What will be the molarity of 30 mL of 0.5 M `H_2SO_4` solution diluted to 500 mL ?

Options

A. 0.3 M
B. 0.03 M
C. 3 M
D. 0.103 M

Explanation

To find the molarity of a diluted solution, we can use the dilution formula:

\[ M_1 V_1 = M_2 V_2 \]

Where:
- \( M_1 \) = initial molarity of the solution
- \( V_1 \) = initial volume of the solution
- \( M_2 \) = final molarity of the solution
- \( V_2 \) = final volume of the solution

### Step-by-Step Solution:

1. **Identify the given values:**
- Initial molarity (\( M_1 \)) = 0.5 M
- Initial volume (\( V_1 \)) = 30 mL
- Final volume (\( V_2 \)) = 500 mL

2. **Convert volumes to liters (if necessary):**
- Since molarity is expressed in moles per liter, we can convert the volumes from mL to L:
- \( V_1 = 30 \text{ mL} = 0.030 \text{ L} \)
- \( V_2 = 500 \text{ mL} = 0.500 \text{ L} \)

3. **Substitute the values into the dilution formula:**
\[ M_1 V_1 = M_2 V_2 \]
\[ 0.5 \, \text{M} \times 0.030 \, \text{L} = M_2 \times 0.500 \, \text{L} \]

4. **Calculate the left side:**
\[ 0.5 \times 0.030 = 0.015 \, \text{moles} \]

5. **Set up the equation to solve for \( M_2 \):**
\[ 0.015 = M_2 \times 0.500 \]

6. **Isolate \( M_2 \):**
\[ M_2 = \frac{0.015}{0.500} \]

7. **Calculate \( M_2 \):**
\[ M_2 = 0.03 \, \text{M} \]

### Final Answer:
The molarity of the diluted solution is **0.03 M**.

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