(a) 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
(1) To calculate the number of faradays needed to liberate 1 mol of x, we can use Faraday's law of electrolysis:
moles of x deposited = current (amperes) × time (seconds) / (96,485 coulombs/mol)
First, we need to convert the time given into seconds:
32 minutes and 10 seconds = 32 × 60 + 10 = 1930 seconds
Now, we can calculate the number of faradays:
moles of x deposited = 0.44 g / molar mass of x
To find the molar mass of x, we need to use the relative atomic mass given. Since the relative atomic mass is the mass of 1 mole in grams, we have:
molar mass of x = 88 g/mol
moles of x deposited = 0.44 g / 88 g/mol = 0.005 mol
Now, we can calculate the number of faradays:
number of faradays = (current × time) / (96,485)
number of faradays = (0.5 A × 1930 s) / (96,485 C/mol)
= 965 mol C / 96,485 C/mol
= 0.01 mol
Therefore, 0.01 faradays are needed to liberate 1 mol of x.
(ii) The formula for x ions can be determined by looking at the charge of x when it is deposited at the cathode. Since x is deposited as a metal, it loses electrons and forms cations with a positive charge. Without further information, we cannot determine the exact charge of x ions or their formula. It would depend on the specific element x.
(iii) The formula for the hydroxide of x would also depend on the specific element x. Generally, the hydroxide formula is written as MOH, where M represents the metal ion. However, without knowing the specific element x, we cannot determine the exact formula for its hydroxide.