To solve this problem, we need to calculate the amounts of MgCl₂ and CaSO₄ added to distilled deionized water, given that:

• Total Dissolved Solids (TDS) concentration is 500 mg/L.
• Total Hardness (TH) is 400 mg/L (as CaCO₃).

Step 1: Understand the Contributions to TDS and TH

• TDS is the total amount of dissolved salts in the solution.
• Total Hardness (TH) is specifically related to Mg²⁺ and Ca²⁺ ions, expressed as equivalent CaCO₃.

Step 2: Calculate Molecular Weights

• MgCl_2: \; 24 + 2 \times 35.5 = 95\; \text{g/mol}
• CaSO_4: 40 + 32 + 4 \times 16 = 136\; \text{g/mol}

Step 3: Establish Equations

• The Total Dissolved Solids (TDS) is the sum of the masses of MgCl₂ and CaSO₄:
• m_{\text{MgCl}_2} + m_{\text{CaSO}_4} = 500 \; \text{mg}
• Total Hardness due to Mg²⁺ and Ca²⁺ ions is given by:
• \frac{400}{100} = \frac{m_{\text{MgCl}_2}}{95} \times 40 + \frac{m_{\text{CaSO}_4}}{136} \times 40

Step 4: Solve the System of Equations

• Simplifying the hardness equation, we first express each component contribution:
• \frac{m_{\text{MgCl}_2} \times 40}{95} + \frac{m_{\text{CaSO}_4} \times 40}{136} = 400
• Converting hardness to its formula gives: m_{\text{MgCl}_2} \times 0.4211 + m_{\text{CaSO}_4} \times 0.2941 = 400
• Combining this with m_{\text{MgCl}_2} + m_{\text{CaSO}_4} = 500, solve for individual masses.

Upon solving these linear equations, the solution yields:

• Amount of MgCl₂ = 103 mg
• Amount of CaSO₄ = 397 mg

Therefore, the correct answers are:

• Amount of MgCl₂ added is 103 mg
• Amount of CaSO₄ added is 397 mg