To change the strength of 25 ml of 0.15 M HCl to 0.1 M the quantity of water that is to be added is

Options

A. 37.5 ml
B. 12.5 ml
C. 25.0 ml
D. 18.75 ml

Explanation

To determine the quantity of water that needs to be added to dilute 25 ml of 0.15 M HCl to a final concentration of 0.1 M, we can use the dilution formula, which is based on the principle of conservation of mass. The formula is:

\[ M_1 V_1 = M_2 V_2 \]

Where:
- \( M_1 \) = initial molarity (0.15 M)
- \( V_1 \) = initial volume (25 ml)
- \( M_2 \) = final molarity (0.1 M)
- \( V_2 \) = final volume (unknown)

### Step 1: Write down the known values
- \( M_1 = 0.15 \, \text{M} \)
- \( V_1 = 25 \, \text{ml} \)
- \( M_2 = 0.1 \, \text{M} \)

### Step 2: Use the dilution formula
We need to find \( V_2 \):
\[ M_1 V_1 = M_2 V_2 \]

Substituting the known values:
\[ 0.15 \times 25 = 0.1 \times V_2 \]

### Step 3: Calculate \( V_2 \)
First, calculate the left side:
\[ 0.15 \times 25 = 3.75 \]

Now, set up the equation:
\[ 3.75 = 0.1 \times V_2 \]

To find \( V_2 \), divide both sides by 0.1:
\[ V_2 = \frac{3.75}{0.1} = 37.5 \, \text{ml} \]

### Step 4: Calculate the quantity of water to be added
Now, we need to find out how much water to add. The quantity of water added is the difference between the final volume \( V_2 \) and the initial volume \( V_1 \):
\[ \text{Water to be added} = V_2 - V_1 \]
\[ \text{Water to be added} = 37.5 \, \text{ml} - 25 \, \text{ml} = 12.5 \, \text{ml} \]

### Final Answer
The quantity of water that needs to be added is **12.5 ml**.

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