Question: Our elder son was born two years ago, in a Caesarian birth. We have just had a second son, through a regular birth; thus, he is the "peter rehem" (the first child who opens the womb). Are we obligated to perform the mitzvah of "pidyon ha-ben" for our second son?

Answer: The mitzvah of pidyon ha-ben (redemption of the firstborn son) is dependent on two factors:
a) The obligation applies to the "peter rehem" (the first to open the womb) - in this case, the second son.
b) The obligation applies to the eldest son - but only on condition that he is the peter rehem. If he does not have this status, there is no mitzvah to perform a pidyon ha-ben.

The special status of the eldest son applies only to the eldest child, and the pidyon (redemption) ceremony is performed only if he is also the peter rehem.In other words, a pidyon ha-ben requires both the chronological status of being the 
(father's) eldest son and also the biological status of being the one whose birth "opened" the mother's womb. Therefore, in this case, there is no mitzvah of pidyon ha-ben., since the second son 
(who is the peter rehem) is not the firstborn. (See Massekhet Bekhorot 47b, and Shulhan Arukh Yoreh De'ah 24).

The firstborn status is also related to the laws of inheritance. According to the Torah, the eldest son receives a double portion of the inheritance. Why is this so? The eldest child is, in some sense, the "guinea pig" for the parents learning parenting 
skills as they go along. At the same time, he bears a greater measure of responsibility than his siblings for the family's welfare. Prior to the sin of the golden calf, it was the eldest son of the family who was responsible for religious ceremony and ritual on 
behalf of the family. There was no designated tribe or even family of kohanim (priests); rather, the firstborn of every family performed religious service. (According to certain midrashim, this is indeed the preferred situation, and this reality will return at the time of our final redemption.)

Both the added responsibility and the spiritual role of the firstborn created a situation in which he would receive a double portion of the inheritance.

Today the firstborn enjoys no such special status. In our times we are unfortunately witness to much conflict and feuding within families as a result of unequal distribution of inheritance. We therefore advise every parent to leave a will in which the entire 
inheritance is to be divided equally among all the children - sons and daughters - and to formulate this as a gift that becomes valid an hour before the time of the parent's death.

This suggestion is based upon a responsum by the Hatam Sofer, and is highly recommended for preventing conflict after 120 years.