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How to calculate the pH of reaction based of Lewis' definition of acid-base?

Can pH be calculated? Since some of the reactions don't have H or OH ions to dissociate, but still have interaction between electrons, the -log[H] or -log[OH] wouldn't be possible to calculate.

If it can, how can I calculate it?

If it can't, is there any other potential to determine the acidity of the reaction, like pNa or pBr instead of pH?
No. pH only refers to aqueous solutions. Arrhenius theory of acidity.

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