50 ml of water sample requires 10 ml of `(M)/(50)HCl` for complete neutralization. Calculate hardness of `H_(2)O` (temporary) in ppm.

Options

A. 2ppm
B. 20 ppm
C. 200ppm
D. 324ppm

Answer

To calculate the temporary hardness of water in ppm (parts per million), we will follow these steps:

### Step 1: Determine the Normality of HCl
Given that the concentration of HCl is \( \frac{1}{50} \) M, we can convert this to normality. Since HCl is a strong acid and has one replaceable hydrogen ion, the normality (N) is equal to the molarity (M).

\[ \text{Normality of HCl} = \frac{1}{50} \, \text{N} \]

### Step 2: Calculate the Milliequivalents of HCl
Milliequivalents (mEq) can be calculated using the formula:

\[ \text{mEq} = \text{Normality} \times \text{Volume (in L)} \]

Here, the volume of HCl used is 10 mL, which is 0.01 L.

\[ \text{mEq of HCl} = \left(\frac{1}{50}\right) \times 0.01 = 0.0002 \, \text{equivalents} = 0.2 \, \text{mEq} \]

### Step 3: Relate Milliequivalents of HCl to Calcium Carbonate
The temporary hardness of water is primarily due to the presence of calcium carbonate (CaCO₃). The equivalent weight of CaCO₃ can be calculated as follows:

- Molar mass of CaCO₃:
- Calcium (Ca) = 40 g/mol
- Carbon (C) = 12 g/mol
- Oxygen (O) = 16 g/mol × 3 = 48 g/mol
- Total = 40 + 12 + 48 = 100 g/mol

The n-factor for CaCO₃ is 2 because it can release 2 equivalents of Ca²⁺ ions.

### Step 4: Calculate the Weight of CaCO₃
Using the equivalence relation, we can find the weight of CaCO₃ that corresponds to the 0.2 mEq of HCl:

\[ \text{Weight of CaCO₃} = \text{mEq of HCl} \times \text{Equivalent weight of CaCO₃} \]

\[ \text{Weight of CaCO₃} = 0.2 \times 100 = 20 \, \text{mg} \]

### Step 5: Calculate Hardness in ppm
Since the weight of CaCO₃ is 20 mg for a 50 mL sample of water, we can convert this to ppm:

\[ \text{Hardness (ppm)} = \left(\frac{\text{Weight of CaCO₃ (mg)}}{\text{Volume of water (L)}}\right) \times 10^6 \]

\[ \text{Hardness (ppm)} = \left(\frac{20 \, \text{mg}}{0.050 \, \text{L}}\right) \times 10^6 = 400000 \, \text{ppm} \]

### Final Calculation
However, since we need to calculate for 1 L (1000 mL):

\[ \text{Hardness (ppm)} = \left(\frac{20 \, \text{mg}}{50 \, \text{mL}}\right) \times 1000 = 400 \, \text{ppm} \]

### Conclusion
The temporary hardness of the water sample is **400 ppm**.

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