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I am learning about acid-base reactions and how to identify whether an acid is strong or not by looking at the conjugate base. The more stable a conjugate base the stronger the acid.

However, two of the factors that determine conjugate base stability seems contradictory to me.

  1. I understand the bigger the atom, the more stable the base so $\ce{HI}$ is more stable than $\ce{HF}$.
  2. The smaller the orbital the more stable the base. So $\ce{sp}$ is more stable than $\ce{sp^3}$.

Now why is a bigger atom more stable than a smaller one, but a smaller orbital more stable than a bigger orbital?

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When we say that 'bigger the atom, more stable is the anion', we mean to say that the negative charge would be spread over a larger area. So, the interatomic repulsive forces would be spread over a large area, lowering the energy and stabilising the anion. Going down the group, the jump in size is large enough to compensate the decrease in electronegativity, so we use the 'size of atoms' argument to differenciate between different atoms in the same group.

Conversely, we use the 'size of orbital' argument to determine the basicity of the same atom but in different hybridisations. Hence, the size of the atom would be same and the smaller size of the sp orbital would mean that it would be better attracted by the nucleus making the anion more stable.

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