Hardness of water sample is 300 ppm `CaCO_3` Hence its molarity is:

Options

A. 0.3 M
B. 0.030 M
C. 0.003 M
D. 0.0015 M

Answer

To find the molarity of a water sample with a hardness of 300 ppm of CaCO₃, we can follow these steps:

### Step 1: Understand the meaning of ppm
- 300 ppm means 300 milligrams of CaCO₃ per liter of water.

### Step 2: Convert milligrams to grams
- Convert 300 mg to grams:
\[ 300 \text{ mg} = 300 \times 10^{-3} \text{ g} = 0.3 \text{ g} \]

### Step 3: Calculate the molar mass of CaCO₃
- The molar mass of CaCO₃ is calculated as follows:
- Atomic mass of Calcium (Ca) = 40 g/mol
- Atomic mass of Carbon (C) = 12 g/mol
- Atomic mass of Oxygen (O) = 16 g/mol (and there are 3 O atoms)

Therefore, the molar mass of CaCO₃ is:
\[ \text{Molar mass of CaCO₃} = 40 + 12 + (3 \times 16) = 40 + 12 + 48 = 100 \text{ g/mol} \]

### Step 4: Calculate the number of moles of CaCO₃
- Use the formula for moles:
\[ \text{Moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]
Substituting the values:
\[ \text{Moles of CaCO₃} = \frac{0.3 \text{ g}}{100 \text{ g/mol}} = 0.003 \text{ moles} \]

### Step 5: Calculate the molarity
- Molarity (M) is defined as moles of solute per liter of solution:
\[ \text{Molarity} = \frac{\text{moles of solute}}{\text{volume of solution in liters}} \]
Since we have 0.003 moles in 1 liter:
\[ \text{Molarity} = \frac{0.003 \text{ moles}}{1 \text{ L}} = 0.003 \text{ M} \]

### Final Answer
The molarity of the water sample is **0.003 M**.

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