Question 36 of 50intermediate🔧 ApplyNumerical2 marks

If the density of some lake water is 1.25g mL-1 and contains 92 g of Na+ ions per kg of water, calculate the molarity of Na+ ions in the lake.

Correct Answer

The molarity of Na⁺ ions in the lake water is 4.58 M.

Exercise: EXERCISES | Q: 1.26 | (Page 29)
For More Understanding

Explanation

This question tests the concept of molarity calculation. Molarity is defined as the number of moles of solute dissolved in one litre of solution. The key steps involve: (1) calculating moles of Na⁺ ions from the given mass, (2) determining the total mass of solution (water + Na⁺ ions), (3) converting mass to volume using density, and (4) applying the molarity formula. Students must remember that the volume is of the solution, not just the solvent.

Solution Steps

  1. Step 1: Calculate moles of Na⁺ ions Moles of Na⁺ = Mass / Molar mass = 92 g / 23 g mol⁻¹ = 4 mol

  2. Step 2: Calculate total mass of solution Mass of water = 1 kg = 1000 g Mass of Na⁺ ions = 92 g Total mass of solution = 1000 g + 92 g = 1092 g

  3. Step 3: Calculate volume of solution Volume = Mass / Density = 1092 g / 1.25 g mL⁻¹ = 873.6 mL = 0.8736 L

  4. Step 4: Calculate molarity Molarity = Moles of solute / Volume of solution in litre Molarity = 4 mol / 0.8736 L = 4.58 mol L⁻¹ or 4.58 M

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