Acid is a substance that releases $\ce{H+}$ ions when mixed with water But if it releases $\ce{H+}$ ions the acid will ultimately not exist. For e.g we take the acid $\ce{H2SO4}$. If we add water then it becomes $$\ce{H2SO4 + H2O -> H+ + SO4^{-2} + H2O}$$ So the bond between hydrogen and sulphate will be broken therefore the acid will not exist, but we see that diluted acids are possible. Why?
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3 Answers
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Your doubts are legitimates, but there are some aspects that you should take in account:
1-Not all acid are fully dissociated
Not all acids fully dissociate, so if you take acetic acid you have in fact an equilibrium with some acetic acid molecules not dissociated. So your question holds only for strong acid like sulfuric acid you mentioned.
2-You are using pseudo-Arrhenius definition, why don't you use Lewis acid definition?
If you think the acid as a 'substance that that releases $H^{+}$' this is still an acid even if it dissociate, and even here you should notice that acidity is linked with $H^{+}$. However if you want to dig deeper there are many definitions of acid if you use Lewis acid theory and so you think the acid as a specie that accepts electrons you can easily see that in fact that the acidity is linked mainly with $H^{+}$!
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$\begingroup$ $BH_3$ will accept a pair of electrons, so it is a Lewis Acid. $\endgroup$– LDC3Commented Jul 6, 2014 at 12:46
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$\begingroup$ @LDC3 Hi! what's the point? I never say that it isn't, I've said that the acidity in that case is linked with the H+ ion $\endgroup$– G MCommented Jul 6, 2014 at 15:48
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$\begingroup$ Your answer seems to indicate that $H^+$ is the "only" acid. Maybe you should omit the word "only"? $\endgroup$– LDC3Commented Jul 6, 2014 at 15:55
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$\begingroup$ @LDC3 ah I see, thank you for the suggestion! i really appreciate it! $\endgroup$– G MCommented Jul 6, 2014 at 16:38
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As a user mentioned, not all acids dissociate that way. Sometimes, there is also the production of Hydronium ions. Refer : http://chemed.chem.purdue.edu/genchem/topicreview/bp/ch17/water.php
$$\ce{2 H2O~(l) <=> H3+O~(aq) + {}^{-}OH~(aq)}$$
The hydronium ions react with the sulphate radical, forming an acid like entity. Hence, the acidity is not lost.
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1$\begingroup$ Well, this answer is technically inaccurate, but it's not delete-worthy. The author did state their opinion; and in this case, the downvotes should indicate its quality. $\endgroup$– M.A.R.Commented Jul 27, 2015 at 17:31
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Yes, exactly; only ions can't not exist. Water molecule has dipole nature. When acid is mixed with water, then because of ion-dipole interaction which is stronger than dipole -dipole interaction b/w water molecules and ion-ion interaction b/w acid molecules, opposite ends of water dipoles surround the ions of acid ( means the dipole getting delta + charge will attract negative ion of acid and vica versa). So, now ions get hydrated as process of hydration takes place. They are still free entities, but surrounded by water dipoles. So, the solution of acid and water exists.
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$\begingroup$ Yes, haven't you studied that?? See, as hydrogen and oxygen both have different electro-negativities( oxygen's is higher ) so oxygen pull the shared pair of electron towards itself. Because of this pull, oxygen gets a slight negative charge (called delta - charge) and hydrogen gets delta positive. This group of charges is called dipole. Because of the positive charge attained by oxygen it surrounds the positive end of acid ( as it is very small charge delta - charge so it can't attract the positive end like that in ionic compounds.) $\endgroup$ Commented Jul 4, 2014 at 14:21