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 20 ml of 1N HCl, 10 ml of \( \frac{1}{2} \) N H2SO4, and 30 ml of \( \frac{1}{3} \) N HNO3, we can follow these steps:

### Step 1: Calculate the equivalent contributions of each acid

1. **For HCl:**
- Normality (N1) = 1 N
- Volume (V1) = 20 ml
- Equivalent contribution from HCl = \( N1 \times V1 = 1 \times 20 = 20 \) equivalents

2. **For H2SO4:**
- Normality (N2) = \( \frac{1}{2} \) N
- Volume (V2) = 10 ml
- H2SO4 is a diprotic acid, so it contributes 2 equivalents per mole.
- Equivalent contribution from H2SO4 = \( N2 \times V2 \times 2 = \frac{1}{2} \times 10 \times 2 = 10 \) equivalents

3. **For HNO3:**
- Normality (N3) = \( \frac{1}{3} \) N
- Volume (V3) = 30 ml
- HNO3 is a monoprotic acid, so it contributes 1 equivalent per mole.
- Equivalent contribution from HNO3 = \( N3 \times V3 = \frac{1}{3} \times 30 = 10 \) equivalents

### Step 2: Calculate total equivalents of \( H^+ \) ions

Now, we add the equivalent contributions from all three acids:

\[ \text{Total equivalents} = 20 + 10 + 10 = 40 \text{ equivalents} \]

### Step 3: Calculate the total volume of the solution

The total volume of the solution after mixing is 1000 ml.

### Step 4: Calculate the normality of \( H^+ \) ions in the resulting solution

Normality (N) is defined as the number of equivalents per liter of solution. Therefore, we can calculate the normality of \( H^+ \) ions as follows:

\[ \text{Normality of } H^+ = \frac{\text{Total equivalents}}{\text{Total volume in liters}} = \frac{40}{1} = 40 \text{ N} \]

### Final Answer

The normality of \( H^+ \) ions in the resulting solution is **40 N**.

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