The hardness of water sample containing .001 mole of MgSO4 dissolved per litre is ?

To determine the hardness of a water sample containing 0.001 moles of MgSO4 (magnesium sulfate) dissolved per liter, we first need to understand what hardness in water means. Hardness is primarily caused by the presence of divalent metal ions, such as calcium (Ca²⁺) and magnesium (Mg²⁺). In this case, we are focusing on magnesium ions from MgSO4.

Understanding Water Hardness

Water hardness is typically expressed in terms of the concentration of calcium carbonate (CaCO3) equivalent. This means we need to convert the amount of magnesium sulfate in the water to its equivalent hardness in terms of CaCO3.

Calculating the Equivalent Hardness

First, let's break down the components of magnesium sulfate:

• MgSO4 dissociates into Mg²⁺ and SO4²⁻ ions in solution.
• Each mole of MgSO4 produces one mole of Mg²⁺ ions.

Since we have 0.001 moles of MgSO4, this means we also have 0.001 moles of Mg²⁺ ions in the solution.

Conversion to Calcium Carbonate Equivalent

To express the hardness in terms of CaCO3, we need to use the molar masses:

• Molar mass of MgSO4 = 24.31 (Mg) + 32.07 (S) + 4 × 16.00 (O) = 120.37 g/mol
• Molar mass of CaCO3 = 40.08 (Ca) + 12.01 (C) + 3 × 16.00 (O) = 100.09 g/mol

Next, we need to find the equivalent weight of Mg²⁺ in terms of CaCO3. The equivalent weight of Mg²⁺ is calculated as follows:

• 1 mole of Mg²⁺ is equivalent to 1 mole of CaCO3 in terms of hardness.
• Thus, 0.001 moles of Mg²⁺ corresponds to 0.001 moles of CaCO3.

Final Calculation

Now, we can calculate the hardness in terms of CaCO3:

• Hardness (as CaCO3) = moles of Mg²⁺ × molar mass of CaCO3
• Hardness = 0.001 moles × 100.09 g/mol = 0.10009 g/L

Therefore, the hardness of the water sample containing 0.001 moles of MgSO4 dissolved per liter is approximately 0.10009 g/L when expressed as calcium carbonate equivalent.

Summary

In summary, the hardness of the water sample can be calculated by determining the moles of magnesium ions present and converting that to an equivalent amount of calcium carbonate. In this case, the hardness is about 0.10009 g/L, which indicates a low level of hardness typical for water with minimal dissolved minerals.