Question

Predict the gravitational and electrostatic forces between molecules of gases? Provide evidence for your prediction.

Answer 1

the electrostatic forces are $10^{36}$ larger than the gravitational force

Explanation:

Let's do the calculation by using two molecules of hydrogen, each containing 2 atoms of hydrogen.

The gravitational force between the two molecules is given by:

$F=\frac{G m_1 m_2}{r^2}$

where

$G=6.67\cdot 10^{-11} m^3 kg^{-1}s^{-2}$ is the gravitational constant

m1 and m2 are the masses of the two molecules: since they are identical,

$m_1 = m_2 = 2m_p = 1.67\cdot 10^{-27} kg$, twice the mass of the proton

r is the distance between the two  molecules

The force can be rewritten as

$F_G=\frac{Gm_p^2}{r^2}$

We can assume instead that electrostatic force between the two molecules is given by the interaction between the positively charged nuclei and the neatively charged electrons. Therefore,

$F_E=\frac{kq_1 q_2}{r^2}$

where

$k=8.99\cdot 10^9 Nm^{-2}C^{-2}$ is the Coulomb's constant

$q_1 = q_2 = 2e$ is the magnitude of the charge of each molecule, where

$e=1.6\cdot 10^{-19}C$ is the fundamental charge

r is the distance between the two molecules

So the force can be  rewritten as

$F_E=\frac{ke^2}{r^2}$

Therefore, the ratio between the two forces is:

$\frac{F_E}{F_G}=\frac{ke^2}{Gm_p^2}=\frac{(8.99\cdot 10^9)(1.6\cdot 10^{-19})^2}{(6.67\cdot 10^{-11})(1.67\cdot 10^{-27})^2}\sim 10^{36}$

So, the electrostatic forces are $10^{36}$ larger than the gravitational force.

Learn more about electric force:

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Learn more about gravitational force:

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