If the law of constant compositon is true, what weights of calcium carbon, and oxygen are present in `1.5 g` of calcium carbonate, if a sample of calcium carbonate from another source contains the following percentage composition: `Ca = 40.0%, C = 12.0%`, and `O = 48.0%`?

Explanation

To solve the problem, we need to determine the weights of calcium (Ca), carbon (C), and oxygen (O) present in 1.5 g of calcium carbonate (CaCO₃) using the given percentage composition.

### Step-by-Step Solution:

1. **Identify the Given Data:**
- Total mass of calcium carbonate (CaCO₃) = 1.5 g
- Percentage composition:
- Ca = 40.0%
- C = 12.0%
- O = 48.0%

2. **Calculate the Weight of Calcium (Ca):**
- Use the formula:
\[ \text{Weight of Ca} = \text{Total mass} \times \left(\frac{\text{Percentage of Ca}}{100}\right) \]
- Substitute the values:
\[ \text{Weight of Ca} = 1.5 \, \text{g} \times \left(\frac{40.0}{100}\right) = 1.5 \, \text{g} \times 0.40 = 0.6 \, \text{g} \]

3. **Calculate the Weight of Carbon (C):**
- Use the formula:
\[ \text{Weight of C} = \text{Total mass} \times \left(\frac{\text{Percentage of C}}{100}\right) \]
- Substitute the values:
\[ \text{Weight of C} = 1.5 \, \text{g} \times \left(\frac{12.0}{100}\right) = 1.5 \, \text{g} \times 0.12 = 0.18 \, \text{g} \]

4. **Calculate the Weight of Oxygen (O):**
- Use the formula:
\[ \text{Weight of O} = \text{Total mass} \times \left(\frac{\text{Percentage of O}}{100}\right) \]
- Substitute the values:
\[ \text{Weight of O} = 1.5 \, \text{g} \times \left(\frac{48.0}{100}\right) = 1.5 \, \text{g} \times 0.48 = 0.72 \, \text{g} \]

5. **Final Weights:**
- Weight of Calcium (Ca) = 0.6 g
- Weight of Carbon (C) = 0.18 g
- Weight of Oxygen (O) = 0.72 g

### Summary of Results:
- Weight of Calcium (Ca) = 0.6 g
- Weight of Carbon (C) = 0.18 g
- Weight of Oxygen (O) = 0.72 g