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.