A \(9.00 \times 10^{2}-\mathrm{mL} 0.200 \mathrm{M} \mathrm{MgI}_{2}\) was electrolyzed. As a result, hydrogen gas was generated at the cathode and iodine was formed at the anode. The volume of hydrogen collected at \(26^{\circ} \mathrm{C}\) and \(779 \mathrm{mmHg}\) was \(1.22 \times 10^{3} \mathrm{~mL}\). (a) Calculate the charge in coulombs consumed in the process. (b) How long (in min) did the electrolysis last if a current of 7.55 A was used? (c) A white precipitate was formed in the process. What was it and what was its mass in grams? Assume the volume of the solution was constant.

At the cathode, hydrogen ions from water are reduced to form hydrogen gas. At the anode, iodide ions are oxidized to form iodine. The equation representing the overall reaction is \[2H_2O + 2MgI_2 \rightarrow 2MgO + 2I_2 + H_2\]. Use the ideal gas law \(n = \frac{PV}{RT}\) to convert the volume of hydrogen gas to moles, where \(P\) is the pressure in atmospheres, \(V\) is the volume in liters, \(R\) is the ideal gas constant in L.atm/K.mol, and \(T\) is the temperature in Kelvin. The given pressure must first be converted from mmHg to atmospheres by multiplying by the conversion factor \(\frac{1 atm}{760 mmHg}\). The resultant number of moles is the stoichiometrically equivalent to the number of moles of electrons moved in the reaction.

Use Faraday's law to calculate the charge. Faraday's law states that the amount of substance produced or used in the electrochemical reaction is directly proportional to the amount of charge that has passed through the circuit. Using the number of moles calculated in previous step, multiply by Avogadro's number, \(6.022 \times 10^{23}\), to get the number of molecules. As 2 electrons are transferred per molecule of \(H_2\), the total number of electrons transferred would be twice the number of molecules. Then, based on the elementary charge, \(1.60 \times 10^{-19} C\), the total charge used can be calculated by multiplying the elementary charge by the total number of electrons transferred.

It's known that current is charge per unit time. Rearranging this to find time, \(t = \frac{Q}{I}\), where \(Q\) is the total charge calculated in the previous step and \(I\) is the current, which is given. By substituting the values into the formula, the time in seconds can be found. If the time in minutes is required, divide the time in seconds by 60.

During electrolysis, \(Mg^{2+}\) ions react with \(OH^-\) ions in water to form a white precipitate, \(Mg(OH)_2\). The moles of \(Mg(OH)_2\) formed are equal to the moles of \(H_2\) formed since the stoichiometric ratio between \(H_2\) and \(Mg(OH)_2\) is 1:1 in the reaction. Then, the mass of \(Mg(OH)_2\) can be found by using its molar mass, which is 58.33 g/mol, and calculating \(mass = Moles \times Molar \, mass\).