Aluminium oxide contains 52.90% aluminium and carbon dioxide contains 27.27% carbon. Calculate the percentage of aluminium in aluminium carbide assuming that the law of reciprocal proportions is true.

Answer

To calculate the percentage of aluminium in aluminium carbide using the law of reciprocal proportions, we can follow these steps:

### Step 1: Determine the percentage of oxygen in aluminium oxide
Given that aluminium oxide (Al₂O₃) contains 52.90% aluminium, we can find the percentage of oxygen as follows:

\[ \text{Percentage of Oxygen} = 100\% - \text{Percentage of Aluminium} = 100\% - 52.90\% = 47.10\% \]

### Step 2: Calculate the mass ratio of aluminium to oxygen in aluminium oxide
From the percentages, we can express the mass of aluminium and oxygen that combine:

- Mass of Aluminium = 52.90 g
- Mass of Oxygen = 47.10 g

To find the ratio of aluminium to oxygen:

\[ \text{Ratio of Al to O} = \frac{52.90}{47.10} \approx 1.123 \]

### Step 3: Determine the percentage of oxygen in carbon dioxide
Given that carbon dioxide (CO₂) contains 27.27% carbon, we can find the percentage of oxygen:

\[ \text{Percentage of Oxygen} = 100\% - \text{Percentage of Carbon} = 100\% - 27.27\% = 72.73\% \]

### Step 4: Calculate the mass ratio of carbon to oxygen in carbon dioxide
From the percentages, we can express the mass of carbon and oxygen that combine:

- Mass of Carbon = 27.27 g
- Mass of Oxygen = 72.73 g

To find the ratio of carbon to oxygen:

\[ \text{Ratio of C to O} = \frac{27.27}{72.73} \approx 0.375 \]

### Step 5: Establish the ratio of aluminium to carbon
According to the law of reciprocal proportions, the ratio of aluminium to carbon in aluminium carbide (Al₄C₃) will be the same as the ratios calculated above. Thus, we can write:

\[ \text{Ratio of Al to C} = \frac{1.123}{0.375} \]

### Step 6: Calculate the total mass in aluminium carbide
To find the percentage of aluminium in aluminium carbide, we first need to find the total mass of aluminium and carbon:

\[ \text{Total mass} = 1.123 + 0.375 = 1.498 \]

### Step 7: Calculate the percentage of aluminium in aluminium carbide
Now, we can calculate the percentage of aluminium in aluminium carbide:

\[ \text{Percentage of Aluminium} = \left( \frac{1.123}{1.498} \right) \times 100 \approx 74.9\% \]

### Final Answer
The percentage of aluminium in aluminium carbide is approximately **75%**.

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