A water sample contains 102mg of CaSO4 per litre. Calculate the hardness in
terms of CaCO3 equivalent.
To calculate the hardness of water in terms of CaCO3 equivalent, you can use the following formula:
Hardness (CaCO3 equivalent) = (CaSO4 concentration) x (molar mass of CaCO3) / (molar mass of CaSO4)
First, let's calculate the molar mass of CaCO3 and CaSO4:
Molar mass of CaCO3 = (atomic mass of Ca x 1) + (atomic mass of C x 1) + (atomic mass of O x 3)
= (40.08 g/mol) + (12.01 g/mol) + (16.00 g/mol) x 3
= 100.09 g/mol
Molar mass of CaSO4 = (atomic mass of Ca x 1) + (atomic mass of S x 1) + (atomic mass of O x 4)
= (40.08 g/mol) + (32.07 g/mol) + (16.00 g/mol) x 4
= 136.14 g/mol
Now, we can calculate the hardness in terms of CaCO3 equivalent:
Hardness (CaCO3 equivalent) = (102 mg/L) x (100.09 g/mol) / (136.14 g/mol)
= (102 mg/L) x (100.09 / 136.14) g/L
≈ 74.8 mg/L
Therefore, the hardness of the water sample in terms of CaCO3 equivalent is approximately 74.8 mg/L.
To calculate the hardness of water in terms of CaCO3 equivalent, you need to convert the amount of CaSO4 in the water sample to CaCO3, since CaSO4 is not directly comparable to CaCO3 in terms of hardness.
The molecular weight of CaSO4 is 136.14 g/mol, while the molecular weight of CaCO3 is 100.09 g/mol. To convert from CaSO4 to CaCO3, you need to use the ratio of their molecular weights.
First, calculate the molar concentration of CaSO4 in the water sample:
Molar concentration of CaSO4 = (mass of CaSO4 / molar weight of CaSO4) / volume of water sample
= (102 mg / 136.14 g/mol) / 1 L
= 0.748 mmol/L
Next, use the stoichiometry between CaSO4 and CaCO3 to convert the molar concentration of CaSO4 to CaCO3:
Molar concentration of CaCO3 = molar concentration of CaSO4 * (molar weight of CaCO3 / molar weight of CaSO4)
= 0.748 mmol/L * (100.09 g/mol / 136.14 g/mol)
= 0.548 mmol/L
Lastly, to convert the molar concentration of CaCO3 to equivalent hardness, you need to multiply it by the hardness factor of CaCO3, which is 2.497:
Hardness in terms of CaCO3 equivalent = molar concentration of CaCO3 * hardness factor of CaCO3
= 0.548 mmol/L * 2.497
= 1.368 mmol/L
Therefore, the hardness of the water sample in terms of CaCO3 equivalent is 1.368 mmol/L.