A water sample (500 mL) has hardness equivalent for 50 mL of 0.1 N CaSO4. What is the hardness in ppm?

To calculate the hardness of water in ppm (parts per million), we need to follow these steps:

1. First, we need to understand that the hardness of water is primarily due to the presence of multivalent cations such as calcium (Ca2+) and magnesium (Mg2+). In this case, we are given the hardness equivalent for 50 mL of 0.1 N CaSO4.

2. The molar mass of CaSO4 is approximately 136.14 g/mol.

3. Since we know the normality (N) of the solution, we can calculate the amount of CaSO4 in grams. Normality is defined as the number of gram-equivalent weights of solute per liter of solution. In this case, the gram-equivalent weight of CaSO4 is its molar mass, 136.14 g. Therefore, in 1 liter (or 1000 mL) of 0.1 N CaSO4 solution, there are 0.1 * 136.14 = 13.614 grams of CaSO4.

4. However, we only have 50 mL of this solution, so the amount of CaSO4 in this volume is 50/1000 * 13.614 = 0.6807 grams.

5. Now, we need to calculate the hardness of the 500 mL water sample. Since the hardness equivalent for 50 mL of 0.1 N CaSO4 is 0.6807 grams, the hardness of the 500 mL water sample is 500/50 * 0.6807 = 6.807 grams.

6. Finally, to express this hardness in ppm, we need to know that 1 ppm is equivalent to 1 mg/L. Therefore, the hardness of the water sample in ppm is 6.807 * 1000 = 6807 ppm.

So, the hardness of the water sample is 6807 ppm.