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Determine the molar mass of copper and Faraday's constant.

Physics

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Answer

30400 C\text{30400 C}

Step-by-step solution

5 steps

To calculate the quantity of electricity required, we will use Faraday's laws of electrolysis. We need the molar mass of copper and Faraday's constant. We will assume copper is in the +2 oxidation state (Cu²⁺), which is common in copper compounds.

  1. Determine the molar mass of copper and Faraday's constant.

    • Molar mass of copper (MCuM_{Cu}) = 63.5 g/mol63.5 \text{ g/mol}
    • Faraday's constant (FF) = 96485 C/mol e⁻96485 \text{ C/mol e⁻}
  2. Write the half-reaction for the liberation of copper.

    Assuming copper is in the +2 oxidation state, the reduction half-reaction is:

    Cu2+(aq)+2e−→Cu(s)\text{Cu}^{2+}(aq) + 2\text{e}^- \to \text{Cu}(s)

    This reaction shows that 2 moles of electrons are required to liberate 1 mole of copper.

  3. Calculate the number of moles of copper to be liberated.

    Given mass of copper (mm) = 10 g10 \text{ g}.
    Number of moles (nCun_{Cu}) = massmolar mass\frac{\text{mass}}{\text{molar mass}}

    nCu=10 g63.5 g/moln_{Cu} = \frac{10 \text{ g}}{63.5 \text{ g/mol}} nCu≈0.15748 moln_{Cu} \approx 0.15748 \text{ mol}
  4. Calculate the total moles of electrons required.

    From the half-reaction, 2 moles of electrons are needed per mole of copper.
    Moles of electrons (nen_e) = nCu×2n_{Cu} \times 2

    ne=0.15748 mol×2n_e = 0.15748 \text{ mol} \times 2 ne≈0.31496 mol e⁻n_e \approx 0.31496 \text{ mol e⁻}
  5. Calculate the quantity of electricity (charge) in coulombs.

    Quantity of electricity (QQ) = ne×Fn_e \times F

    Q=0.31496 mol e⁻×96485 C/mol e⁻Q = 0.31496 \text{ mol e⁻} \times 96485 \text{ C/mol e⁻} Q≈30398.9 CQ \approx 30398.9 \text{ C}

    Rounding to three significant figures:

    Q≈30400 CQ \approx 30400 \text{ C}

    The quantity of electricity required is:

    30400 C\text{30400 C}
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