Question

Problem PageQuestion When a lead acid car battery is recharged by the alternator, it acts essentially as an electrolytic cell in which solid lead(II) sulfate is reduced to lead at the cathode and oxidized to solid lead(II) oxide at the anode. Suppose a current of is fed into a car battery for seconds. Calculate the mass of lead deposited on the cathode of the battery. Round your answer to significant digits. Also, be sure your answer contains a unit symbol.

Answer 1

The mass is
`mass = 3.813 g`

Step-by-step explanation:

From the question we are told that

The current supplied is
`I = 96.06 A`

The time taken is t = 37.0 sec

Generally the charge been deposited on the cathode is mathematically represented as

`Q = It`

Substituting values

`Q = 96.0 * 37`

`= 3552C`

Generally 1 mole of the lead deposited contains
`96500C`

Then
`3552C` would contain how many moles

Not let say x is the number of moles deposited then

Using this mathematical relation

`1 mole ---------> 96500C \\x mole ----------> 3552C`

`x = (3552)/(96500)`

`= 0.0368 \ moles`

From the the question we are told that lead is been oxidized to lead 2 oxide which implies that the two electron would be accepted by the lead cation

Hence the number of moles that would be deposited at the cathode is

`n = (x)/(2) = (0.036808)/(2) = 0.018404 \ moles`

Now the molar mass of lead is constant with a value
`M= 207.2 g/mol`

Generally mass is mathematically represented as

`mass = n * M`

For lead

Substituting values

`mass =0.018404 * 207.2`

`mass = 3.813 g`