Calculate the total hardness of water in °Fr and °Cl from the following analysis of water sample. Mg(HCO3)2=20.8 mg/L, Mg(NO3)2=28.8 mg/L, MgCl2=21.0 mg/L, MgSO4=20 mg/L, CaCO3=21.2 mg/L, KCl=73.2 mg/L

To calculate the total hardness of water, we need to consider the concentration of calcium and magnesium ions, as these are the main contributors to water hardness. The hardness of water is usually expressed in terms of equivalent quantity of CaCO3.

1. Convert the concentration of each compound to equivalent concentration of CaCO3 using the following conversion factors:

   • Mg(HCO3)2: 1 mg/L = 2.497 °dH = 4.456 °Fr = 2.5 °e = 35.8 ppm CaCO3
   • Mg(NO3)2: 1 mg/L = 2.26 °dH = 4.04 °Fr = 2.27 °e = 32.6 ppm CaCO3
   • MgCl2: 1 mg/L = 2.95 °dH = 5.28 °Fr = 2.97 °e = 42.7 ppm CaCO3
   • MgSO4: 1 mg/L = 2.445 °dH = 4.375 °Fr = 2.47 °e = 35.5 ppm CaCO3
   • CaCO3: 1 mg/L = 1 °dH = 1.78 °Fr = 1 °e = 14.3 ppm CaCO3

2. Multiply the concentration of each compound in the water sample by the corresponding conversion factor to get the equivalent concentration of CaCO3:

   • Mg(HCO3)2: 20.8 mg/L * 35.8 ppm CaCO3/mg/L = 744.64 ppm CaCO3
   • Mg(NO3)2: 28.8 mg/L * 32.6 ppm CaCO3/mg/L = 938.88 ppm CaCO3
   • MgCl2: 21.0 mg/L * 42.7 ppm CaCO3/mg/L = 896.7 ppm CaCO3
   • MgSO4: 20 mg/L * 35.5 ppm CaCO3/mg/L = 710 ppm CaCO3
   • CaCO3: 21.2 mg/L * 14.3 ppm CaCO3/mg/L = 302.96 ppm CaCO3

3. Add up all the equivalent concentrations of CaCO3 to get the total hardness:

   Total hardness = 744.64 ppm + 938.88 ppm + 896.7 ppm + 710 ppm + 302.96 ppm = 3593.18 ppm CaCO3

4. Convert the total hardness from ppm CaCO3 to °Fr and °Cl:

   • 1 ppm CaCO3 = 0.056 °Fr = 0.07 °Cl
   • Total hardness in °Fr = 3593.18 ppm * 0.056 = 201.21 °Fr
   • Total hardness in °Cl = 3593.18 ppm * 0.07 = 251.52 °Cl

So, the total hardness of the water sample is 201.21 °Fr and 251.52 °Cl.