What must be the atomic mass of Cd from this experiment?

Question

A 1.5276 g sample of CdCl2 was converted to metallic cadmium and cadmium-free products by an electrolytic process. The weight of the metallic cadmium was 0.9376 g. If the atomic mass of chlorine is taken as 35.453, what must be the atomic mass of Cd from this experiment?

Answer 1

If we call the atomic weight of cadmium x, we can say that some number N relates the weight in grams to its atomic weight, i.e., Nx=0.9376. Similarly the molecular weight of CdCl₂ is related by N to its weight in grams.

The molecular weight of cadmium chloride is x+2×35.453=x+70.906, and (x+70.906)N=1.5276.

So N=0.9376/x=1.5276/(x+70.906).

Therefore, cross-multiplying: 0.9376(x+70.906)=1.5276x.

0.9376x+66.4815=1.5276x, 0.59x=66.4815 and x=112.68. So the atomic weight of Cd is about 112.68.