The volume of water that must be added to a mixture of 250ml of 0.6 M HCl and 750 ml of 0.2 M HCl to obtain 0.25 M solution of HCl is:

Options

A. 750 ml
B. 100 ml
C. 200 ml
D. 300 ml

Answer

To solve the problem of finding the volume of water that must be added to a mixture of HCl solutions to obtain a final concentration of 0.25 M, we can follow these steps:

### Step 1: Calculate the moles of HCl in each solution.

For the first solution (0.6 M HCl):
- Volume (V1) = 250 ml = 0.250 L
- Molarity (M1) = 0.6 M

Moles of HCl in the first solution (n1):
\[ n_1 = M_1 \times V_1 = 0.6 \, \text{mol/L} \times 0.250 \, \text{L} = 0.15 \, \text{mol} \]

For the second solution (0.2 M HCl):
- Volume (V2) = 750 ml = 0.750 L
- Molarity (M2) = 0.2 M

Moles of HCl in the second solution (n2):
\[ n_2 = M_2 \times V_2 = 0.2 \, \text{mol/L} \times 0.750 \, \text{L} = 0.15 \, \text{mol} \]

### Step 2: Calculate the total moles of HCl in the mixture.

Total moles of HCl (n_total):
\[ n_{\text{total}} = n_1 + n_2 = 0.15 \, \text{mol} + 0.15 \, \text{mol} = 0.30 \, \text{mol} \]

### Step 3: Calculate the total initial volume of the mixture.

Total initial volume (V_total_initial):
\[ V_{\text{total initial}} = V_1 + V_2 = 250 \, \text{ml} + 750 \, \text{ml} = 1000 \, \text{ml} = 1.0 \, \text{L} \]

### Step 4: Set up the equation for the final concentration after adding water.

Let \( V \) be the volume of water added. The total volume after adding water will be:
\[ V_{\text{total final}} = V_{\text{total initial}} + V = 1.0 \, \text{L} + V \]

We want the final concentration to be 0.25 M:
\[ \frac{n_{\text{total}}}{V_{\text{total final}}} = 0.25 \]

Substituting the values we have:
\[ \frac{0.30 \, \text{mol}}{1.0 \, \text{L} + V} = 0.25 \]

### Step 5: Solve for \( V \).

Cross-multiplying gives:
\[ 0.30 = 0.25 \times (1.0 + V) \]

Expanding:
\[ 0.30 = 0.25 + 0.25V \]

Rearranging gives:
\[ 0.30 - 0.25 = 0.25V \]
\[ 0.05 = 0.25V \]

Dividing both sides by 0.25:
\[ V = \frac{0.05}{0.25} = 0.20 \, \text{L} = 200 \, \text{ml} \]

### Conclusion:
The volume of water that must be added to the mixture is **200 ml**.

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