For a science experiment you need to electroplate a 150nm-thick zinc coating onto both sides of a very thin, 1.0cm * 1.0cm copper sheet. You know that the charge carriers in the ionic solution are divalent (charge 2e) zinc ions. The density of zinc is 7140kg/m^3.If the electroplating apparatus operates at 1.9 mA, how long will it take the zinc to reach the desired thickness?
i have the basic formula, you have to convert to proper units t (T * d * A * F * e) / (I * M) t time in sec T thickness in cm d density of zinc in g/cc A total surface area to be plated in cm2 F faraday constant 96 485.34 C/mol for ionic equation Zn(2+) + 2e Zn there are 2 electrons transfer per mol of Zn deposit so e 2 M molecular weight of zinc in g/mol I current in amp
Basically you determine the number of zinc atoms in the plating, multiply by 2 to get the number of electrons needed, convert to Coulombs and divide by the current. Look up the atomic weight of zinc Wz 65.38 g/mole Zinc atom mass mz Wz/(1000*Avogadro) 1.0857E-25 kg Zinc atom volume Vz mz/rho 1.5206E-29 m^3 V(plating) 150E-9*2*0.01^2 3E-11 m^3 Natoms V(plating)/Vz 1.973E18 Nelectrons 2*Natoms 3.946E18 Total charge Q Nelectrons*1.6022E-19 6.322E-1 C t Q/I 333 s EDIT: I did the lookup of Wz, corrected an error (had the plating volume wrong) and added the numeric results. The 2nd answer's formula yields the same result.
i have the basic formula, you have to convert to proper units t (T * d * A * F * e) / (I * M) t time in sec T thickness in cm d density of zinc in g/cc A total surface area to be plated in cm2 F faraday constant 96 485.34 C/mol for ionic equation Zn(2+) + 2e Zn there are 2 electrons transfer per mol of Zn deposit so e 2 M molecular weight of zinc in g/mol I current in amp
Basically you determine the number of zinc atoms in the plating, multiply by 2 to get the number of electrons needed, convert to Coulombs and divide by the current. Look up the atomic weight of zinc Wz 65.38 g/mole Zinc atom mass mz Wz/(1000*Avogadro) 1.0857E-25 kg Zinc atom volume Vz mz/rho 1.5206E-29 m^3 V(plating) 150E-9*2*0.01^2 3E-11 m^3 Natoms V(plating)/Vz 1.973E18 Nelectrons 2*Natoms 3.946E18 Total charge Q Nelectrons*1.6022E-19 6.322E-1 C t Q/I 333 s EDIT: I did the lookup of Wz, corrected an error (had the plating volume wrong) and added the numeric results. The 2nd answer's formula yields the same result.
