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Calculate the mass of ethanol produced from 1.0 kg of ethene according to the reaction C2H4 + H2O -> C2H5OH.

Chemistry

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Answer

1.64 kg\text{1.64 kg}

Step-by-step solution

4 steps
  1. Calculate the molar mass of ethene (C2H4\text{C}_2\text{H}_4) and ethanol (C2H5OH\text{C}_2\text{H}_5\text{OH}).

    The relative atomic masses are Ar\text{A}_r: C = 12, H = 1, O = 16.
    Molar mass of ethene (C2H4\text{C}_2\text{H}_4):

    M(C2H4)=(2×12)+(4×1)=24+4=28 g/molM(\text{C}_2\text{H}_4) = (2 \times 12) + (4 \times 1) = 24 + 4 = 28 \text{ g/mol}

    Molar mass of ethanol (C2H5OH\text{C}_2\text{H}_5\text{OH}):

    M(C2H5OH)=(2×12)+(5×1)+(1×16)+(1×1)=24+5+16+1=46 g/molM(\text{C}_2\text{H}_5\text{OH}) = (2 \times 12) + (5 \times 1) + (1 \times 16) + (1 \times 1) = 24 + 5 + 16 + 1 = 46 \text{ g/mol}
  2. Convert the given mass of ethene to moles.

    Given mass of ethene = 1.0 kg=1000 g1.0 \text{ kg} = 1000 \text{ g}.

    Moles of ethene=MassMolar mass=1000 g28 g/mol\text{Moles of ethene} = \frac{\text{Mass}}{\text{Molar mass}} = \frac{1000 \text{ g}}{28 \text{ g/mol}} Moles of ethene≈35.714 mol\text{Moles of ethene} \approx 35.714 \text{ mol}
  3. Determine the moles of ethanol produced.

    The balanced chemical equation is C2H4+H2O→C2H5OH\text{C}_2\text{H}_4 + \text{H}_2\text{O} \rightarrow \text{C}_2\text{H}_5\text{OH}.
    From the equation, 1 mole of ethene produces 1 mole of ethanol.
    Therefore, moles of ethanol produced = moles of ethene.

    Moles of ethanol=100028 mol\text{Moles of ethanol} = \frac{1000}{28} \text{ mol}
  4. Calculate the mass of ethanol.

    Mass of ethanol=Moles of ethanol×Molar mass of ethanol\text{Mass of ethanol} = \text{Moles of ethanol} \times \text{Molar mass of ethanol} Mass of ethanol=(100028 mol)×(46 g/mol)\text{Mass of ethanol} = \left(\frac{1000}{28} \text{ mol}\right) \times (46 \text{ g/mol}) Mass of ethanol=1000×4628 g\text{Mass of ethanol} = \frac{1000 \times 46}{28} \text{ g} Mass of ethanol=4600028 g\text{Mass of ethanol} = \frac{46000}{28} \text{ g} Mass of ethanol≈1642.857 g\text{Mass of ethanol} \approx 1642.857 \text{ g}

    Convert the mass to kilograms:

    Mass of ethanol=1642.8571000 kg≈1.642857 kg\text{Mass of ethanol} = \frac{1642.857}{1000} \text{ kg} \approx 1.642857 \text{ kg}

    Rounding to three significant figures:

    Mass of ethanol=1.64 kg\text{Mass of ethanol} = \boxed{\text{1.64 kg}}
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