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. 20ppm
C. 200ppm
D. 324ppm

Answer

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

### Step 1: Calculate the Normality of HCl
Given that the concentration of HCl is \( \frac{M}{50} \), we can express this in terms of normality (N).

\[ \text{Normality (N)} = \frac{M}{50} \]

Since \( M \) is the molarity of HCl, the normality will be:

\[ N = \frac{1}{50} \text{ N} \]

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

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

Convert the volume from mL to L:

\[ \text{Volume} = 10 \text{ mL} = 0.01 \text{ L} \]

Now, substituting the values:

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

### Step 3: Equivalent of CaCO3
The equivalent of CaCO3 can be calculated using the formula:

\[ \text{Equivalent} = \frac{\text{Weight}}{\text{Molecular Weight}} \times n \]

The molecular weight of CaCO3 is:

\[ \text{Molecular Weight} = 40 \text{ (Ca)} + 12 \text{ (C)} + 3 \times 16 \text{ (O)} = 100 \text{ g/mol} \]

The n-factor for CaCO3 is 2 (as it can release 2 equivalents of ions).

### Step 4: Set Up the Equation
Since the milliequivalents of HCl will neutralize the same amount of CaCO3, we can set up the equation:

\[ 0.2 = \frac{\text{Weight of CaCO3}}{100} \times 2 \]

### Step 5: Solve for Weight of CaCO3
Rearranging gives:

\[ \text{Weight of CaCO3} = 0.2 \times \frac{100}{2} = 10 \text{ mg} \]

### Step 6: Calculate Hardness in ppm
To find the hardness in ppm, we need to know how much CaCO3 is present in 1 million mL (1 L) of water.

Using the unitary method:

\[ \text{Hardness (ppm)} = \left(\frac{10 \text{ mg}}{50 \text{ mL}}\right) \times 1000000 \text{ mL} \]

Calculating this gives:

\[ \text{Hardness (ppm)} = \frac{10 \times 10^6}{50} = 200 \text{ ppm} \]

### Final Answer
The temporary hardness of the water sample is **200 ppm**.

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