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b) 7.50g of a hydrated copper(II) sulphate (CuSO4.nH2O) on heating gave 4.8g of anhydrous copper(II) sulphate, determine the value of n (moles of water of crystallization)

Chemistry

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ii

5\text{5}

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Part i

**Avogadro number

The Avogadro number is the number of constituent particles (atoms, molecules, ions, or other particles) that are contained in one mole of a substance. It is defined as the number of atoms in exactly 12 grams12 \text{ grams} of the carbon-12 isotope. Its approximate value is 6.022×1023 mol−16.022 \times 10^{23} \text{ mol}^{-1}.

Part ii

5\text{5}

Determine the value of nn in CuSO4⋅nH2O\text{CuSO}_4 \cdot n\text{H}_2\text{O}.

Given:
Mass of hydrated copper(II) sulfate (CuSO4⋅nH2O\text{CuSO}_4 \cdot n\text{H}_2\text{O}) = 7.50 g7.50 \text{ g}
Mass of anhydrous copper(II) sulfate (CuSO4\text{CuSO}_4) = 4.80 g4.80 \text{ g}

  1. Calculate the mass of water of crystallization.

    The mass of water lost upon heating is the difference between the mass of the hydrated salt and the anhydrous salt.

    Mass of H2O=Mass of hydrated CuSO4−Mass of anhydrous CuSO4\text{Mass of } \text{H}_2\text{O} = \text{Mass of hydrated } \text{CuSO}_4 - \text{Mass of anhydrous } \text{CuSO}_4 Mass of H2O=7.50 g−4.80 g=2.70 g\text{Mass of } \text{H}_2\text{O} = 7.50 \text{ g} - 4.80 \text{ g} = 2.70 \text{ g}
  2. Calculate the moles of anhydrous copper(II) sulfate.

    First, determine the molar mass of CuSO4\text{CuSO}_4.
    (Atomic masses: Cu=63.5\text{Cu} = 63.5, S=32.1\text{S} = 32.1, O=16.0\text{O} = 16.0)

    Molar mass of CuSO4=63.5+32.1+(4×16.0)=63.5+32.1+64.0=159.6 g/mol\text{Molar mass of } \text{CuSO}_4 = 63.5 + 32.1 + (4 \times 16.0) = 63.5 + 32.1 + 64.0 = 159.6 \text{ g/mol}

    Now, calculate the moles of CuSO4\text{CuSO}_4.

    Moles of CuSO4=Mass of CuSO4Molar mass of CuSO4=4.80 g159.6 g/mol≈0.030075 mol\text{Moles of } \text{CuSO}_4 = \frac{\text{Mass of } \text{CuSO}_4}{\text{Molar mass of } \text{CuSO}_4} = \frac{4.80 \text{ g}}{159.6 \text{ g/mol}} \approx 0.030075 \text{ mol}
  3. Calculate the moles of water.

    First, determine the molar mass of H2O\text{H}_2\text{O}.
    (Atomic masses: H=1.0\text{H} = 1.0, O=16.0\text{O} = 16.0)

    Molar mass of H2O=(2×1.0)+16.0=18.0 g/mol\text{Molar mass of } \text{H}_2\text{O} = (2 \times 1.0) + 16.0 = 18.0 \text{ g/mol}

    Now, calculate the moles of H2O\text{H}_2\text{O}.

    Moles of H2O=Mass of H2OMolar mass of H2O=2.70 g18.0 g/mol=0.15 mol\text{Moles of } \text{H}_2\text{O} = \frac{\text{Mass of } \text{H}_2\text{O}}{\text{Molar mass of } \text{H}_2\text{O}} = \frac{2.70 \text{ g}}{18.0 \text{ g/mol}} = 0.15 \text{ mol}
  4. Determine the mole ratio to find nn.

    The value of nn is the ratio of moles of water to moles of anhydrous copper(II) sulfate.

    n=Moles of H2OMoles of CuSO4=0.15 mol0.030075 mol≈4.987n = \frac{\text{Moles of } \text{H}_2\text{O}}{\text{Moles of } \text{CuSO}_4} = \frac{0.15 \text{ mol}}{0.030075 \text{ mol}} \approx 4.987

    Rounding to the nearest whole number, n=5n = 5.

    The value of nn is 5\boxed{\text{5}}.

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