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Question: A 6.50 molal solution of KOH(aq.) has a density of 1.89gcm$^{-3}$. The molarity of the solution is _...

A 6.50 molal solution of KOH(aq.) has a density of 1.89gcm−3^{-3}. The molarity of the solution is ______ mol dm−3^{-3}. (Round off to the Nearest Integer).

Answer

9 mol dm−3^{-3}

Explanation

Solution

Here's how to calculate the molarity of the KOH solution:

  1. Understand Molality: A 6.50 molal solution means there are 6.50 moles of KOH per 1 kg of solvent (water).

  2. Calculate Mass of KOH:

    • Molar mass of KOH ≈ 39.1 (K) + 16 (O) + 1 (H) = 56.1 g/mol
    • Mass of KOH = 6.50 mol × 56.1 g/mol ≈ 364.65 g

  3. Calculate Total Mass of Solution:

    • Total mass = 1000 g (water) + 364.65 g (KOH) = 1364.65 g

  4. Calculate Volume of Solution:

    • Density = 1.89 g/cm³ = 1890 g/dm³
    • Volume = Total mass / Density = 1364.65 g / 1890 g/dm³ ≈ 0.7225 dm³

  5. Calculate Molarity:

    • Molarity = Moles of solute / Volume in dm³ = 6.50 mol / 0.7225 dm³ ≈ 9.00 mol/dm³

  6. Round to Nearest Integer: The molarity is approximately 9 mol/dm³.