A sample of hard water contains 1 mg `CaCl_2` and 1 mg `MgCl_2` per litre. Calculate the hardness of water in terms of `CaCO_3` present in per `10^(6)` parts of water.

Options

A. `2.5 p p m`
B. `1.95 p p m`
C. `2.15 p p m`
D. `195 p p m`

Explanation

To calculate the hardness of water in terms of `CaCO3` present in per `10^6` parts of water, we can follow these steps:

### Step 1: Understand the composition of hard water
We have a sample of hard water containing:
- 1 mg of `CaCl2` per litre
- 1 mg of `MgCl2` per litre

### Step 2: Calculate the equivalent amount of `CaCO3` from `CaCl2`
The molar mass of `CaCl2` is approximately 111 g/mol, and the molar mass of `CaCO3` is 100 g/mol.

Using the relationship:
- 1 mole of `CaCl2` gives 1 mole of `CaCO3`

We can set up the conversion:
\[ \text{Amount of } CaCO3 = \left( \frac{100 \text{ mg } CaCO3}{111 \text{ mg } CaCl2} \right) \times 1 \text{ mg } CaCl2 \]

Calculating this gives:
\[ \text{Amount of } CaCO3 = \frac{100}{111} \approx 0.90 \text{ mg} \]

### Step 3: Calculate the equivalent amount of `CaCO3` from `MgCl2`
The molar mass of `MgCl2` is approximately 95 g/mol.

Using the relationship:
- 1 mole of `MgCl2` gives 1 mole of `CaCO3`

We can set up the conversion:
\[ \text{Amount of } CaCO3 = \left( \frac{100 \text{ mg } CaCO3}{95 \text{ mg } MgCl2} \right) \times 1 \text{ mg } MgCl2 \]

Calculating this gives:
\[ \text{Amount of } CaCO3 = \frac{100}{95} \approx 1.05 \text{ mg} \]

### Step 4: Calculate the total amount of `CaCO3` in the sample
Now, we add the amounts of `CaCO3` derived from both `CaCl2` and `MgCl2`:
\[ \text{Total } CaCO3 = 0.90 \text{ mg} + 1.05 \text{ mg} = 1.95 \text{ mg} \]

### Step 5: Convert the total amount of `CaCO3` to parts per million (ppm)
Since 1 litre of water is equivalent to `10^6` mg, we can express the hardness in ppm:
\[ \text{Hardness in ppm} = \frac{1.95 \text{ mg } CaCO3}{10^6 \text{ mg water}} \times 10^6 = 1.95 \text{ ppm} \]

### Final Answer
The hardness of water in terms of `CaCO3` present in per `10^6` parts of water is **1.95 ppm**.

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