Question

The total hardness in raw water is 500 milligram per liter as CaCO\(_3\). The total hardness of this raw water, expressed in milligram equivalent per liter, is

• A. 10
• B. 100
• C. 1
• D. 5

Hint:

To calculate the hardness in milligram equivalents, divide the hardness in milligrams by the equivalent weight of the substance.

Answer 1

The Correct Option is A

The total hardness is given as 500 mg/L as CaCO\(_3\). To convert this to milligram equivalent per liter, we use the following formula: \[ \text{Milligram equivalent per liter} = \frac{\text{Given hardness in mg/L}}{\text{Equivalent weight of CaCO}_3} \] The equivalent weight of CaCO\(_3\) is calculated as: \[ \text{Equivalent weight of CaCO}_3 = \frac{\text{Molar mass of CaCO}_3}{2} = \frac{40 + 12 + 3 \times 16}{2} = \frac{100}{2} = 50 \text{ g/mol}. \] Now, converting to milligram equivalents: \[ \text{Milligram equivalent per liter} = \frac{500 \text{ mg/L}}{50 \text{ mg/equiv}} = 10 \text{ mg/equiv/L}. \] Thus, the total hardness in milligram equivalent per liter is 10, corresponding to option (A).