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Solve this using method use in understanding chemistry textbook

Chemistry

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Answer

+2\text{+2}

Step-by-step solution

5 steps

Here's the solution using a method commonly found in chemistry textbooks, breaking down the steps to calculate the oxidation state.

Given:

  • Current (II) = 3.0 A
  • Time (tt) = 4 hours
  • Mass of tin deposited (mSnm_{Sn}) = 26.6 g
  • Molar mass of tin (MSnM_{Sn}) = 119 g/mol
  • Faraday's constant (FF) = 96500 C/mol

Goal: Determine the oxidation state of tin, which is the number of electrons (zz) involved in the reduction of tin ions to tin metal. The general half-reaction is Snz++ze−→Sn(s)\text{Sn}^{z+} + ze^- \to \text{Sn}(s).

  1. Convert time from hours to seconds.

    t=4 hours×60 minutes1 hour×60 seconds1 minutet = 4 \text{ hours} \times \frac{60 \text{ minutes}}{1 \text{ hour}} \times \frac{60 \text{ seconds}}{1 \text{ minute}} t=14400 st = 14400 \text{ s}
  2. Calculate the total quantity of electricity (charge, QQ) passed.

    The formula for charge is Q=I×tQ = I \times t.

    Q=3.0 A×14400 sQ = 3.0 \text{ A} \times 14400 \text{ s} Q=43200 CQ = 43200 \text{ C}
  3. Calculate the moles of tin (Sn) deposited.

    The formula for moles is n=massmolar massn = \frac{\text{mass}}{\text{molar mass}}.

    nSn=26.6 g119 g/moln_{Sn} = \frac{26.6 \text{ g}}{119 \text{ g/mol}} nSn≈0.223529 moln_{Sn} \approx 0.223529 \text{ mol}
  4. Calculate the moles of electrons (nen_e) transferred.

    One mole of electrons carries a charge equal to Faraday's constant (FF).

    ne=QFn_e = \frac{Q}{F} ne=43200 C96500 C/moln_e = \frac{43200 \text{ C}}{96500 \text{ C/mol}} ne≈0.447668 moln_e \approx 0.447668 \text{ mol}
  5. Determine the oxidation state (zz) of tin.

    From the half-reaction Snz++ze−→Sn(s)\text{Sn}^{z+} + ze^- \to \text{Sn}(s), we know that zz moles of electrons are required to deposit 1 mole of tin. Therefore, the ratio of moles of electrons to moles of tin gives the oxidation state.

    z=nenSnz = \frac{n_e}{n_{Sn}} z=0.447668 mol0.223529 molz = \frac{0.447668 \text{ mol}}{0.223529 \text{ mol}} z≈2.0027z \approx 2.0027

    Rounding to the nearest whole number, as oxidation states are typically integers:

    z=2z = 2

    The oxidation state of tin in the salt is +2\text{+2}.

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