5 mL of N HCI, 20 mL of `N/2 H_2SO_4` and 30 mL of `N/3 HNO_3` are mixed together and the volume made to 1 litre. The normality of the resulting solution is:

Options

A. `N/5`
B. `N/10`
C. `N/20`
D. `N/40`

Explanation

To find the normality of the resulting solution when mixing different solutions of HCl, H2SO4, and HNO3, we can follow these steps:

### Step 1: Identify the normalities and volumes of each solution
- For HCl:
- Normality (N1) = 1 N
- Volume (V1) = 5 mL
- For H2SO4:
- Normality (N2) = 1/2 N
- Volume (V2) = 20 mL
- For HNO3:
- Normality (N3) = 1/3 N
- Volume (V3) = 30 mL

### Step 2: Convert volumes to liters
- V1 = 5 mL = 0.005 L
- V2 = 20 mL = 0.020 L
- V3 = 30 mL = 0.030 L

### Step 3: Calculate the equivalents of each solution
- Equivalents of HCl = N1 × V1 = 1 N × 0.005 L = 0.005 equivalents
- Equivalents of H2SO4 = N2 × V2 = (1/2) N × 0.020 L = 0.010 equivalents
- Equivalents of HNO3 = N3 × V3 = (1/3) N × 0.030 L = 0.010 equivalents

### Step 4: Sum the equivalents
Total equivalents = Equivalents of HCl + Equivalents of H2SO4 + Equivalents of HNO3
= 0.005 + 0.010 + 0.010 = 0.025 equivalents

### Step 5: Calculate the final normality
The final volume of the solution is 1 L (1000 mL).
Using the formula for normality:
\[ N_{final} = \frac{\text{Total equivalents}}{\text{Total volume in liters}} \]
\[ N_{final} = \frac{0.025 \text{ equivalents}}{1 \text{ L}} = 0.025 N \]

### Step 6: Express the final normality in terms of N
0.025 N can be expressed as:
\[ N_{final} = \frac{25}{1000} N = \frac{N}{40} \]

### Conclusion
The normality of the resulting solution is \( \frac{N}{40} \).

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