Here is a precise problem for the student to solve:A copper electrode is placed in a solution of copper nitrate with a concentration of 0.1 M, while a platinum electrode is placed in a solution of hydrogen peroxide. The potential difference of the half-reactions for the copper/copper(II) and hydrogen peroxide/water couples are +0.34 V and +1.77 V, respectively. Calculate the current density (in A/m²) at the copper electrode when a current of 0.25 A is passed through the cell for 10 minutes.

Question

Here is a precise problem for the student to solve:A copper electrode is placed in a solution of copper nitrate with a concentration of 0.1 M, while a platinum electrode is placed in a solution of hydrogen peroxide. The potential difference of the half-react

Answer 1

To calculate the current density at the copper electrode, we first need to determine the amount of charge passed through the cell and the area of the copper electrode.1. Calculate the total charge passed through the cell:We know that the current  I  is 0.25 A and the time  t  is 10 minutes  600 seconds . The total charge  Q  can be calculated using the formula:Q = I  tQ = 0.25 A  600 s = 150 Coulombs2. Calculate the moles of electrons transferred:The charge of one mole of electrons is equal to the Faraday constant  F , which is approximately 96485 C/mol. We can calculate the moles of electrons  n  transferred using the formula:n = Q / Fn = 150 C / 96485 C/mol  0.00155 mol3. Calculate the moles of copper deposited:The balanced half-reaction for the copper/copper II  couple is:Cu + 2e  CuFrom the stoichiometry of the reaction, we can see that 2 moles of electrons are required to deposit 1 mole of copper. Therefore, the moles of copper deposited  n_Cu  can be calculated as:n_Cu = n / 2n_Cu = 0.00155 mol / 2  0.000775 mol4. Calculate the mass of copper deposited:The molar mass of copper  M_Cu  is approximately 63.5 g/mol. We can calculate the mass of copper deposited  m_Cu  using the formula:m_Cu = n_Cu  M_Cum_Cu = 0.000775 mol  63.5 g/mol  0.0492 g5. Calculate the volume of copper deposited:The density of copper  _Cu  is approximately 8.96 g/cm. We can calculate the volume of copper deposited  V_Cu  using the formula:V_Cu = m_Cu / _CuV_Cu = 0.0492 g / 8.96 g/cm  0.00549 cm6. Calculate the area of the copper electrode:Assuming the copper electrode has a uniform thickness  h , we can calculate the area  A  of the electrode using the formula:A = V_Cu / hTo proceed further, we need the thickness of the copper electrode. Let's assume the thickness of the copper electrode is 0.01 cm. Now, we can calculate the area:A = 0.00549 cm / 0.01 cm  0.549 cm7. Convert the area to m:A = 0.549 cm   1 m / 100 cm   5.49  10 m8. Calculate the current density  J  at the copper electrode:J = I / AJ = 0.25 A / 5.49  10 m  4550 A/mTherefore, the current density at the copper electrode is approximately 4550 A/m.