Question

Here is a question for a chemistry student to solve in the subtopic Calculation of current density in an electrochemical cell: What is the current density (in amperes per square meter) in a zinc-copper galvanic cell, given that the mass of zinc electrode is 10 g and the rate of zinc dissolution is 0.1 g/min, the area of copper electrode is 5 cm², and the potential difference between the electrodes is 1.5 V?

Answer 1

To calculate the current density in the zinc-copper galvanic cell, we need to find the current flowing through the cell and divide it by the area of the copper electrode.First, we need to find the number of moles of zinc dissolving per minute. The molar mass of zinc  Zn  is 65.38 g/mol.Moles of Zn dissolving per minute =  rate of dissolution  /  molar mass of Zn Moles of Zn dissolving per minute =  0.1 g/min  /  65.38 g/mol  = 0.00153 mol/minIn a zinc-copper galvanic cell, the half-reaction for the zinc electrode is:Zn  Zn + 2eSo, for every mole of zinc dissolving, 2 moles of electrons are released. Therefore, the number of moles of electrons released per minute is:Moles of electrons per minute = 2  moles of Zn dissolving per minuteMoles of electrons per minute = 2  0.00153 mol/min = 0.00306 mol/minNow we need to convert moles of electrons to charge  coulombs . The charge of one mole of electrons is equal to the Faraday constant  F , which is approximately 96485 C/mol.Charge per minute = moles of electrons per minute  Faraday constantCharge per minute = 0.00306 mol/min  96485 C/mol = 295.3 C/minTo find the current  I , we need to convert the charge per minute to charge per second  coulombs per second, or amperes .Current  I  = Charge per minute / 60 secondsCurrent  I  = 295.3 C/min  60 s = 4.922 ANow we can calculate the current density  J . First, we need to convert the area of the copper electrode from square centimeters to square meters:Area  A  = 5 cm   1 m / 10000 cm  = 0.0005 mFinally, we can find the current density:Current density  J  = Current  I  / Area  A Current density  J  = 4.922 A / 0.0005 m = 9844 A/mThe current density in the zinc-copper galvanic cell is 9844 A/m.