The volume of 10.50 M solution required to prepare
1.0 L of 0.25 M solution of `HNO_(3)` is :

Options

A. 250 mL
B. 500 mL
C. 230 mL
D. 23.8 mL

Explanation

To solve the problem of finding the volume of a 10.50 M solution required to prepare 1.0 L of a 0.25 M solution of HNO₃, we can use the dilution formula:

\[ m_1 V_1 = m_2 V_2 \]

Where:
- \( m_1 \) = molarity of the concentrated solution (10.50 M)
- \( V_1 \) = volume of the concentrated solution (unknown)
- \( m_2 \) = molarity of the diluted solution (0.25 M)
- \( V_2 \) = volume of the diluted solution (1.0 L)

### Step 1: Write down the known values
- \( m_1 = 10.50 \, \text{M} \)
- \( m_2 = 0.25 \, \text{M} \)
- \( V_2 = 1.0 \, \text{L} \)

### Step 2: Substitute the known values into the dilution formula
Using the formula \( m_1 V_1 = m_2 V_2 \):

\[ 10.50 \, \text{M} \times V_1 = 0.25 \, \text{M} \times 1.0 \, \text{L} \]

### Step 3: Calculate the volume \( V_1 \)
Rearranging the equation to solve for \( V_1 \):

\[ V_1 = \frac{0.25 \, \text{M} \times 1.0 \, \text{L}}{10.50 \, \text{M}} \]

Calculating this gives:

\[ V_1 = \frac{0.25}{10.50} \]

\[ V_1 = 0.0238 \, \text{L} \]

### Step 4: Convert the volume from liters to milliliters
To convert liters to milliliters, multiply by 1000:

\[ V_1 = 0.0238 \, \text{L} \times 1000 = 23.8 \, \text{mL} \]

### Final Answer
The volume of the 10.50 M solution required to prepare 1.0 L of a 0.25 M solution of HNO₃ is **23.8 mL**.

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