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 the diluted solution, we can use the dilution formula, which states:

\[ M_1 \times V_1 = M_2 \times V_2 \]

Where:
- \( M_1 \) = initial molarity of the solution
- \( V_1 \) = initial volume of the solution
- \( M_2 \) = final molarity of the solution (what we need to find)
- \( V_2 \) = final volume of the solution

### Step 1: Identify the given values
From the question:
- \( M_1 = 0.5 \, \text{M} \) (initial molarity)
- \( V_1 = 30 \, \text{mL} \) (initial volume)
- \( V_2 = 500 \, \text{mL} \) (final volume)

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

### Step 3: Substitute the values into the dilution formula
Now we can substitute the values into the dilution formula:
\[ 0.5 \, \text{M} \times 0.030 \, \text{L} = M_2 \times 0.500 \, \text{L} \]

### Step 4: Solve for \( M_2 \)
Rearranging the equation to solve for \( M_2 \):
\[ M_2 = \frac{0.5 \, \text{M} \times 0.030 \, \text{L}}{0.500 \, \text{L}} \]

Calculating the right side:
\[ M_2 = \frac{0.015 \, \text{mol}}{0.500 \, \text{L}} \]
\[ M_2 = 0.03 \, \text{M} \]

### Final Answer
The molarity of the diluted \( H_2SO_4 \) solution is \( 0.03 \, \text{M} \).

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