In a common car battery, six identical cells each carry out the following reaction: Pb + PbO₂ + 2HSO₄^- + 2H⁺ $\rightarrow$ 2PbSO₄ + 2H₂O
Suppose that to start a car on a cold morning, 126 amperes is drawn for 13.0 seconds from such a cell. How many grams of Pb are consumed? (The atomic mass of Pb is 207.19 g/mol.)

Question

In a common car battery, six identical cells each carry out the following reaction: Pb + PbO₂ + 2HSO₄^- + 2H⁺

\rightarrow

2PbSO₄ + 2H₂O
Suppose that to start a car on a cold morning, 126 amperes is drawn for 13.0 seconds from such a cell. How many grams of Pb are consumed? (The atomic mass of Pb is 207.19 g/mol.)

Quizplus · Accepted Answer

First, we need to calculate the moles of electrons that were transferred during the reaction by using the given current and time:
Q = It = (126 A)(13.0 s) = 1638 C
n = Q/F = (1638 C)/(96485 C/mol) = 0.017 mol e-

Since each reaction equation involves the transfer of two electrons, we can say that 0.0085 mol of the reaction occurred in one cell. And since we have 6 identical cells, the total number of moles of the reaction that occurred is 6 × 0.0085 mol = 0.051 mol.

From the stoichiometry of the reaction, we can see that 1 mol of the reaction involves the consumption of 2 moles of Pb. Therefore, the number of moles of Pb consumed is 0.051 mol × 2 = 0.102 mol

Finally, we can calculate the mass of Pb consumed:
Mass of Pb = (0.102 mol)(207.19 g/mol) = 21.12 g
Dividing 21.12 g by 6 (to account for 6 identical cells), we get the mass of Pb consumed by one cell:
Mass of Pb consumed by one cell = 3.52 g

Therefore, the correct answer is C.

In a Common Car Battery, Six Identical Cells Each Carry →\rightarrow→

In a Common Car Battery, Six Identical Cells Each Carry $\rightarrow$