(A) 40 K undergoes radioactive decay by electron capture to 40 Ar and by emission...

(A) ⁴⁰K undergoes radioactive decay by electron capture to ⁴⁰Ar and by β^– emission to ⁴⁰Ca. The fraction of the decay that occurs by electron capture is 0.110. The half-life of ⁴⁰K is 1.26 x 10⁹ years. Assuming that a rock in which ⁴⁰K has undergone decay retains all the ⁴⁰Ar produced, what would be the ⁴⁰Ar/⁴⁰K mass ratio in a rock that is 1.5 x 10⁹ years old?

(B) Most nuclear power plants use zirconium in the fuel rods because zirconium maintains its structural integrity under exposure to the radiation in the nuclear reactor. The nuclear accidents at Three Mile Island, Chernobyl, and Fukushima involved the evolution of hydrogen gas from the reduction of water. The half-cell reduction potential for Zr is

(a) Can Zr reduce water under standard-state conditions?

(b) Calculate the equilibrium constant for the reduction of water by zirconium.

(c) Is the reaction spontaneous if the pH = 7 and Zr, ZrO₂, and water are in their standard states?

(d) Was the reduction of water by Zr the culprit in the reactor accidents mentioned above?

Transcribed Image Text:

ZrO₂(s) + 4 H30+ (aq) + 4e - Zr(s) + 6 H₂O(1) E° = -1.43 V