20 ml of 1N HCl, 10 ml of 'N/2 H_2SO_4` and 30ml of 'N/3 HNO_3` are mixed together and volume made to 1000 ml. Find out the normality of 'H^+ ions in the resulting solution

Options

A. '7/100N'
B. 7/200N'
C. 7/18N'
D. 7/9N'

Answer

To find the normality of \( H^+ \) ions in the resulting solution after mixing the given solutions, we can follow these steps:

### Step 1: Identify the normalities and volumes of the solutions
- For HCl:
- Normality \( N_1 = 1 \, N \)
- Volume \( V_1 = 20 \, ml \)

- For \( H_2SO_4 \):
- Normality \( N_2 = \frac{1}{2} \, N \)
- Volume \( V_2 = 10 \, ml \)

- For \( HNO_3 \):
- Normality \( N_3 = \frac{1}{3} \, N \)
- Volume \( V_3 = 30 \, ml \)

### Step 2: Calculate the total contribution of \( H^+ \) ions from each acid
The total contribution of \( H^+ \) ions from each acid can be calculated using the formula:
\[ \text{Total } H^+ = N_1 \times V_1 + N_2 \times V_2 + N_3 \times V_3 \]

Substituting the values:
\[ \text{Total } H^+ = (1 \, N \times 20 \, ml) + \left(\frac{1}{2} \, N \times 10 \, ml\right) + \left(\frac{1}{3} \, N \times 30 \, ml\right) \]

Calculating each term:
- From HCl: \( 1 \times 20 = 20 \)
- From \( H_2SO_4 \): \( \frac{1}{2} \times 10 = 5 \)
- From \( HNO_3 \): \( \frac{1}{3} \times 30 = 10 \)

Adding these contributions together:
\[ \text{Total } H^+ = 20 + 5 + 10 = 35 \, N \cdot ml \]

### Step 3: Calculate the total volume of the resulting solution
The total volume of the resulting solution is given as:
\[ V_{\text{total}} = 1000 \, ml \]

### Step 4: Calculate the normality of \( H^+ \) ions in the resulting solution
The normality of \( H^+ \) ions can be calculated using the formula:
\[ N_{H^+} = \frac{\text{Total } H^+}{V_{\text{total}}} \]

Substituting the values:
\[ N_{H^+} = \frac{35 \, N \cdot ml}{1000 \, ml} \]

This simplifies to:
\[ N_{H^+} = \frac{35}{1000} \, N = \frac{7}{200} \, N \]

### Final Answer
The normality of \( H^+ \) ions in the resulting solution is \( \frac{7}{200} \, N \).

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