a voltaic cell is made of Fe^2+(aq)/ Fe and Mg/Mg^2+(aq). If iron electrode undergoes a mass change of 0.328g, what will be the change in mass of the magnesium electrode?
To determine the change in mass of the magnesium electrode, we need to calculate the stoichiometric ratio between the mass changes of iron and magnesium in the voltaic cell.
From the given information, we know that the iron electrode undergoes a mass change of 0.328g. We need to find the stoichiometric ratio between the mass changes of iron and magnesium to determine the change in mass of the magnesium electrode.
To calculate this stoichiometric ratio, we can use the balanced half-reactions of the voltaic cell:
Fe^2+(aq) + 2e- -> Fe (reduction half-reaction)
Mg -> Mg^2+(aq) + 2e- (oxidation half-reaction)
Based on these half-reactions, we can see that 2 moles of electrons are transferred for every 1 mole of Fe (reduction half-reaction), and 2 moles of electrons are transferred for every 1 mole of Mg (oxidation half-reaction).
Since the mass change of the iron electrode is 0.328g, we can calculate the corresponding moles of Fe:
Molar mass of Fe = 55.845 g/mol
Moles of Fe = mass of Fe / molar mass of Fe
Moles of Fe = 0.328g / 55.845 g/mol
Moles of Fe = 0.00587 mol
Since the moles of electrons transferred for every 1 mole of Fe is 2, we can calculate the moles of electrons transferred in the reduction half-reaction:
Moles of electrons = moles of Fe * (2 moles of electrons / 1 mole of Fe)
Moles of electrons = 0.00587 mol * (2 moles of electrons / 1 mole of Fe)
Moles of electrons = 0.0117 mol
Since 2 moles of electrons are transferred for every 1 mole of Mg, we can now calculate the moles of Mg:
Moles of Mg = Moles of electrons / (2 moles of electrons / 1 mole of Mg)
Moles of Mg = 0.0117 mol / (2 moles of electrons / 1 mole of Mg)
Moles of Mg = 0.0117 mol / 2
Moles of Mg = 0.00585 mol
Finally, we can calculate the change in mass of the magnesium electrode by using the moles of Mg:
Molar mass of Mg = 24.305 g/mol
Change in mass of Mg = Moles of Mg * Molar mass of Mg
Change in mass of Mg = 0.00585 mol * 24.305 g/mol
Change in mass of Mg = 0.142 g
Therefore, the change in mass of the magnesium electrode is 0.142 g.