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An exhausted zeolite bed was revived by ...

An exhausted zeolite bed was revived by 250 L of NaCl solution containing `50gL^(-1)` of NaCl solution. How many litres of hard water of hardness 250 ppm can be softened on the zeolite bed?

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To solve the problem of how many liters of hard water with a hardness of 250 ppm can be softened using an exhausted zeolite bed revived by a NaCl solution, we will follow these steps: ### Step 1: Calculate the total mass of NaCl in the solution The concentration of NaCl in the solution is given as 50 g/L, and the volume of the solution is 250 L. \[ \text{Total mass of NaCl} = \text{Concentration} \times \text{Volume} = 50 \, \text{g/L} \times 250 \, \text{L} = 12500 \, \text{g} \] ### Step 2: Calculate the equivalent mass of NaCl The molar mass of NaCl is calculated as follows: - Na (Sodium) = 23 g/mol - Cl (Chlorine) = 35.5 g/mol \[ \text{Molar mass of NaCl} = 23 + 35.5 = 58.5 \, \text{g/mol} \] Since NaCl has an n-factor of 1, the equivalent mass is the same as the molar mass. ### Step 3: Calculate the total equivalents of NaCl The total equivalents of NaCl can be calculated using the formula: \[ \text{Equivalents of NaCl} = \frac{\text{Total mass of NaCl}}{\text{Equivalent mass of NaCl}} = \frac{12500 \, \text{g}}{58.5 \, \text{g/equiv}} \approx 213.68 \, \text{equiv} \] ### Step 4: Calculate the hardness of hard water in terms of CaCO3 Hardness is given as 250 ppm, which means 250 mg of CaCO3 per liter of water. To convert this to equivalents, we need to know the equivalent weight of CaCO3: - Molar mass of CaCO3 = 100 g/mol - n-factor = 2 (because it can release two moles of ions) \[ \text{Equivalent weight of CaCO3} = \frac{100 \, \text{g/mol}}{2} = 50 \, \text{g/equiv} \] ### Step 5: Calculate the equivalents of CaCO3 in V liters of hard water If V liters of hard water are treated, the total mass of CaCO3 in V liters is: \[ \text{Mass of CaCO3} = 250 \, \text{mg/L} \times V \, \text{L} = 250V \, \text{mg} = 0.25V \, \text{g} \] Now, we can find the equivalents of CaCO3: \[ \text{Equivalents of CaCO3} = \frac{0.25V \, \text{g}}{50 \, \text{g/equiv}} = \frac{0.25V}{50} = 0.005V \, \text{equiv} \] ### Step 6: Set the equivalents of NaCl equal to the equivalents of CaCO3 Since the equivalents of NaCl will equal the equivalents of CaCO3 for softening to occur, we can set them equal: \[ 213.68 \, \text{equiv} = 0.005V \, \text{equiv} \] ### Step 7: Solve for V Now, solving for V gives: \[ V = \frac{213.68}{0.005} = 42736 \, \text{L} \] ### Final Answer The zeolite bed can soften approximately **42736 liters** of hard water with a hardness of 250 ppm. ---
To solve the problem of how many liters of hard water with a hardness of 250 ppm can be softened using an exhausted zeolite bed revived by a NaCl solution, we will follow these steps: ### Step 1: Calculate the total mass of NaCl in the solution The concentration of NaCl in the solution is given as 50 g/L, and the volume of the solution is 250 L. \[ \text{Total mass of NaCl} = \text{Concentration} \times \text{Volume} = 50 \, \text{g/L} \times 250 \, \text{L} = 12500 \, \text{g} \] ...
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