THE MULTI-COMBINATIONAL THEORY AS A PREDICTIVE MODEL IN CHEMISTRY

THE MULTI-COMBINATIONAL THEORY AS A PREDICTIVE MODEL IN CHEMISTRY

                                                 

My multi-combinational theory (mathematics) has useful effects on chemistry. One of the areas to be considered now is the Atomic structure. The multiple combinations of copper, chlorine and oxygen is the multiple combinations of their masses, relative atomic masses and percentage abundances. The relative percentage abundance or decimal fractions of the combine elements should sum up to 100(r+1) where r+1 is denoted as number of combined elements. The combined element x₁x_2*…_*x_i*…._*x_r  has the combined isotopes A and B. The combined relative atomic masses of x₁x_2*…._*x_i*…_*x_r is;

x₁x_2*…._*x_i*…_*x_r  of Ar=[A*%(1) +B*%(2)]100(R+1), where

A= combined masses of isotope A

B=combined masses of isotope B

1=combined relative abundances of A

2=combined relative abundances of B

Given the respective combined percentage abundances be x₁x_2*…._*x_i*…_*x_r and x₂x_3*.._*x_i*…*x_r. This implies that;

x₁x_2*…._*x_i*…_*x_r+ x₂x_3*.._*x_i*…*x_r=100(r+1)

EXAMPLE

Copper, chlorine, and oxygen have the four isotopes ⁶³cu and 65cu for copper; ³⁵cl and ³⁷cl for chlorine. The relative atomic masses of the naturally occurring copper and chlorine are 63.55 and 35.0 respectively.

What will be the relative percentage abundance of ³⁷cl if the relative percentage abundance of ⁶³cu is 72.5%

SOLUTION

Let, ⁶³cu⁶⁵cu³⁵cl=x₁x₂x₃ and ⁶⁵cu³⁵cl³⁷cl= x₂x₃x₄

x₁x₂x₃ +  x₂x₃x₄=100(4)

combined-Ar = [(⁶³cu⁶⁵cu³⁵cl* x₁x₂x₃)+( ⁶⁵cu³⁵cl³⁷cl* x₂x₃x₄)]/400

63.5*35 = [(63*65*35 x₁x₂x₃)+(65*35*37* x₂x₃x₄)]/400

2224.22 = [143325x₁x₂x₃+ 84175(400- x₁x₂x₃)]/400

x₁x₂x₃ = 554.1896

x₂x₃x₄ = 400-554.1896=154.1896.

Applying the sequential comparison rule, we have;

x₄=x₁[x₂x₃x₄/x₁x₂x₃]

x₄=72.5[154.189/554.1896]

x₄=20.17%.

Hence, the isotope ³⁷cl  is 20.17% if the percentage abundance of isotope ⁶³cu is 72,5%.

NOTE: All negations are nullified. 




REFERENCE
Chowla, S.(1940). "The Last Entry in Gauss's Diary"