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 definition of ppm
PPM (parts per million) indicates the mass of solute (in grams) per million grams of solution. In this case, 300 ppm means there are 300 grams of CaCO₃ in 1,000,000 grams of water.

### Step 2: Convert ppm to grams per liter
Since 1 liter of water has a mass of approximately 1000 grams, we can convert 300 ppm to grams per liter:
- 300 ppm = 300 grams of CaCO₃ in 1,000,000 grams of water
- To find how many grams are in 1 liter (1000 grams), we can set up a proportion:

\[ \text{grams of CaCO₃ in 1 liter} = \frac{300 \text{ grams}}{1,000,000 \text{ grams}} \times 1000 \text{ grams} = 0.3 \text{ grams} \]

### Step 3: Calculate the number of moles of CaCO₃
To find the number of moles, we use the formula:

\[ \text{Number of moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]

The molar mass of CaCO₃ (calcium carbonate) is approximately 100 g/mol. Therefore:

\[ \text{Number of moles of CaCO₃} = \frac{0.3 \text{ grams}}{100 \text{ g/mol}} = 0.003 \text{ moles} \]

### Step 4: Calculate the molarity
Molarity (M) is defined as the number of moles of solute per liter of solution. Since we have 0.003 moles of CaCO₃ in 1 liter of solution:

\[ \text{Molarity} = \frac{\text{Number of moles}}{\text{Volume of solution in liters}} = \frac{0.003 \text{ moles}}{1 \text{ liter}} = 0.003 \text{ M} \]

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

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