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MgCl\(_2\) and CaSO\(_4\) salts are added to 1 litre of distilled deionized water and mixed until completely dissolved. The total dissolved solids (TDS) concentration is 500 mg/L, and the total hardness (TH) is 400 mg/L as CaCO\(_3\). The amounts of MgCl\(_2\) and CaSO\(_4\) added are calculated, rounded off to the nearest integer. Which of the following options is/are true?

1. Amount of MgCl\(_2\) added is 143 mg
2. Amount of CaSO\(_4\) added is 357 mg
3. Amount of MgCl\(_2\) added is 103 mg
4. Amount of CaSO\(_4\) added is 397 mg

Correct answer: Amount of MgCl\(_2\) added is 143 mg

Solution

Total mass of salts is 500 mg/L, so if MgCl\(_2\) is \(x\) mg, CaSO\(_4\) is \(500-x\) mg. Using equivalent weights, MgCl\(_2\) contributes hardness proportional to \(x\), and CaSO\(_4\) contributes the rest; solving the hardness equation gives \(x \approx 143\) mg. Hence the correct statement is that MgCl\(_2\) added is 143 mg.

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