Which of the following `is//are` correct?
`100 mL` of `3.0 M HClO_(3)` reacts with excess of `Ba(OH)_(2)` according to the equation:
`Ba(OH)_(2) + 2 HClO_(3) rarr Ba (ClO_(3)) + 2H_(2) O`
`(Mw` of `Ba(ClO_(3))_(2) = 304 g mol^(-1))`

Options

A. 1.5 mol of `Ba(ClO_(3))_(2)` is formed
B. 3 mol of `Ba(ClO_(3))_(2)` is formed
C. `45.6 g` of `Ba(ClO_(3))_(2)` is obtained
D. `4.56 g` of `Ba(ClO_(3))_(2)` is obtained.

Explanation

To solve the problem, we need to analyze the provided chemical reaction and calculate the quantities involved step by step.

### Given Information:
- Volume of HClO₃ = 100 mL
- Molarity of HClO₃ = 3.0 M
- Reaction: Ba(OH)₂ + 2 HClO₃ → Ba(ClO₃)₂ + 2 H₂O
- Molar mass of Ba(ClO₃)₂ = 304 g/mol

### Step 1: Calculate the number of moles of HClO₃
To find the number of moles of HClO₃, we can use the formula:
\[ \text{Moles} = \text{Volume (L)} \times \text{Molarity (M)} \]
First, convert the volume from mL to L:
\[ 100 \, \text{mL} = 0.1 \, \text{L} \]
Now, calculate the moles:
\[ \text{Moles of HClO₃} = 0.1 \, \text{L} \times 3.0 \, \text{M} = 0.3 \, \text{moles} \]

### Step 2: Determine the moles of Ba(ClO₃)₂ produced
From the balanced equation, we see that 2 moles of HClO₃ produce 1 mole of Ba(ClO₃)₂. Therefore, the moles of Ba(ClO₃)₂ produced can be calculated as follows:
\[ \text{Moles of Ba(ClO₃)₂} = \frac{\text{Moles of HClO₃}}{2} = \frac{0.3}{2} = 0.15 \, \text{moles} \]

### Step 3: Convert moles of Ba(ClO₃)₂ to grams
To find the mass of Ba(ClO₃)₂ produced, we use the formula:
\[ \text{Mass} = \text{Moles} \times \text{Molar Mass} \]
Substituting the values:
\[ \text{Mass of Ba(ClO₃)₂} = 0.15 \, \text{moles} \times 304 \, \text{g/mol} = 45.6 \, \text{g} \]

### Summary of Results
1. Moles of HClO₃ = 0.3 moles
2. Moles of Ba(ClO₃)₂ produced = 0.15 moles
3. Mass of Ba(ClO₃)₂ produced = 45.6 g

### Conclusion
Based on the calculations:
- The first statement (1.5 moles of Ba(ClO₃)₂ is formed) is incorrect; it should be 0.15 moles.
- The second statement (45.6 g of Ba(ClO₃)₂ is obtained) is correct.
- The third statement (4.6 g of Ba(ClO₃)₂ is obtained) is incorrect.

Thus, the correct options are:
- **Correct options are: Option B (45.6 g of Ba(ClO₃)₂ is obtained)**