Question

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.

Answer 1

The question is incomplete, here is the complete question:

When a lead acid car battery is recharged by the alternator, it acts essentially as an electrolytic cell in which solid lead(II) sulfate PbSO₄ is reduced to lead at the cathode and oxidized to solid lead(II) oxide PbO at the anode.

Suppose a current of 96.0 A is fed into a car battery for 37.0 seconds. Calculate the mass of lead deposited on the cathode of the battery. Round your answer to 3 significant digits. Also, be sure your answer contains a unit symbol.

Answer: The mass of lead deposited on the cathode of the batter is 3.81 grams

Step-by-step explanation:

To calculate the charge deposited, we use the equation:

`\text{Charge}=\text{Current}* \text{Time (in seconds)}`

We are given:

Current supplied = 96.0 A

Time = 37.0 seconds

Putting values in above equation, we get:

`\text{Charge}=96.0* 37=3552C`

We know that:

96500 C of charge deposition is contained in 1 mole of electrons

So, 3552 C of charge deposition will be contained in =
`(1)/(96500)* 3552=0.0368moles` of electrons

The half reaction follows:

At cathode:
`Pb(aq.)+2e^-\rightarrow Pb(s)`

Number of electrons exchanged are 2

So, moles of lead deposited =
`\text{Number of moles of electrons}}{\text{Number of electrons}}=(0.0368)/(2)=0.0184mol`

To calculate the number of moles, we use the equation:

`\text{Number of moles}=\frac{\text{Given mass}}{\text{Molar mass}}`

Molar mass of lead = 207.2 g/mol

Moles of lead = 0.0184 moles

Putting values in above equation, we get:

`0.0184mol=\frac{\text{Mass of lead}}{207.2g/mol}\\\\\text{Mass of lead}=(0.0184mol* 207.2g/mol)=3.81g`

Hence, the mass of lead deposited on the cathode of the batter is 3.81 grams