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I think I have trouble interpreting reaction enthalpy in these kind of situations:

I am given that $\Delta _rH^0 = 25,9$kJ/mole in the reaction: $$\ce{1/2 H2 + 1/2 I2 \rightarrow HI}$$ which I interpret as: if this reaction takes place where 1 mole HI forms, the the produced heat is equal to 25,9kJ.

Now suppose we double the amounts, so that we have the reaction $$\ce{H2 + I2 \rightarrow 2HI}$$ then clearly the difference in enthalpy should be doubled and be equal to 51,8kJ. Then why do chemists write that $\Delta _rH^0 = 51,8$kJ/mole and not $\Delta _rH^0 = 25,9$kJ/mole? Because I would think that we can calculate the enthalpy change like this: $2mole\times25,9$kJ/mole.

There is cleary some fundemantel thing I'm missing here or misinterpreting, so I would like some help.

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25.9 kJ/mol refers to one mole of $\ce{HI}$ produced while 51.8 kJ/mol corresponds to one mole of $\ce{H2}$ consumed. It is good practice to give the full equation, especially when dealing with reaction enthalpies/energies $\Delta_rX$. For formation quantities $\Delta_fX$, I would always assume one mole of product.

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