[nelson13]

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[susan53]

Your argument is logical. But "the" reflects the fact that the speaker is referring to a specific word and not any of the myriad possibilities.

For example :

A : Those slices of bread are very fat.
B : You've used the wrong word. Thick, not fat

In other words : The word which you've used to describe the size is wrong.

If you look at this last sentence, you can see that "a" would not be possible. In saying "You've used the wrong word", the same meaning is being conveyed - that a specific word in the sentence was wrong, The alternative would be :

A : Those slices of bread are very fat.
B : You've used a wrong word. Can you identify which one it is?

ie : One of the seven words is wrong, but I'm not telling you which one.

[nelson13]

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[susan53]

Remember that "the" indicates shared knowledge - ie something known to both the speaker/writer and listener /reader. Here, this is the first mention of "second time", so it is not yet "known" to the reader. Compare :

I got it wrong at first, so I did it a second time and the second time I got it right.

"I did it a second time" introduces the idea - at this point it's new to the reader. But after that, the concept is "shared" and therefore "the" is used.

[nelson13]

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