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How many grams of solid aluminum sulfide can be prepared by the reaction of 10.0 g of aluminum and 15.0 g of sulfur? How many grams of the nonlimiting reactant are in excess?

Chemistry

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Step-by-step solution

6 steps
  1. Write and balance the chemical equation for the combustion of butane.

    Butane (C4H10\text{C}_4\text{H}_{10}) burns in oxygen (O2\text{O}_2) to produce carbon dioxide (CO2\text{CO}_2) and water vapor (H2O\text{H}_2\text{O}).

    2C4H10(g)+13O2(g)⟶8CO2(g)+10H2O(g)2\text{C}_4\text{H}_{10}(g) + 13\text{O}_2(g) \longrightarrow 8\text{CO}_2(g) + 10\text{H}_2\text{O}(g)
  2. Calculate the molar masses of the reactants and products.

    • Molar mass of C4H10=(4×12.01)+(10×1.008)=48.04+10.08=58.12 g/mol\text{C}_4\text{H}_{10} = (4 \times 12.01) + (10 \times 1.008) = 48.04 + 10.08 = 58.12 \text{ g/mol}
    • Molar mass of O2=2×16.00=32.00 g/mol\text{O}_2 = 2 \times 16.00 = 32.00 \text{ g/mol}
    • Molar mass of CO2=12.01+(2×16.00)=12.01+32.00=44.01 g/mol\text{CO}_2 = 12.01 + (2 \times 16.00) = 12.01 + 32.00 = 44.01 \text{ g/mol}
  3. Convert the given masses of reactants to moles.

    Given: 4.65 g4.65 \text{ g} of butane and 40.0 g40.0 \text{ g} of oxygen.

    Moles of C4H10\text{C}_4\text{H}_{10}:

    nC4H10=4.65 g58.12 g/mol=0.07999 moln_{\text{C}_4\text{H}_{10}} = \frac{4.65 \text{ g}}{58.12 \text{ g/mol}} = 0.07999 \text{ mol}

    Moles of O2\text{O}_2:

    nO2=40.0 g32.00 g/mol=1.25 moln_{\text{O}_2} = \frac{40.0 \text{ g}}{32.00 \text{ g/mol}} = 1.25 \text{ mol}
  4. Determine the limiting reactant.

    Using the stoichiometric coefficients from the balanced equation:
    For C4H10\text{C}_4\text{H}_{10}: 0.07999 mol C4H10×13 mol O22 mol C4H10=0.5199 mol O20.07999 \text{ mol C}_4\text{H}_{10} \times \frac{13 \text{ mol O}_2}{2 \text{ mol C}_4\text{H}_{10}} = 0.5199 \text{ mol O}_2 needed.
    Since we have 1.25 mol O21.25 \text{ mol O}_2, which is more than 0.5199 mol O20.5199 \text{ mol O}_2 needed, C4H10\text{C}_4\text{H}_{10} is the limiting reactant.
    O2\text{O}_2 is the excess reactant.

  5. Calculate the mass of carbon dioxide produced based on the limiting reactant.

    From the balanced equation, 2 mol C4H102 \text{ mol C}_4\text{H}_{10} produces 8 mol CO28 \text{ mol CO}_2.

    Moles of CO2\text{CO}_2 produced:

    nCO2=0.07999 mol C4H10×8 mol CO22 mol C4H10=0.31996 mol CO2n_{\text{CO}_2} = 0.07999 \text{ mol C}_4\text{H}_{10} \times \frac{8 \text{ mol CO}_2}{2 \text{ mol C}_4\text{H}_{10}} = 0.31996 \text{ mol CO}_2

    Mass of CO2\text{CO}_2 produced:

    MassCO2=0.31996 mol×44.01 g/mol=14.08 g\text{Mass}_{\text{CO}_2} = 0.31996 \text{ mol} \times 44.01 \text{ g/mol} = 14.08 \text{ g}

    The mass of carbon dioxide produced is 14.08 g\boxed{\text{14.08 g}}.

  6. Calculate the mass of the excess reactant (O2\text{O}_2) remaining.

    Moles of O2\text{O}_2 consumed:

    nO2,consumed=0.07999 mol C4H10×13 mol O22 mol C4H10=0.5199 mol O2n_{\text{O}_2, \text{consumed}} = 0.07999 \text{ mol C}_4\text{H}_{10} \times \frac{13 \text{ mol O}_2}{2 \text{ mol C}_4\text{H}_{10}} = 0.5199 \text{ mol O}_2

    Moles of O2\text{O}_2 remaining:

    nO2,remaining=1.25 mol (initial)−0.5199 mol (consumed)=0.7301 mol O2n_{\text{O}_2, \text{remaining}} = 1.25 \text{ mol (initial)} - 0.5199 \text{ mol (consumed)} = 0.7301 \text{ mol O}_2

    Mass of O2\text{O}_2 remaining:

    MassO2,remaining=0.7301 mol×32.00 g/mol=23.36 g\text{Mass}_{\text{O}_2, \text{remaining}} = 0.7301 \text{ mol} \times 32.00 \text{ g/mol} = 23.36 \text{ g}

    The mass of excess reactant remaining is 23.36 g\boxed{\text{23.36 g}}.

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