Which of the following data illustrates the law of conservation of mass?

Options

A. 56 g of CO reacts with 32 g oxygen to produce 44 g of `CO_(2)`
B. 1.70 g of `AgNO_(3)` reacts with 100 mL of 0.1 MHCl to produce 1.435 g of AgCl and 0.63 g of `HNO_(3)`.
C. 12 g of C is heated in vaccume and on cooling there is no change on mass.
D. None of the above.

Explanation

To determine which of the provided data illustrates the law of conservation of mass, we need to analyze each option step by step.

### Step 1: Understand the Law of Conservation of Mass
The law of conservation of mass states that in a closed system, the mass of the reactants must equal the mass of the products in a chemical reaction. This means that matter cannot be created or destroyed in a chemical reaction.

### Step 2: Analyze Option 1
**Data:** 56 grams of CO reacts with 32 grams of oxygen to produce 44 grams of CO2.

- **Calculate the total mass of reactants:**
\[ \text{Mass of reactants} = \text{Mass of CO} + \text{Mass of O}_2 = 56 \, \text{g} + 32 \, \text{g} = 88 \, \text{g} \]

- **Given mass of products:**
\[ \text{Mass of products} = 44 \, \text{g} \]

- **Comparison:**
\[ \text{Mass of reactants} (88 \, \text{g}) \neq \text{Mass of products} (44 \, \text{g}) \]

**Conclusion:** This option does not illustrate the law of conservation of mass.

### Step 3: Analyze Option 2
**Data:** 1.70 grams of AgNO3 reacts with 100 ml of 0.1 molar HCl to produce 1.435 grams of AgCl and 0.63 grams of HNO3.

- **Calculate the mass of reactants:**
- Mass of AgNO3 = 1.70 g
- Calculate the mass of HCl using molarity:
\[ \text{Molarity} = \frac{\text{Number of moles}}{\text{Volume in liters}} \implies \text{Number of moles} = \text{Molarity} \times \text{Volume in liters} \]
\[ \text{Number of moles of HCl} = 0.1 \, \text{mol/L} \times 0.1 \, \text{L} = 0.01 \, \text{mol} \]
- Molar mass of HCl = 36.5 g/mol
\[ \text{Mass of HCl} = 0.01 \, \text{mol} \times 36.5 \, \text{g/mol} = 0.365 \, \text{g} \]

- **Total mass of reactants:**
\[ \text{Mass of reactants} = 1.70 \, \text{g} + 0.365 \, \text{g} = 2.065 \, \text{g} \]

- **Calculate the mass of products:**
\[ \text{Mass of products} = 1.435 \, \text{g} + 0.63 \, \text{g} = 2.065 \, \text{g} \]

- **Comparison:**
\[ \text{Mass of reactants} (2.065 \, \text{g}) = \text{Mass of products} (2.065 \, \text{g}) \]

**Conclusion:** This option illustrates the law of conservation of mass.

### Step 4: Analyze Option 3
**Data:** 12 grams of carbon is heated in vacuum, and on cooling, there is no change in mass.

- **Analysis:**
- There is no chemical reaction occurring here; only physical changes are happening (heating and cooling).

**Conclusion:** This option does not illustrate the law of conservation of mass because there are no reactants and products involved in a chemical reaction.

### Final Answer
The correct answer is **Option 2**, as it illustrates the law of conservation of mass.

---