Question

# A small dry-cell battery of zinc, ammonium chloride, and MnO2 weighing 85 g will operate continuously...

A small dry-cell battery of zinc, ammonium chloride, and MnO2 weighing 85 g will operate continuously through a 4-ohm resistance for 450 min before its voltage falls below 0.75V. The initial voltage is 1.60, and the effective voltage over the whole life of the battery is taken to be 1.00V. How much work is obtained from the battery, in Joules? How many moles of Zn are converted to ZnCl2 in this process, and what is the weight of this amount of ZnCl2? How much MnO2 is required to carry out this oxidation? What fraction of the total 85-g weight of the battery consists of chemical reagents? About how many kilometers above the earth’s surface could this 85-g battery be raised with this amount of work? (Hints: Remember that the current pushed by a battery through a resistance R is given by I=V/R. The power it generates is P=IV=V2 /R, and the total work it performs over a period of time τ is given by w =V ∫0 τ I(t) dt ≈ VQ = VIτ = τV2 /R. Q is the total charge that the battery pushes through a roughly-constant voltage. So the essence of this problem is to calculate the values of w and Q, the total electrical charge that can be generated by the battery, and then to assume that all that charge is generated by the conversion of a certain amount of Zn and Cl- to ZnCl2).