GATE CE 2025 Set 1 — Question 44
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Environmental Engineering → Water Quality → pH, Turbidity, Hardness & Alkalinity
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Question
and salts are added to 1 litre of distilled deionized water and mixed until completely dissolved. Total Dissolved Solids (TDS) concentration is 500 mg/l, and Total Hardness (TH) is 400 mg/l (as ). The amounts of and added are calculated (rounded off to the nearest integer). Which of the following options is/are true:Atomic weights: Ca(40), Mg(24), S(32), O(16), Cl(35.5), C(12)
Correct answer
(C) Amount of MgCl₂ added is 103 mg; (D) Amount of CaSO₄ added is 397 mg
Solution
Let be the mass of added (mg) and be the mass of added (mg) in 1 litre of water.
g/mol
g/molConcentrations of ions:
mg/l
mg/lSubstitute into TH equation:
mg
mgRounding to the nearest integer, mg and mg. The closest options provided are mg and mg. Checking these values:
TDS = mg/l.
TH = mg/l.
Thus, options (C) and (D) are the intended correct answers.
1.TDS Equation:
TDS = mg/l.2.Total Hardness (TH) Equation:
TH (as ) = Molecular weights:g/mol
g/molConcentrations of ions:
mg/l
mg/lSubstitute into TH equation:
3.Solving the system:
From , .mg
mgRounding to the nearest integer, mg and mg. The closest options provided are mg and mg. Checking these values:
TDS = mg/l.
TH = mg/l.
Thus, options (C) and (D) are the intended correct answers.
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