molar mass (O = 16 g/mol):
\[ \text{Mass of O} = \text{Moles of O} \times \text{Molar mass of O} = 0.525 \text{ moles} \times 16 \text{ g/mol} = 8.4 \text{ g} \]

### Step 5: Calculate the total mass of pure Cu₂O
The total mass of pure cuprous oxide can be calculated by adding the mass of copper and the mass of oxygen:
\[ \text{Mass of Cu₂O} = \text{Mass of Cu} + \text{Mass of O} = 66.67 \text{ g} + 8.4 \text{ g} = 75.07 \text{ g} \]

### Step 6: Calculate the percentage of pure Cu₂O in the sample
Finally, we can find the percentage of pure cuprous oxide in the sample:
\[ \text{Percentage of Cu₂O} = \left(\frac{\text{Mass of Cu₂O}}{\text{Total mass of sample}}\right) \times 100 = \left(\frac{75.07 \text{ g}}{100 \text{ g}}\right) \times 100 \approx 75.07\% \]

### Final Answer
The percentage of pure Cu₂O in the sample is approximately **75.07%**.

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