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Electroplating is a way to coat a complex metal object with a very thin (and hence inexpensive) layer of a precious metal, such as silver or gold. In essence the metal object is made the cathode of an electrolytic cell in which the precious metal cations are dissolved in aqueous solution. Suppose a current of 0.770A is passed through an electroplating cell with an aqueous solution of AgNO3 in the cathode compartment for 19.0 seconds. Calculate the mass of pure silver deposited on a metal object made into the cathode of the cell. Be sure your answer has a unit symbol and the correct number of significant digits.

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Answer:

0.0164 g

Explanation:

Let's consider the reduction of silver (I) to silver that occurs in the cathode during the electroplating.

Ag⁺(aq) + 1 e⁻ → Ag(s)

We can establish the following relations.

  • 1 A = 1 C/s
  • The charge of 1 mole of electrons is 96,468 C (Faraday's constant)
  • 1 mole of Ag(s) is deposited when 1 mole of electrons circulate.
  • The molar mass of silver is 107.87 g/mol

The mass of silver deposited when a current of 0.770 A circulates during 19.0 seconds is:

[tex]19.0s \times \frac{0.770c}{s} \times \frac{1mole^{-} }{96,468C} \times \frac{1molAg}{1mole^{-}} \times \frac{107.87g}{1molAg} = 0.0164 g[/tex]

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