Which of the following statements are correct?

Options

A. A sample of `CaCO_(3)` contains `Ca = 40%`, C = 12%`, and ``O = 48%`. If the law of constant compositon is true, then the mass of `Ca` in `10 g` `CaCO_(3)` from another source is `4.0 g`
B. `12 g` of carbon is heated in vacuum and there is no change in the mass, is the best example of the law of conservation of mass.
C. Air is heated at constant pressure and there is no change in mass but the increases, is the best example of the law of conservation of mass.
D. `SO_(2)` gas was prepared by (i) heating `Cu` with cone `H_(2)SO_(4)` (ii) burning sulphur in oxygen, (iii) reacting observed that is each case, `S` and `O` combines in the ratio of 1:1. This data illustrates the law of constant composition.

Answer

To determine which statements are correct, we will analyze each statement based on the laws of chemistry, specifically the law of constant composition and the law of conservation of mass.

### Step-by-Step Solution:

1. **Analyzing Statement 1:**
- The statement claims that a sample of CaCO3 contains Calcium 40%, Carbon 12%, and Oxygen 48%.
- According to the law of constant composition, a chemical compound always contains its elements in a fixed ratio by mass, regardless of its source.
- In 100 grams of CaCO3, the mass of Calcium is 40 grams. Therefore, in 10 grams of CaCO3, the mass of Calcium can be calculated as:
\[ \text{Mass of Calcium in 10g of CaCO3} = \left(\frac{40 \text{ g}}{100 \text{ g}}\right) \times 10 \text{ g} = 4 \text{ g} \]
- This matches the statement, so **Statement 1 is correct**.

2. **Analyzing Statement 2:**
- This statement claims that 12 grams of carbon heated in vacuum shows no change in mass.
- According to the law of conservation of mass, the mass of reactants must equal the mass of products in a closed system.
- Since there is no mass change during the heating of carbon in a vacuum (no reaction with oxygen), this statement is consistent with the law of conservation of mass. Thus, **Statement 2 is correct**.

3. **Analyzing Statement 3:**
- The statement mentions that air is heated at constant pressure and there is no change in mass.
- Again, this is an application of the law of conservation of mass. If the mass remains constant during the heating process, it adheres to this law. Therefore, **Statement 3 is correct**.

4. **Analyzing Statement 4:**
- This statement claims that SO2 gas was prepared by two methods and states that S and O combine in a 1:1 ratio, illustrating the law of constant proportion.
- However, in SO2, sulfur and oxygen combine in a 1:2 ratio (1 sulfur atom combines with 2 oxygen atoms). Therefore, the statement is incorrect regarding the ratio and misrepresents the law of constant composition. Thus, **Statement 4 is incorrect**.

### Conclusion:
The correct statements are:
- Statement 1: Correct
- Statement 2: Correct
- Statement 3: Correct
- Statement 4: Incorrect

**Final Answer: Statements 1, 2, and 3 are correct.**