Praise be to Allah.
If your wife was not able to fast because of sickness from which there is the hope that she will recover and be able to make up for fasts in the future, she does not have to give fidyah, and feeding others is not valid in her case; rather she must make up the fasts.
If someone is unable to fast because of old age, or because of a sickness from which there is no hope of recovery, this is the one who must feed one poor person for every day, because Allah, may He be exalted, says (interpretation of the meaning):
“And upon those who are able [to fast, but with hardship] - a ransom [as substitute] of feeding a poor person [each day]”
Al-Bukhaari (4505) narrated that Ibn ‘Abbaas said: It has not been abrogated; it refers to an old man and an old woman who are not able to fast; they may feed one poor person for each day.
Al-Bukhaari (may Allah have mercy on him) said in his Saheeh: Chapter on the verse “[Fasting for] a limited number of days. So whoever among you is ill or on a journey [during them] - then an equal number of days [are to be made up]. And upon those who are able [to fast, but with hardship] - a ransom [as substitute] of feeding a poor person [each day]….” [al-Baqarah 2:184]. As for an old man, if he is not able to fast, we may note that after Anas grew old, he gave food for one year or two years, feeding one poor person for each day, giving him bread and meat, and he did not fast.
In Fataawa al-Lajnah ad-Daa’imah (10/198) it says: If the doctors determine that there is no hope of recovery from this sickness from which you are suffering, and because of which you are not able to fast, then you must feed one poor person for each day, giving half a saa‘ of the local staple food, such as dates and the like, for past and future months. If you give dinner or lunch to a poor person for the number of days that you owe, that will suffice. As for giving cash, it is not valid to give cash instead. End quote.
The amount that must be given when feeding the poor is a matter concerning which there is a difference of scholarly opinion. The majority are of the view that it is a mudd of foodstuff, i.e., one quarter of a saa‘.
The Hanbalis are of the view that it is a mudd of wheat or half a saa‘ of other types of foodstuff. Half a saa‘ is equivalent to approximately one and a half kilograms.
In al-Mawsoo‘ah al-Fiqhiyyah (32/67) it says: The Maalikis and Shaafa‘is are of the view that the amount of the fidyah is one mudd for each day. This is also the view of Taawoos, Sa‘eed ibn Jubayr, ath-Thawri and al-Awzaa‘i.
The Hanafis are of the view that the amount that must be given for this fidyah is a saa‘ of dates, or a saa‘ of barley, or half a saa‘ of wheat. That must be given for each day that the person does not fast; this food must be given to a poor person.
According to the Hanbalis, what must be given is a mudd of wheat, or half a saa‘ of dates or barley. End quote.
If you give dinner or lunch to the poor, that is sufficient, as mentioned above from Anas.
Based on that, if this soup was not sufficient to be regarded as lunch or dinner; rather it was something additional to the main food, or an appetizer, what you gave was not valid and you must give the fidyah again.
It is sufficient for you to follow the view of the majority, so you may give each poor person 750 grams of rice. It is permissible for this fidyah to be given to one poor person or to a number of poor people.
It should be noted that giving food to people in i‘tikaaf or giving iftar to one who is fasting is not acceptable as fidyah unless the people in i‘tikaaf or the people who are fasting, who will eat this food, are poor.
But if they have sufficient food of their own, then it is not acceptable to give the fidyah to them, because Allah, may He be exalted, says in the verse quoted above: “- a ransom [as substitute] of feeding a poor person [each day]”
What must be done is to give the fidyah specifically to the poor, and no one else.
And Allah knows best.