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All mechanisms of the addition of a halogen acid to ethylene (ethene) I can find involves a primary carbocation as the intermediate ion.

However, primary carbocations are generally unstable and unlikely to form. This can indeed explain why the first step is the rate-determining step, but does primary carbocations really form in the process? Is there no other plausible explanations?

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    $\begingroup$ What conditions do you consider? For example, bubbling ethene through a polar solvent containing HBr, or a gas phase reaction between HBr and ethene? If you have HBr in a polar solvent, you get H+ that could start the reaction with ethene; however, if you have HBr in the gas phase, you don't get any H+ ions. $\endgroup$ – Loong Jan 4 '17 at 14:35
  • $\begingroup$ You can always consider the cation to be a bridged hydro-ene ion. $\endgroup$ – Jan Jan 4 '17 at 23:27
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    $\begingroup$ The ethyl carbocation is a non-classical carbocation. See this earlier answer for a description of the ethyl carbocation. $\endgroup$ – ron Jan 11 '17 at 15:29
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There is quite an evidence that carbocations are involved in this process, and that no concerted pathways exist for this transformation.

While the case of ethyne may be difficult to analyse, lets consider 3-methylbut-1-ene:

enter image description here

If you consider the regular Markovnikov's rule to predict the product, you would probably get this:

enter image description here

While in actuality, the major product is actually this:

enter image description here

You can't really explain why that happens without accepting the existence of carbocations and the following mechanism:

enter image description here

This shows that carbocations are involved in the addition of $\ce{HBr}$ to an alkene.

Note: Since this question is about carbocations, I'd like to mention George A. Olah, a reputed chemist who studied carbocations by preparing them in superacid environments, where they were stabilized and studied using spectroscopid techniques. It was his research that led to the conclusion that carbocations have a planar structure. Have a look at his wikipedia page for more information.

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