A sample of well water contains 140 gm/m³ Ca²⁺ ions and 345 gm/m³ Na⁺ ions. The hardness of the sample of water, expressed in terms of equivalent CaCO₃ in gm/m³ is (assuming atomic masses of Ca :40, Na : 23, C : 12, O : 16)

ANS:A - 350

To find the hardness of the water sample expressed in terms of equivalent CaCO3, we need to calculate the concentration of calcium carbonate (CaCO3) equivalent to the concentration of calcium ions (Ca2+) and sodium ions (Na+). First, let's find the equivalent concentration of CaCO3 for Ca2+ ions:

1. Calculate the equivalent weight of CaCO3: Equivalent weight of CaCO3=100.092=50.045 g/molEquivalent weight of CaCO3=2100.09​=50.045g/mol
2. Calculate the equivalent concentration of CaCO3 for Ca2+ ions: Concentration of CaCO3 equivalent to Ca2+ ions=Concentration of Ca2+ ions×Equivalent weight of CaCO3Molar mass of CaConcentration of CaCO3 equivalent to Ca2+ ions=Molar mass of CaConcentration of Ca2+ ions×Equivalent weight of CaCO3​ =140 g/m3×50.045 g/mol40 g/mol=40g/mol140g/m3×50.045g/mol​ =700710=700.7 g/m3=107007​=700.7g/m3

Next, let's find the equivalent concentration of CaCO3 for Na+ ions:

1. Calculate the equivalent weight of Na2CO3 (sodium carbonate): Equivalent weight of Na2CO3=2×23+12+3×162=105 g/molEquivalent weight of Na2CO3=22×23+12+3×16​=105g/mol
2. Calculate the equivalent concentration of CaCO3 for Na+ ions: Concentration of CaCO3 equivalent to Na+ ions=Concentration of Na+ ions×Equivalent weight of Na2CO3Molar mass of CaConcentration of CaCO3 equivalent to Na+ ions=Molar mass of CaConcentration of Na+ ions×Equivalent weight of Na2CO3​ =345 g/m3×105 g/mol40 g/mol=40g/mol345g/m3×105g/mol​ =3622510=3622.5 g/m3=1036225​=3622.5g/m3

Finally, the total hardness of the water sample in terms of equivalent CaCO3 is the sum of the equivalent concentrations of CaCO3 for Ca2+ ions and Na+ ions: Total hardness=Concentration of CaCO3 equivalent to Ca2+ ions+Concentration of CaCO3 equivalent to Na+ ionsTotal hardness=Concentration of CaCO3 equivalent to Ca2+ ions+Concentration of CaCO3 equivalent to Na+ ions =700.7 g/m3+3622.5 g/m3=700.7g/m3+3622.5g/m3 =4323.2 g/m3=4323.2g/m3 So, the hardness of the water sample, expressed in terms of equivalent CaCO3 in g/m^3, is approximately 4323.2 g/m^3. Among the provided options, none exactly matches this value. However, the closest option is 485 g/m^3. Therefore, 485 g/m^3 is the closest option to the calculated value.