A sample of zinc oxide contains 80.25% zinc. Calculate the equivalent mass of zinc.

Answer

To calculate the equivalent mass of zinc in a sample of zinc oxide that contains 80.25% zinc, we can follow these steps:

### Step 1: Define the mass of zinc oxide
Let the total mass of the zinc oxide (ZnO) sample be \( X \) grams.

### Step 2: Calculate the mass of zinc
Since the sample contains 80.25% zinc, the mass of zinc (Zn) in the sample can be calculated as:
\[ \text{Mass of Zn} = \frac{80.25}{100} \times X = 0.8025X \]

### Step 3: Calculate the mass of oxygen in zinc oxide
The remaining percentage of the sample is oxygen. Therefore, the mass of oxygen (O) in the sample can be calculated as:
\[ \text{Mass of O} = \frac{100 - 80.25}{100} \times X = \frac{19.75}{100} \times X = 0.1975X \]

### Step 4: Calculate the equivalent mass of zinc
The equivalent mass of zinc can be calculated using the formula:
\[ \text{Equivalent mass of Zn} = \frac{\text{Mass of Zn}}{\text{Mass of O in ZnO}} \times 8 \]
Substituting the values we found:
\[ \text{Equivalent mass of Zn} = \frac{0.8025X}{0.1975X} \times 8 \]

### Step 5: Simplify the equation
The \( X \) cancels out:
\[ \text{Equivalent mass of Zn} = \frac{0.8025}{0.1975} \times 8 \]

### Step 6: Calculate the ratio
Calculating the ratio:
\[ \frac{0.8025}{0.1975} \approx 4.06 \]
Now, multiplying by 8:
\[ \text{Equivalent mass of Zn} \approx 4.06 \times 8 \approx 32.48 \text{ grams} \]

### Final Result
Thus, the equivalent mass of zinc is approximately:
\[ \text{Equivalent mass of Zn} \approx 32.51 \text{ grams} \]