In what ratio `"0.183 M HCl and 0.381 M HCl"` be added to form `"0.243M HCl"` solution ?

Options

A. `7:3`
B. `3:7`
C. `1:1`
D. `2:1`

Answer

To find the ratio in which 0.183 M HCl and 0.381 M HCl should be mixed to obtain a 0.243 M HCl solution, we can follow these steps:

### Step 1: Define Variables
Let:
- \( x \) = volume of 0.183 M HCl solution (in liters)
- \( y \) = volume of 0.381 M HCl solution (in liters)

### Step 2: Write the Molarity Equation
The total moles of HCl from both solutions must equal the moles of HCl in the final solution. The molarity (M) is defined as moles of solute per liter of solution. Therefore, we can express the moles of HCl from both solutions as follows:

- Moles from 0.183 M solution: \( 0.183 \times x \)
- Moles from 0.381 M solution: \( 0.381 \times y \)

The total moles of HCl in the final solution (0.243 M) can be expressed as:

\[ \text{Total moles} = 0.243 \times (x + y) \]

### Step 3: Set Up the Equation
Now we can set up the equation based on the total moles:

\[ 0.183x + 0.381y = 0.243(x + y) \]

### Step 4: Expand and Rearrange the Equation
Expanding the right side gives:

\[ 0.183x + 0.381y = 0.243x + 0.243y \]

Rearranging this equation leads to:

\[ 0.183x - 0.243x + 0.381y - 0.243y = 0 \]

This simplifies to:

\[ -0.060x + 0.138y = 0 \]

### Step 5: Solve for the Ratio
Now, we can isolate \( x \) and \( y \):

\[ 0.060x = 0.138y \]

Dividing both sides by \( y \) and \( 0.060 \):

\[ \frac{x}{y} = \frac{0.138}{0.060} = 2.3 \]

### Step 6: Express the Ratio
Thus, the ratio \( x:y \) can be expressed as:

\[ x:y = 2.3:1 \]

To express this in whole numbers, we can multiply both sides by 10:

\[ x:y = 23:10 \]

### Step 7: Final Ratio
To simplify further, we can express it in a more manageable form. The ratio can be approximated to \( 7:3 \) when rounded.

### Conclusion
The ratio of 0.183 M HCl to 0.381 M HCl that should be mixed to obtain a 0.243 M HCl solution is approximately \( 7:3 \).

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