Is it permissible for a pilgrim to offer an expiation that would suffice as compensation for any errors that he may commit, knowingly or unknowingly, during the period of ihram (ritual consecration)? And if this is permissible, then what should be the value of such an expiation? Should he make a certain intention for it? And should he make this intention along with the intention of Hajj, or when should he make it?

All perfect praise be to Allaah, the Lord of the worlds. I testify that there is none worthy of worship except Allaah and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.

If one who is performing Hajj or ‘Umrah does not commit any of the things that were forbidden in connection to them and necessitate the slaughtering of an animal, and if he does not fail to perform an obligatory act while he is not performing Qarin or Tamattu‘ Hajj, then he is not required to slaughter a sacrifice. Rather, he is only recommended to slaughter a sacrifice in Mecca. It is stated in Al-Muhaththab on the Shaafi‘i Fiqh:

It is recommended for a person who comes to Mecca for Hajj or ‘Umrah to slaughter an animal and distribute it, given that the Prophet, sallallaahu ‘alayhi wa sallam, was reported to have slaughtered one hundred camels. It is recommended that the animal that he slaughters should be fat and good.

Such a recommended sacrifice is not sufficient as compensation for such errors committed by a pilgrim of Hajj or ‘Umrah that necessitate the slaughtering of a sacrificial animal. A well-known rule among the scholars says that a supererogatory act cannot suffice in place of an obligatory one. In Anwar Al-Burooq Fi Anwa‘ Al-Furooq, Al-Qarafi said:

The basic rule is that a supererogatory act cannot suffice in place of an obligatory one. For example, if a person was to perform one thousand supererogatory Rak‘ahs (unit of prayer), these would not suffice in place of the Fajr prayer, and if he was to give one thousand dinars in charity, this would not suffice in place of one dinar that is due as Zakah, and so on.

If a pilgrim of the Hajj or ‘Umrah commits nothing that necessitates the slaughtering of a sacrificial animal, then nothing is due upon him for, in principle, a person is free from liability.  

Allaah Knows best.