The volume of water that must be added to a mixture of 250 ml of 6M HCl and 650 ml of 3 M HCl to obtain 3M solution is

Options

A. 75 ml
B. 150 ml
C. 300 ml
D. 250 ml

Explanation

To solve the problem of determining the volume of water that must be added to a mixture of 250 ml of 6M HCl and 650 ml of 3M HCl to obtain a 3M solution, we can follow these steps:

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

1. **For the 6M HCl solution:**
- Volume = 250 ml = 0.250 L
- Molarity = 6 M
- Moles of HCl = Molarity × Volume = 6 mol/L × 0.250 L = 1.5 moles

2. **For the 3M HCl solution:**
- Volume = 650 ml = 0.650 L
- Molarity = 3 M
- Moles of HCl = Molarity × Volume = 3 mol/L × 0.650 L = 1.95 moles

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

Total moles of HCl = Moles from 6M solution + Moles from 3M solution
Total moles of HCl = 1.5 moles + 1.95 moles = 3.45 moles

### Step 3: Determine the total volume of the initial mixture

Total volume of the mixture = Volume of 6M solution + Volume of 3M solution
Total volume = 250 ml + 650 ml = 900 ml = 0.900 L

### Step 4: Set up the equation for the final solution

Let \( V_L \) be the final volume of the solution after adding water. We want the final molarity to be 3M. The number of moles of HCl in the final solution can be expressed as:

\[ \text{Molarity} = \frac{\text{Total moles of solute}}{\text{Total volume in L}} \]

So, we have:

\[ 3 = \frac{3.45}{V_L} \]

### Step 5: Solve for \( V_L \)

Rearranging the equation gives:

\[ V_L = \frac{3.45}{3} = 1.15 \, \text{L} \]

### Step 6: Calculate the volume of water to be added

Now, we need to find out how much water to add:

Volume of water to add = Final volume - Initial volume
Volume of water to add = \( V_L - 0.900 \, \text{L} \)

Calculating this gives:

\[ \text{Volume of water to add} = 1.15 \, \text{L} - 0.900 \, \text{L} = 0.25 \, \text{L} \]

### Step 7: Convert to milliliters

To convert liters to milliliters:

\[ 0.25 \, \text{L} = 0.25 \times 1000 \, \text{ml} = 250 \, \text{ml} \]

### Final Answer

The volume of water that must be added is **250 ml**.

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