For converting a solution if 100 ml KCl of 0.4 M concentration into a solution of KCl 0.05 M concentration. The quantity of water added is

Options

A. 900 ml
B. 700 ml
C. 500 ml
D. 300 ml

Explanation

To solve the problem of converting a 100 ml KCl solution of 0.4 M concentration into a solution of 0.05 M concentration, we can use the dilution formula, which states:

\[ M_1 V_1 = M_2 V_2 \]

Where:
- \( M_1 \) = initial molarity (0.4 M)
- \( V_1 \) = initial volume (100 ml)
- \( M_2 \) = final molarity (0.05 M)
- \( V_2 \) = final volume (unknown)

### Step 1: Calculate the initial moles of KCl
First, we need to calculate the number of moles of KCl in the initial solution:

\[ \text{Moles of KCl} = M_1 \times V_1 = 0.4 \, \text{M} \times 0.1 \, \text{L} = 0.04 \, \text{moles} \]

### Step 2: Set up the dilution equation
Using the dilution equation:

\[ M_1 V_1 = M_2 V_2 \]

Substituting the known values:

\[ 0.4 \, \text{M} \times 100 \, \text{ml} = 0.05 \, \text{M} \times V_2 \]

### Step 3: Solve for \( V_2 \)
Now, we can solve for \( V_2 \):

\[ 40 = 0.05 \times V_2 \]

\[ V_2 = \frac{40}{0.05} = 800 \, \text{ml} \]

### Step 4: Calculate the quantity of water added
To find the quantity of water that needs to be added, we subtract the initial volume from the final volume:

\[ \text{Volume of water added} = V_2 - V_1 = 800 \, \text{ml} - 100 \, \text{ml} = 700 \, \text{ml} \]

### Final Answer
The quantity of water added is **700 ml**.

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