Question

You pre-lab it mentioned a AA battery which holds a charge of 2400 mA-h (milliamp hours), convert this value to units of coulombs and moles of e^- (show work). The charge of the standard lead-acid automobile battery which helps start your car is 85 Ah (amp hours). How would the battery for your cell phone compare in relation to a car battery and a AA rechargeable battery? Explain.
Both please and thank you!! :))

Answer 1

2) The charge that the AA battery can hold is 2400 mA.h

We know that 1 A = 1 C/s

Therefore, charge contained in the 2400 mA.h battery = (2400 mA)*(1 A/1000 mA)*(1 h) = 2.4 A.h = (2.4 A)*(1 C/s)/(1 A) = 2.4 h.C/s.

Now 1 h = 3600 sec; plug this value above to get

2.4 h.C/s = (2.4)*(3600 s/1 h).(1 C/1 s).(1 h)= 8640 C (ans).

Again, 1 Faraday of electricity = 1 mole of electrons.

Now, 1 Faraday of electricity = 96485 C.

Therefore, 8640 C = (8640 C)*(1 Faraday/96485 C)*(1 mole e^-/1 Faraday) = 0.089 mole e^- ≈ 0.09 mole e^- (ans).

3) Charge of the lead acid car battery = 85 A.h = (85 C/s)*(3600 s) = 306000 C = 3.06*10⁵ C.

A typically cellphone battery is about 2000-3000 mAh battery (for example, the iPhone has a battery of about 1900 mAh). Charge that a cellphone battery can hold is 2000 mA.h = (2000 mA)*(1 A/1000 mA)*(1 C/1 s)*(3600 s/1 h).(1 h) = 7200 C.

Ratio of the charge of a lead-acid battery to a cellphone battery = (3.06*10⁵ C)(7200 C) = 42.5:1 ,i.e, a lead-acid battery can contain almost 42 times as much charge as a cell phone battery (ans).

We have already shown above that a typical AA battery contains 8640 C. Therefore, ratio of the charge of a lead-acid car battery to AA is (3.06*10⁵ C /8640 C) = 35.42:1 ,i.e., the lead-acid car battery has almost 35 times more charge than an AA battery.