Given molar mass (M) = 74 g⁻¹ and percentage of oxygen by mass = 43.24\%.

Mathematics

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2.5.1

  1. Calculate the mass of oxygen in one mole of the compound.

    Given molar mass (MM) = 74 g⋅mol−174 \text{ g}\cdot\text{mol}^{-1} and percentage of oxygen by mass = 43.24%43.24\%.
    Mass of oxygen = 0.4324×74 g⋅mol−1=31.9976 g⋅mol−10.4324 \times 74 \text{ g}\cdot\text{mol}^{-1} = 31.9976 \text{ g}\cdot\text{mol}^{-1}.

  2. Determine the number of oxygen atoms (z).

    The molar mass of oxygen is 16 g⋅mol−116 \text{ g}\cdot\text{mol}^{-1}.
    Number of oxygen atoms (zz) = 31.9976 g⋅mol−116 g⋅mol−1≈2\frac{31.9976 \text{ g}\cdot\text{mol}^{-1}}{16 \text{ g}\cdot\text{mol}^{-1}} \approx 2.
    So, there are 2 oxygen atoms in the compound. The formula is CxHyO2C_xH_yO_2.

  3. Calculate the remaining mass for carbon and hydrogen.

    Mass of 2 oxygen atoms = 2×16 g⋅mol−1=32 g⋅mol−12 \times 16 \text{ g}\cdot\text{mol}^{-1} = 32 \text{ g}\cdot\text{mol}^{-1}.
    Remaining mass for carbon and hydrogen = 74 g⋅mol−1−32 g⋅mol−1=42 g⋅mol−174 \text{ g}\cdot\text{mol}^{-1} - 32 \text{ g}\cdot\text{mol}^{-1} = 42 \text{ g}\cdot\text{mol}^{-1}.

  4. Determine the number of carbon (x) and hydrogen (y) atoms.

    Let the formula for the carbon and hydrogen part be CxHyC_xH_y.
    We know 12x+1y=4212x + 1y = 42.
    By trial and error, or by considering common organic structures:
    If x=1x=1, y=30y=30 (too many hydrogens).
    If x=2x=2, y=18y=18 (too many hydrogens).
    If x=3x=3, y=42−(12×3)=42−36=6y=42 - (12 \times 3) = 42 - 36 = 6. This gives C3H6C_3H_6.
    This ratio (C3H6C_3H_6) is plausible for an organic compound.

  5. Combine the atoms to form the molecular formula.

    The molecular formula is C3H6O2\boxed{C_3H_6O_2}.

    2.5.2
    The molecular formula C3H6O2C_3H_6O_2 can represent several functional isomers. Two common functional groups for this formula are carboxylic acids and esters.

    1. Propanoic acid (a carboxylic acid):

      CH3CH2COOHCH_3CH_2COOH

      This is a 3-carbon chain with a carboxylic acid group.

    2. Methyl ethanoate (an ester):

      CH3COOCH3CH_3COOCH_3

      This is an ester formed from ethanoic acid and methanol.

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