He uttered the word of divorce (talaaq) whilst explaining the rulings on divorce and its wording to his wife
Question

                The other day me & my wife were having this topic on Talaq and i told her that if one says 3 times talaq verbally it is counted as divorce and during the conversation i said talaq talaq talaq 3 times verbally.
Now i am worried about this thing does this count as valid or null.There was no such intention of divorce or like that.
Praise be to Allah.
    Firstly: 

    If you were speaking by way of explanation and giving 
    examples, and you had no intention of divorce, then no divorce has occurred, 
    because the Prophet (blessings and peace of Allah be upon him) said: “Deeds 
    are but by intentions and each man will have but that which he intended.” 
    Narrated by al-Bukhaari (1) and Muslim (1907) from ‘Umar ibn al-Khattaab 
    (may Allah be pleased with him). 

    Hence the wife of a teacher or faqeeh who says, when 
    explaining and discussing issues of divorce, “My wife is divorced”, is not 
    actually divorced. The same applies in the case of one who utters the word 
    of divorce without meaning to (a slip of the tongue). 

    Zakariya al-Ansaari (may Allah have mercy on him) said: The 
    third condition (of divorce being valid) is the intention of divorce. So it 
    is stipulated that he should intend to utter the words and intend the 
    meaning of the words, both together, so as to break the bond of marriage… 
    Because what matters is intention to say the word and intention of the 
    meaning thereof, both together. The reason why there is a second condition 
    for divorce to take place, namely intending to divorce one’s wife, is so as 
    to exclude other scenarios such as when narrating that someone else divorced 
    his wife, or when a faqeeh is explaining how divorce takes place, or calling 
    by name a woman who is called Taaliq (which means divorced). 

    End quote from Asna’l-Mataalib, 3/280 

    What is meant by calling by name a woman who is called Taaliq 
    is saying, Yaa Taaliq (O Taaliq) 

    In Sharh Manhaj at-Tullaab ma‘a Futoohaat al-Wahhaab 
    (4/336) it says: 

    The condition is that he should intend divorce and intend to 
    utter the word talaaq for what it means, in the sense that he intended to 
    use the word for that purpose. For example, divorce does not take place on 
    the part of one who asks some people for something but they do not give it 
    to him, so he says: “I divorce you all,” and his wife happens to be among 
    them but he did not realise that. Nor does divorce take place on the part of 
    one who is telling how someone else divorced his wife, such as if he says 
    “So and so said, ‘My wife is divorced.’” End quote. 

    And Allah knows best.