In what ratio should a ` 6.5 N HNO_(3)` be diluted with water to get `3.5 N HNO_(3)` ?

Options

A. ` 6:7 `
B. ` 7:6 `
C. ` 5:6 `
D. ` 6:5 `

Explanation

To solve the problem of diluting a 6.5 N HNO₃ solution to obtain a 3.5 N HNO₃ solution, we can use the dilution formula:

### Step-by-Step Solution:

1. **Identify the Known Values**:
- Initial Normality (N₁) = 6.5 N
- Final Normality (N₂) = 3.5 N
- Let the volume of the initial solution be V₁ (in liters).
- Let the volume of water added be x (in liters).
- The final volume after dilution will be V₂ = V₁ + x.

2. **Apply the Dilution Formula**:
The dilution formula states that:
\[ N₁V₁ = N₂V₂ \]
Substituting the known values:
\[ 6.5 \, N \cdot V₁ = 3.5 \, N \cdot (V₁ + x) \]

3. **Rearranging the Equation**:
Expanding the equation gives:
\[ 6.5V₁ = 3.5V₁ + 3.5x \]
Now, isolate the terms involving V₁ on one side:
\[ 6.5V₁ - 3.5V₁ = 3.5x \]
This simplifies to:
\[ 3V₁ = 3.5x \]

4. **Solving for x**:
To find x in terms of V₁, divide both sides by 3.5:
\[ x = \frac{3V₁}{3.5} = \frac{6V₁}{7} \]

5. **Finding the Ratio**:
We need the ratio of the volume of HNO₃ (V₁) to the volume of water (x):
\[ \text{Ratio} = \frac{V₁}{x} = \frac{V₁}{\frac{6V₁}{7}} = \frac{7}{6} \]

### Final Answer:
The ratio in which 6.5 N HNO₃ should be diluted with water to get 3.5 N HNO₃ is **7:6**.

---