One litre of a sample of hard water contain `4.44mg CaCl_(2) and 1.9mg "of" MgCl_(2)`. What is the total hardness in terms of ppm of `CaCO_(3)?`

Options

A. 2ppm
B. 3ppm
C. 4ppm
D. 6ppm

Answer

To determine the total hardness of the given hard water sample in terms of ppm of CaCO₃, we will follow these steps:

### Step 1: Calculate the equivalents of CaCl₂
Given:
- Mass of CaCl₂ = 4.44 mg
- Molecular weight of CaCl₂ = 111 g/mol

First, we need to calculate the number of equivalents of CaCl₂. The formula for equivalents is:

\[ \text{Number of equivalents} = \frac{\text{mass (g)}}{\text{molecular weight (g/mol)}} \times \text{valency factor} \]

The valency factor for CaCl₂ is 2 (since it dissociates into Ca²⁺ and 2Cl⁻).

Convert mg to g:
\[ 4.44 \text{ mg} = 4.44 \times 10^{-3} \text{ g} \]

Now, calculate the number of equivalents:
\[ \text{Equivalents of CaCl₂} = \frac{4.44 \times 10^{-3}}{111} \times 2 \]

### Step 2: Calculate the weight of CaCO₃ from CaCl₂
Using the equivalents calculated, we can find the weight of CaCO₃ produced from CaCl₂:

\[ \text{Weight of CaCO₃} = \text{Equivalents of CaCl₂} \times \text{molecular weight of CaCO₃ (100 g/mol)} \]

### Step 3: Calculate the equivalents of MgCl₂
Given:
- Mass of MgCl₂ = 1.9 mg
- Molecular weight of MgCl₂ = 95 g/mol

Convert mg to g:
\[ 1.9 \text{ mg} = 1.9 \times 10^{-3} \text{ g} \]

Calculate the number of equivalents of MgCl₂:
\[ \text{Equivalents of MgCl₂} = \frac{1.9 \times 10^{-3}}{95} \times 2 \]

### Step 4: Calculate the weight of CaCO₃ from MgCl₂
Using the equivalents calculated, we can find the weight of CaCO₃ produced from MgCl₂:

\[ \text{Weight of CaCO₃} = \text{Equivalents of MgCl₂} \times \text{molecular weight of CaCO₃ (100 g/mol)} \]

### Step 5: Total weight of CaCO₃
Now, sum the weights of CaCO₃ from both CaCl₂ and MgCl₂ to find the total weight of CaCO₃:

\[ \text{Total weight of CaCO₃} = \text{Weight from CaCl₂} + \text{Weight from MgCl₂} \]

### Step 6: Calculate the total hardness in ppm
To find the hardness in ppm, we use the formula:

\[ \text{Hardness (ppm)} = \frac{\text{Total weight of CaCO₃ (mg)}}{\text{mass of water (g)}} \times 10^6 \]

Given that the volume of water is 1 liter (which is 1000 g), we can substitute this value into the equation.

### Final Calculation
Now, substituting all the values and calculating will give us the total hardness in ppm.