Question

If a 1.5 V AAA alkaline battery can power a 1.4 Watt device for 1 hour, how many grams of zinc (65.38g/mol) does it contain?

Overall reaction in battery: MnO₂ + 2H₂O + Zn --> Mn(OH)₂+ ZnO

The answer is 1.1 g

Please explain step by step and how to reach this answer.

Answer 1

The equation

P = I*V

then

I = P/V

P = 1.4 watt; V = 1.5

then

I = 1.4/1.5 = 0.9333 Amp

1 amp = 1 C/s = 0.9333 C/s

t = 3600 s so

0.9333*3600 = 3359.88 C

convert to mol of electrons

1 mol of e- = 96500 C

then

3359.88/96500 = 0.0348174 mol of electrons being transferred

MnO2 + 2H2O + Zn --> Mn(OH)2+ ZnO

Zn goes from 0 to +2 therefore

2 mol of e are being transferred

for every mol of Zn

0.0348174/2 --> 0.0174087mol of Zn

mass of Zn = mol*MW = 0.0174087*65.38 = 1.138180806 g of Zn