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Calculate the mass of coke needed to react with 0.302 kg of pure tin oxide (SnO2) given the reaction SnO2 + 2C -> Sn + 2CO and that coke is 80% carbon.

Chemistry

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Step-by-step solution

5 steps

To solve this problem, we need to follow these steps:

  1. Calculate the molar mass of tin oxide (SnO2\text{SnO}_2).
  2. Determine the number of moles of SnO2\text{SnO}_2 from the given mass.
  3. Use the stoichiometry of the balanced chemical equation to find the moles of carbon (C) required.
  4. Calculate the mass of carbon required.
  5. Calculate the mass of coke needed, considering it is 80% carbon.

Given:

  • Reaction: SnO2+2C→Sn+2CO\text{SnO}_2 + 2\text{C} \rightarrow \text{Sn} + 2\text{CO}
  • Mass of pure tin oxide (SnO2\text{SnO}_2) = 0.302 kg
  • Atomic masses: Sn = 119 g/mol, O = 16 g/mol, C = 12 g/mol
  • Coke contains 80% carbon by mass.
  1. Calculate the molar mass of SnO2\text{SnO}_2.

    The molar mass of SnO2\text{SnO}_2 is the sum of the atomic mass of Sn and two times the atomic mass of O.

    Molar mass of SnO2=(1×119)+(2×16)=119+32=151 g/mol\text{Molar mass of SnO}_2 = (1 \times 119) + (2 \times 16) = 119 + 32 = 151 \text{ g/mol}
  2. Determine the number of moles of SnO2\text{SnO}_2.

    First, convert the mass of SnO2\text{SnO}_2 from kg to g.

    Mass of SnO2=0.302 kg=0.302×1000 g=302 g\text{Mass of SnO}_2 = 0.302 \text{ kg} = 0.302 \times 1000 \text{ g} = 302 \text{ g}

    Now, calculate the moles of SnO2\text{SnO}_2.

    Moles of SnO2=Mass of SnO2Molar mass of SnO2=302 g151 g/mol=2 mol\text{Moles of SnO}_2 = \frac{\text{Mass of SnO}_2}{\text{Molar mass of SnO}_2} = \frac{302 \text{ g}}{151 \text{ g/mol}} = 2 \text{ mol}
  3. Use stoichiometry to find the moles of carbon (C) required.

    From the balanced chemical equation, 1 mole of SnO2\text{SnO}_2 reacts with 2 moles of C.

    SnO2+2C→Sn+2CO\text{SnO}_2 + 2\text{C} \rightarrow \text{Sn} + 2\text{CO}

    Since we have 2 moles of SnO2\text{SnO}_2, the moles of carbon required will be:

    Moles of C=2×(Moles of SnO2)=2×2 mol=4 mol\text{Moles of C} = 2 \times (\text{Moles of SnO}_2) = 2 \times 2 \text{ mol} = 4 \text{ mol}
  4. Calculate the mass of carbon required.

    The molar mass of carbon is 12 g/mol.

    Mass of C=Moles of C×Molar mass of C=4 mol×12 g/mol=48 g\text{Mass of C} = \text{Moles of C} \times \text{Molar mass of C} = 4 \text{ mol} \times 12 \text{ g/mol} = 48 \text{ g}
  5. Calculate the mass of coke needed.

    Coke contains 80% carbon by mass. This means that the mass of carbon calculated (48 g) represents 80% of the total mass of coke.
    Let the mass of coke be xx.

    0.80×x=48 g0.80 \times x = 48 \text{ g} x=48 g0.80=60 gx = \frac{48 \text{ g}}{0.80} = 60 \text{ g}

    Finally, convert the mass of coke from g to kg.

    Mass of coke=60 g=0.060 kg\text{Mass of coke} = 60 \text{ g} = 0.060 \text{ kg}

    Comparing this result with the given options:
    A. 0.40 kg
    B. 0.20 kg
    C. 0.06 kg
    D. 0.04 kg

    The calculated mass of coke is 0.06 kg.

    The final answer is 0.06 kg\boxed{\text{0.06 kg}}

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