The molarity of a solution made by mixing 50 ml of conc. `H_(2)SO_(4)`
(18M) with 50 ml of water, is

Options

A. 36 M
B. 18 M
C. 9 M
D. 6 M

Answer

To find the molarity of the solution made by mixing 50 ml of concentrated H₂SO₄ (18 M) with 50 ml of water, we can follow these steps:

### Step 1: Understand the Molarity Formula
The molarity (M) of a solution is defined as the number of moles of solute per liter of solution. The formula we will use is:
\[ M_1 V_1 = M_2 V_2 \]
Where:
- \( M_1 \) = initial molarity of the concentrated solution (H₂SO₄)
- \( V_1 \) = volume of the concentrated solution
- \( M_2 \) = final molarity of the diluted solution
- \( V_2 \) = final volume of the solution

### Step 2: Identify the Given Values
From the problem:
- \( M_1 = 18 \, \text{M} \) (molarity of H₂SO₄)
- \( V_1 = 50 \, \text{ml} \) (volume of H₂SO₄)
- Volume of water added = 50 ml

### Step 3: Calculate the Final Volume
The final volume \( V_f \) after mixing H₂SO₄ and water is:
\[ V_f = V_1 + \text{Volume of water} = 50 \, \text{ml} + 50 \, \text{ml} = 100 \, \text{ml} \]

### Step 4: Convert Volume to Liters
Since molarity is expressed in moles per liter, we need to convert the final volume from milliliters to liters:
\[ V_f = 100 \, \text{ml} = \frac{100}{1000} \, \text{L} = 0.1 \, \text{L} \]

### Step 5: Calculate the Number of Moles of H₂SO₄
Using the formula for molarity:
\[ \text{Moles of H₂SO₄} = M_1 \times V_1 \]
Convert \( V_1 \) to liters:
\[ V_1 = 50 \, \text{ml} = \frac{50}{1000} \, \text{L} = 0.05 \, \text{L} \]
Now calculate the moles:
\[ \text{Moles of H₂SO₄} = 18 \, \text{M} \times 0.05 \, \text{L} = 0.9 \, \text{moles} \]

### Step 6: Calculate the Final Molarity
Now we can find the final molarity \( M_2 \):
\[ M_2 = \frac{\text{Moles of H₂SO₄}}{V_f} = \frac{0.9 \, \text{moles}}{0.1 \, \text{L}} = 9 \, \text{M} \]

### Final Answer
The molarity of the solution after mixing is **9 M**.

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