What volume of 10M HCl and 3M HCl should be mixed to obtain 1L of 6M HCl solution?

Answer

To solve the problem of mixing 10M HCl and 3M HCl to obtain 1L of 6M HCl solution, we can follow these steps:

### Step 1: Define Variables
Let:
- \( V_1 \) = volume of 10M HCl (in liters)
- \( V_2 \) = volume of 3M HCl (in liters)

Since we want a total volume of 1L, we can express \( V_2 \) as:
\[ V_2 = 1 - V_1 \]

### Step 2: Use the Dilution Equation
We can use the equation for mixing solutions:
\[ M_1 V_1 + M_2 V_2 = M_f V_f \]
Where:
- \( M_1 = 10 \)M (molarity of HCl solution 1)
- \( M_2 = 3 \)M (molarity of HCl solution 2)
- \( M_f = 6 \)M (final molarity of the mixture)
- \( V_f = 1 \)L (final volume of the mixture)

Substituting the known values into the equation:
\[ 10V_1 + 3(1 - V_1) = 6(1) \]

### Step 3: Simplify the Equation
Expanding the equation:
\[ 10V_1 + 3 - 3V_1 = 6 \]

Combine like terms:
\[ 7V_1 + 3 = 6 \]

### Step 4: Solve for \( V_1 \)
Subtract 3 from both sides:
\[ 7V_1 = 6 - 3 \]
\[ 7V_1 = 3 \]

Now, divide by 7:
\[ V_1 = \frac{3}{7} \]

### Step 5: Calculate \( V_1 \) in Liters and Milliliters
Calculating \( V_1 \):
\[ V_1 \approx 0.4286 \text{ L} \]

To convert to milliliters:
\[ V_1 \times 1000 = 0.4286 \times 1000 \approx 428.57 \text{ mL} \]

### Step 6: Calculate \( V_2 \)
Now, calculate \( V_2 \):
\[ V_2 = 1 - V_1 = 1 - \frac{3}{7} = \frac{4}{7} \]

Calculating \( V_2 \) in liters:
\[ V_2 \approx 0.5714 \text{ L} \]

To convert to milliliters:
\[ V_2 \times 1000 = 0.5714 \times 1000 \approx 571.43 \text{ mL} \]

### Final Answer
- Volume of 10M HCl required: **428 mL**
- Volume of 3M HCl required: **572 mL**

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