50 ml of water sample, containing temporary hardness only, required 0.1 ml of M/50 HCl for complete neutralisation. Calculate the temporary hardness of water in ppm.

Explanation

To solve the problem of calculating the temporary hardness of water in ppm, we will follow these steps:

### Step 1: Write down the given data
- Volume of water sample (V1) = 50 ml
- Volume of HCl used (V2) = 0.1 ml
- Concentration of HCl (M2) = M/50 = 1/50 molar

### Step 2: Use the neutralization equation
The neutralization reaction can be expressed as:
\[ M_1 \times V_1 = M_2 \times V_2 \]
Where:
- \( M_1 \) = molarity of bicarbonate (HCO₃⁻)
- \( V_1 \) = volume of water sample (50 ml)
- \( M_2 \) = molarity of HCl (1/50 molar)
- \( V_2 \) = volume of HCl used (0.1 ml)

### Step 3: Substitute the values into the equation
Assuming \( M_1 = x \):
\[ x \times 50 = \frac{1}{50} \times 0.1 \]

### Step 4: Calculate \( M_1 \)
Rearranging the equation gives:
\[ x = \frac{\frac{1}{50} \times 0.1}{50} \]
Calculating this:
\[ x = \frac{0.1}{2500} = \frac{1}{25000} \text{ mol/L} \]

### Step 5: Convert molarity to millimoles
Since 1 mol = 1000 mmol, we convert:
\[ x = \frac{1}{25000} \text{ mol/L} = \frac{1 \times 1000}{25000} \text{ mmol/L} = \frac{1000}{25000} \text{ mmol/L} = 0.04 \text{ mmol/L} \]

### Step 6: Calculate the equivalent millimoles of CaCO₃
The temporary hardness is caused by bicarbonate, which can be converted to calcium carbonate (CaCO₃). The relationship is:
\[ \text{Millimoles of Ca}^{2+} = \text{Millimoles of HCO}_3^{-} \]
Thus:
\[ \text{Millimoles of CaCO}_3 = 0.04 \text{ mmol} \]

### Step 7: Calculate the weight of CaCO₃
Using the molar mass of CaCO₃ (approximately 100 g/mol):
\[ \text{Weight of CaCO}_3 = \text{Millimoles} \times \text{Molar Mass} = 0.04 \text{ mmol} \times 100 \text{ g/mol} = 4 \text{ mg} \]

### Step 8: Calculate the hardness in ppm
Hardness in ppm is given by:
\[ \text{Hardness (ppm)} = \frac{\text{Weight of CaCO}_3}{\text{Volume of water sample (L)}} \times 10^6 \]
Converting 50 ml to liters:
\[ \text{Volume of water sample} = 50 \text{ ml} = 0.050 \text{ L} \]
Now substituting the values:
\[ \text{Hardness (ppm)} = \frac{4 \text{ mg}}{0.050 \text{ L}} \times 10^6 = 80000 \text{ ppm} \]

### Final Answer
The temporary hardness of the water sample is **80000 ppm**.

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