An element x has a relative atomic mass of 88. When a current of 0.5 ampere was passed through the fused chloride of x for 32 minutes and 10 seconds, 0.44g of x was deposited at cathode.
(1) Calculate the number of faradays needed to liberate Imol of x
(ii) Write the formula for x ions
(iii) Write the formula for the hydroxide of x
To calculate the number of faradays needed to liberate 1 mol of x, we can use the formula:
Faradays = (Amount of substance deposited at cathode / Relative atomic mass) / (Current × Time)
Plugging in the values:
Amount of substance deposited at cathode = 0.44g
Relative atomic mass = 88
Current = 0.5 ampere
Time = 32 minutes and 10 seconds = 32.167 minutes
Faradays = (0.44g / 88) / (0.5 × 32.167) = 0.0025 moles
Therefore, the number of faradays needed to liberate 1 mol of x is 0.0025.
(ii) To determine the formula for x ions, we need to consider the charge on the ion. From the process of electrolysis, x ions were reduced to x atoms at the cathode. This means that x ions gained electrons. Since Faraday's constant is approximately 96,500 coulombs, 1 Faraday corresponds to the transfer of 1 mole of electrons. Therefore, to find the charge of x ions, we need to multiply the number of faradays by Faraday's constant.
Charge on x ions = Number of faradays × Faraday's constant
Charge on x ions = 0.0025 × 96,500 = 242.5 coulombs
Based on the charge, we can determine the formula for x ions. Let's assume the charge on x ions is +q. For the total charge to be 242.5 coulombs, the charge q must be +2.
Therefore, the formula for x ions is X^2+.
(iii) To write the formula for the hydroxide of x, we need to determine the valency of x ions. Since the charge on x ions is +2, the valency is 2. The formula for the hydroxide of x will be X(OH)2.