Final answer:
To calculate the number of Faraday needed to liberate 1 mole of X, use Faraday's Law of Electrolysis. The formula for the X ions is Xz+, where z is the charge on the X ions. The formula for the X hydroxide of X is X(OH)z.
Step-by-step explanation:
(i) To calculate the number of Faraday needed to liberate 1 mole of X, we need to find the charge required to deposit 1 mole of X. We can use Faraday's Law of Electrolysis, which states that the amount of substance liberated at an electrode is directly proportional to the charge passed through the cell. The charge passed can be calculated using the formula: charge (C) = current (A) x time (s). In this case, the charge is 0.5A x (32 minutes x 60 seconds/minute + 10 seconds) = 0.5A x 1930 seconds. The mole of electrons can be calculated using the formula: mole of electrons = charge (C) / Faraday constant. The Faraday constant is approximately 96,485 C/mol. Therefore, mole of electrons = (0.5A x 1930s) / 96,485C/mol. To find the number of Faraday needed to liberate 1 mole of X, we divide the mole of electrons by 1 mole: number of Faraday = mole of electrons / 1 mole.
(ii) To write the formula for the X ions, we need to determine the charge on the X ions. The charge on X ions can be determined from the number of Faraday needed to liberate 1 mole of X. For every Faraday of charge, there is one mole of X ions. Therefore, the formula for the X ions is Xz+, where z is the charge on the X ions.
(iii) To write the formula for the X hydroxide of X, we need to determine the charge on the X ions as well as the charge on the hydroxide ion. The charge on the hydroxide ion is always 1-. Since the X hydroxide of X is electrically neutral, the charges on X ions and hydroxide ions must balance. Therefore, if the charge on the X ion is z, the formula for the X hydroxide would be X(OH)z.