One litre of `0.15 M HCl` and one ltire of `0.3 M HCl` is given. What is the maximum volume of `0.2 M HCl` which one can make from these two solution. Now water is added.

Options

A. `1.2 L`
B. 1.5 L`
C. `1.3 L`
D. 1.4 L`

Explanation

To solve the problem of finding the maximum volume of 0.2 M HCl that can be made from 1 liter of 0.15 M HCl and 1 liter of 0.3 M HCl, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Solutions:**
- We have 1 liter of 0.15 M HCl.
- We have 1 liter of 0.3 M HCl.

2. **Define Variables:**
- Let \( x \) be the volume (in liters) of the 0.3 M HCl solution that we will mix with the 1 liter of 0.15 M HCl.

3. **Calculate Total Volume:**
- The total volume of the new solution will be \( V = 1 + x \) liters (1 liter from the 0.15 M solution and \( x \) liters from the 0.3 M solution).

4. **Set Up the Molarity Equation:**
- We know that the total number of moles of HCl from both solutions must equal the number of moles in the final solution:
\[ \text{Moles from 0.15 M solution} + \text{Moles from 0.3 M solution} = \text{Moles in final solution} \]
- This can be expressed as:
\[ 0.15 \times 1 + 0.3 \times x = 0.2 \times (1 + x) \]

5. **Substitute and Simplify:**
- Substitute the values into the equation:
\[ 0.15 + 0.3x = 0.2(1 + x) \]
- Expanding the right side:
\[ 0.15 + 0.3x = 0.2 + 0.2x \]

6. **Rearranging the Equation:**
- Move all terms involving \( x \) to one side and constant terms to the other:
\[ 0.3x - 0.2x = 0.2 - 0.15 \]
- This simplifies to:
\[ 0.1x = 0.05 \]

7. **Solve for \( x \):**
- Divide both sides by 0.1:
\[ x = \frac{0.05}{0.1} = 0.5 \text{ liters} \]

8. **Calculate Maximum Volume:**
- Now, substitute \( x \) back into the total volume equation:
\[ V = 1 + x = 1 + 0.5 = 1.5 \text{ liters} \]

### Final Answer:
The maximum volume of 0.2 M HCl that can be made from the given solutions is **1.5 liters**.