Coulomb force – Gravitational force (Salze-51) Someone claims that the gravitational forces in a salt are primarily determined by the gravitational forces (FG) of the ions involved. How much stronger is the pull due to the Coulomb force (Fc) compared to the gravitational force (FG)? For the calculation, take the gravitational forces between a sodium ion and a chloridion. two ions equal to 2.82·10-10 m.

  Exercise: Salze-51    

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Someone claims that the gravitational forces in a salt are primarily determined by the gravitational forces (F_G) of the ions involved. How much stronger is the pull due to the Coulomb force (F_c) compared to the gravitational force (F_G)?
For the calculation, take the gravitational forces between a sodium ion and a chloridion. two ions equal to 2.82·10^-10 m.

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Solution:

1. F_c = k·Q₁·Q₂/r²
       Q₁ = Q₂ = elementary load = 1.60222·10^-19 C
       F_c = (8.9875·10⁹)·(1.6022·10^-19)² / r²
       F_c = 2.31·10^-28 / r² [N]
2. F_G = G·m₁·m₂/r²
       · Individual atoms take … u (unit)
       · 1 u = 1.66·10^-27 kg
       · m(Na⁺) = 22.99 u
       · m(Cl^–) = 35.45 u
       · F_G = 6.67·10^-11·22.99u·35.45u / r²
       · F_G = 1.5·10^-61 / r² [N]
3. Factor x = F_c/F_G
       x = (2.31·10^-28 / r² ) / (1.5·10^-61 / r² ) = 1.5·10³³

The distance between the ions shrinks in the equation, and as a result, it can be said that the Coulomb force is clearly stronger than the gravitational force.

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