In order to completely remove chametz from one's property and not to violate the prohibition of owning chametz on Pesach, there is a procedure in which one nullifies one's chametz, called Bitul Chametz. This text is said twice; once after the bedikat chametz at night, and again in the morning of Erev Pesach before the sixth hour of the day. 
Procedure of Bitul Chametz
- Everyone in the family should say the text of Bitul Chametz.
- Even if somebody appointed an agent to search for chametz for him, the owner should do the bitul for himself. But after the fact, if the agent did the bitul for him, and said "all the chametz in the possession of so-and-so should be nullified," this works as well. 
- If one recites the bitul, but doesn't understand what he is saying, that chametz has not been nullified. Rather, he should say it in a language that he understands. 
- One should speak out the bitul and not just think it. 
- A good custom is to say the Bitul Chametz three times to strengthen the point.
- If somebody is not home, he should do the bitul from wherever he is.  If the husband is not home and they don't know if he did the bitul, his wife should do it, and say all the chametz that is in my husband's possession, even if he didn't tell her to do this. 
- No bracha is made upon the bitul chametz.
Bitul at Night
- After one does Bedikat Chametz and again after burning one’s Chametz in the morning, one should do Bitul including the text of LiBateil VeLehavei Hefker. 
- If one is selling his Chametz via his local rabbi, it is preferable to burn his remaining Chametz after the sale takes effect. 
- The bitul at night should be done immediately following the Bedika.  One should not talk about things other than the bedika from when he says the beracha until after the bitul, but if he did he need not repeat the beracha. 
- If someone scattered the ten pieces for the bedika in accordance with the custom  and really cannot find one of the pieces, he doesn't need to go crazy and he can just rely on the bitul that he does after the bedika. 
- According to Ashkenazim, the text of the bitul which is said after the Bedika is: "כל חמירא וחמיעא דאיכא ברשותי, דלא חזיתיה ודלא בערתיה, לבטיל ולהוי הפקר כעפרא דארעא" meaning, "All chametz or leaven in my possession that I have not seen, and have not destroyed, shall be nullified and become ownerless, like the dust of the earth." 
- The Sephardic text is: "כל חמירא דאיכא ברשותי, דלא חזיתיה ודלא בערתיה, לבטיל ולהוי כעפרא דארעא" meaning, "All Chametz in my possession that I have not seen, and have not destroyed, shall be nullified like the dust of the earth."  However, it is preferable to insert הפקר meaning "become ownerless" as in the Ashkenazic text above, for at least one of three times one says the Bitul.
Bitul During the Day
- In addition to the bitul at night, one should be recited during the day. 
- The nullification done after the burning in the morning includes all remaining chametz. Therefore, the text is: "כל חמירא וחמיעא דאיכא ברשותי, דחזיתיה ודלא חזיתיה, דבערתיה ודלא בערתיה, לבטיל ולהוי הפקר כעפרא דארעא" meaning, "All chametz or leaven in my possession that I have seen and that I have not seen, that I have destroyed and that I have not destroyed, shall be nullified and become ownerless, like the dust of the earth". 
- The Sephardic text is: "כל חמירא דאיכא ברשותי, דחזיתיה ודלא חזיתיה, דבערתיה ודלא בערתיה, לבטיל ולהוי כעפרא דארעא" meaning, "All chametz in my possession that I have seen and that I have not seen, that I have destroyed and that I have not destroyed, shall be nullified like the dust of the earth". 
- The nullification during the day should be done before the sixth hour, so that the chametz that you nullify is still yours when you nullify it because otherwise the bitul doesn't work.  but after the burning. 
- Shulchan Aruch 434:2. Rashi Pesachim 4a "bi'bitul bi'alma", the Ritva Pesachim 4a, Ran Pesachim 4a and Rambam chametz u'matza 2:2 say that this declaration is a mental destrcution and fulfills the requirement of tashbitu recorded in Shemot 12:15. Tosafot Pesachim 4b "midiorayta" says the bitul makes the chametz hefker, or ownerless. The gemara in Pesachim 6b writes that really physical destruction is enough to fulfill the torah obligation to destroy chametz but we are concerned that somebody may find chametz during pesach so the rabbis established bitul. The gemara also says that from the torah bitul alone would be enough, but Tosafot 2a writes that we are worried if somebody has chametz in his house, even though it is not really his, he may come to eat it. The Ran there explains that we fear that the person will on do the bitul half-heartedly and that would not be enough.
- * Rabbi Hershel Schachter (OU Kosher Pre-Pesach Webcast 5770, min 4-5) said that since nowadays all members of the household have their own spending money and sometimes buy Chametz, it is proper that everyone do his own Bitul Chametz.
- The Ran (3b s.v. VeKatav) quotes the Baal HaItur, who says that one may appoint an agent to do Bitul Chametz according to the general principle of Shlucho Shel Adam K’moto (Kiddushin 42b). The Ran, however, quotes those who disagree because they understand Bitul to be based on Hefker, which cannot be done through an agent. The Beit Yosef 434:4 asserts that even if Bitul is based on Hefker, in reality it is more lenient than Hefker, because when the Chametz becomes forbidden one will not really own the Chametz. Thus, by declaring that one isn’t interested in the Chametz, one doesn’t violate owning Chametz on pesach (see Mekor Chaim 431 s.v. Lechen).
- The Tur and S”A 434:6 rule that one may appoint an agent to do Bitul. Mishna Brurah 434:15 writes that in extenuating circumstances, one may rely on S”A.
- Chazon Ovadia Pesach 5763 part 1 page 56. Tur 434 and Shulchan Aruch and Rama 434:4, Orchot Chaim Chametz U'Matza 22, Maharam Chalava Pesachim 6b. The Nimukei Yosef Pesachim 6b quotes the Ritva that even though bedika can be done through an agent, bitul can not. He also quotes the Baal Ha'Ittur 120b that an agent can do the bitul as well. The Tur 434 also say it is permissible. The Beit Yosef there defends this by saying that even though according to some bitul is hefker and you cannot make somebody else's things hefker, chametz is different because it's not really his anyway because it is forbidden to him, and this is brought down in the Mishna Brurah 434:15. The Bach (434) offers another reason why one would not be able to appoint an agent to do Bitul; he explains that bitul is a mental decision which does not need to be expressed verbally, according to many opinions. Accordingly, one can not appoint an agent to fulfill a mental obligation.
- Rama 434:2, Mishna Brurah 434:9, Chazon Ovadia 5763 part 1 page 54. Rama in Darchei Moshe 434:2 explains that this is why the kol chamira was written in aramaic and not hebrew, because aramaic was the spoken language of that time. Chazon Ovadyah (vol 1, pg 54) agrees. Magen Avraham 434:5, Baer Heitev 434:5, Kaf Hachayim 434:19 all write that preferably one should use use Aramaic so that other people and angels will not understand, because the bitul involves somewhat of degradation towards the bread.
- Shulchan aruch 434:2. The tur 436 says that thinking is enough but the beit Yosef 431 quotes the ran that it is not enough.
- Chazon Ovadyah (vol 1, pg 54), Nitei Gavriel (vol 1, 34:8), Chida in Moreh Bi'etzba 203
- Tur and Shulchan Aruch 434:4, Orchot Chaim Chametz U'Matza 22, Chazon Ovadia Pesach 5763 Part 1 page 56-57. Mishna Brurah 434:17 adds that this is true even if he appointed an agent to do the bitul for him
- Shulchan Aruch 434:4, Mishna Brurah 434:19, Chazon Ovadia Pesach 5763 Page 57, Kaf Hachayim 434:60
- Bet Yosef 432:1 explains that there's no bracha for bitul chametz since according to many opinions it is a mental obligation and can be fulfilled without any verbal declaration. Hagadat Ohalei Shem p. 45 asks that according to the Gra, there is a bracha for Talmud Torah even if it is fulfilled mentally without any verbal expression (see Siman 47). He answers that bitul chametz can be fulfilled instantaneously in one's mind, however, thinking torah is a lengthy process and can endure for a long period of time. Additionally, he answers that primarily the bracha for torah is made for verbally learning torah, however, bitul is completely fulfilled in one's mind.
- * The Gemara (Pesachim 4b) establishes that if one does Bitul Chametz, he need not physically get rid of the Chametz on a d’oriata level. D’rabanan, though, one still must do Bedikat Chametz. Rashi (s.v. BeBitul) explains that Bitul satisfies the Torah’s command of Tashbitu, the positive Mitzvah to remove one’s Chametz from his ownership. Tosfot (s.v. MiD’oraita), however, argue that Bitul does not fulfill the Mitzvah of Tashbitu but simply makes one’s Chametz ownerless (Hefker) and thereby avoids the prohibition of owning Chametz on Pesach. See Ran (Pesachim 1a) and Rambam (Chametz U’Matzah 2:2) for an elaboration of this dispute.
- The Hagahot Maimoniyot (Chametz U’Matzah 3:8) writes that based on the opinion of Tosfot, the text of the Kol Chamira should include “LiBateil VeLehavei Hefker.” Although the Beit Yosef 434:2 writes that the Minhag is to say Kol Chamira without any reference to Hefker, the Mishna Brurah 434:8, Kaf HaChaim 434:26-7, and Chazon Ovadia (p. 55) advise saying it.
- Rav Yehuda (Pesachim 6b) explains that after doing Bedikat Chametz, one must do Bitul. The Gemara explains that Chazal instituted it at this time because one already is involved in getting rid of his Chametz through Bedikat Chametz. If one would wait until daytime to do Bitul, he might forget to say it before the beginning of the sixth hour, at which point the Chametz becomes forbidden and Bitul thus becomes impossible. The Rosh 1:9 quotes Rashi, who writes that some have the Minhag to do Bitul at the end of the fifth hour when burning their Chametz. Based on the Rosh, S”A 434:2 writes that one should do Bitul at night and again during the day at the end of the fifth hour. The Rama adds that one should make sure that the Bitul of the daytime is done after one burns the Chametz so that he can fulfill the Mitzvah of Biur Chametz.
- * The Mishna (Pesachim 21a) records a dispute between Rabbi Yehuda, who holds that one must burn one’s Chametz in order to fulfill Biur Chametz, and Rabanan, who say that one can fulfill Biur Chametz even by throwing it to the wind or into the ocean. The Rosh (2:3) quotes a dispute amongst the Rishonim regarding which opinion is normative. While the S”A 445:1 rules like Rabanan, the Rama says the Minhag is to burn it.
- Rabbi Mordechai Willig (Am Mordechai Moadim p. 152-3) defends the Minhag of those who burn the Chametz in the morning before going to work even though it is before the Rabbi sells the rest of their Chametz. He explains that even though they aren’t burning their last K’zayit, nonetheless, they fulfill Tashbitu when the Rabbi sells the Chametz on their behalf. He bases this argument on the Tur 436, who according to the Pri Chadash 436:3, holds that selling one’s Chametz to a non-Jew is a fulfillment of Tashbitu. He adds that even though there is a Mitzvah to burn the Chametz, Rosh and Beit Yosef maintain that if one gets rid of his Chametz before the fifth hour, even Rabbi Yehuda agrees that one need not burn it.
- Rabbi Hershel Schachter (B’ikvei HaTzon B’ikvei HaTzon p. 76) argues that some Rishonim hold that one does not fulfill Tashbitu by selling one’s Chametz (see Tosfot Rabbenu Peretz Pesachim 28b). Accordingly, if one burns his Chametz in the morning before the Rabbi sells the rest of one’s Chametz, one might not fulfill Tashbitu. Furthermore, the Bracha one made before Bedikat Chametz may turn out to be a Bracha Levatala.
- Shulchan Aruch 434:2, Chazon Ovadia 5763 Part 1 page 52
- Chazon Ovadia 5763 Part 1 page 44
- Rama 432:2, Mishna Brurah 432:13
- Chazon Ovadia 5763 part 1 page 38
- http://ph.yhb.org.il/en/04-05-01/. The Bach (434 s.v. Katuv BeHagahot) concludes that since many hold that Bitul is based on Hefker, one should mention it in one’s Kol Chamira. Mishna Brurah 434:7 writes that this doesn't include chametz we know about because we still have chametz that we can eat the next morning and chametz that we find we burn. Shulchan Aruch 434:2 says this text without including the "vilihave hefker" but Mishna Brurah 434:8 based on the Bach says to add that in because of the opinion of Tosafot 4b. Nitei Gavriel (vol 1, 34:7) has a very similar text including the word Hefker. The Ravyah Pesachim 431 page 63 has the word hefker, and the peri chadash 434:2 doesn't.
- Chazon Ovadia Part 1 page 52.
- Chazon Ovadyah (vol 1, pg 54-55)
- Shulchan Aruch 434:2. The tur and beit yosef 434 explain that this is for the chametz acquired between the two bituls and the chametz left over to eat in the morning before the prohibited time, and this is the reason brought by Mishnah berura 434:11, shaar hatzfyun 434:20, and kaf hachayim 434:39.
- http://ph.yhb.org.il/en/04-05-01/. Shulchan Aruch 434:4
- Chazon Ovadyah (vol 1, pg 59)
- Pesachim 7a, Rambam Chametz U'Matza 3:7, Tur and Shulchan Aruch 434:2, Chazon Ovadia part 1 page 60-61
- Rama 434:2, Chazon Ovadia Pesach 5763 part 1 page 59. This is because according to tosafot pesachim 4b the bitul makes the chametz ownerless and then you wouldn't be burning your own chametz. Rav Yaakov Emden in Mor U-ketzia 434 says that one can say the bitul before burning the chametz even lechatchila.