Chapter 20, Problem 126RQ

A complex ion of chromium(III) with oxalate ion was prepared from ${}^{\text{51}}{\text{Cr-labeled K}}_{\text{2}}{\text{Cr}}_{\text{2}}{\text{O}}_{\text{7}}$, having a specific activity of 843 cpm/g (counts per minute per gram), and ${}^{\text{14}}\text{C}$

-labeled oxalic acid, ${\text{H}}_{\text{2}}{\text{C}}_{\text{2}}{\text{O}}_{\text{4}}$, having an specific activity of 345 cpm/g. Chromium-51 decays by electron capture with the emission of gamma radiation, whereas ${}^{\text{14}}\text{C}$ is a pure beta emitter. Because of the characteristics of the beta and gamma detectors, each of these isotopes may be counted independently. A sample of the complex ion was observed to give a gamma count of 165 cpm and a beta count of 83 cpm. From these data, determine the number of oxalate ions bound to each Cr(III) in the complex ion. (Hint: For the starting materials calculate the cpm per mole of Cr and oxalate, respectively.)