Maseches Terumos, chapter 5, mishnah 1. In this mishnah we will finally learn explicitly what the law is when Terumah falls into chullin and the chullin does not contain a hundred times its amount to nullify it completely. But the mishnah weighs an additional complicating factor as well: what is the law when the Terumah that fell was tamei, or when the chullin it fell into was tamei?
Let us begin with the basic rule: tamei Terumah may not be eaten by a kohen, but it may be burned and used as a source of fuel. So, for example, oil received as tamei Terumah may be burned by the kohen and used for light. That is the law under ordinary circumstances.
"Se'ah terumah teme'ah shenaflah lefachos mimei'ah chullin" - a se'ah of tamei Terumah that fell into less than a hundred of chullin:
One se'ah of tamei Terumah falls into a large vessel containing fewer than a hundred units of chullin. Here we have a classic medumah mixture: the Terumah is not nullified, at least not on the rabbinic level, and therefore the entire mixture is forbidden to a non-kohen. Normally the solution is that the non-kohen sells the whole mixture to a kohen, who eats it on account of the Terumah mixed into it. Here, however, the kohen cannot eat it, since the Terumah that fell is tamei and not tahor, and at most he could burn it.
But the Sages were stricter with a medumah mixture than with ordinary tamei Terumah. Even though tamei Terumah on its own may be burned, they did not permit a kohen to keep this large mixture of tamei Terumah and chullin together, lest he leave it sitting in his kitchen for a long time as a source of fuel and come to eat some of it - a serious prohibition. For this reason they were stringent and ruled that even a Yisrael may not be permitted to give the whole mixture to a kohen; rather, it is left until it rots.
And it makes no difference what the substance was that it fell into, nor whether that substance was tamei or tahor. In every case the halachah is that the mixture is left to rot, for otherwise the kohen might keep it in his kitchen for a long time as a source of fuel and come to eat it by mistake; and because of the concern that people would be lax about this, the Sages said: leave it be, and let it rot.
The mishnah lists several alternatives to ordinary chullin:
Chullin: food from which all the tithes have been properly separated.
Maaser rishon: the portion given to the Levi, from which terumas maaser still must be separated.
Maaser sheni: which is taken up to Jerusalem and eaten there.
Hekdesh: food consecrated to the Beis HaMikdash as bedek habayis, as a monetary gift; the Beis HaMikdash would convert it into money by selling it to someone else and use the money for the upkeep of the Mikdash.
In all of these cases it makes no difference whether they were tamei or tahor: since tamei Terumah fell into them, the entire mixture is left to rot - provided that there are fewer than a hundred units of the non-Terumah substance mixing with the Terumah.
"Ve'im terumah - hayah chayav leshalem dameihen" - and if it was Terumah, he was obligated to pay their value:
If that se'ah which fell was tahor Terumah, we have the classic case, and its law is: "yimacheru lakohanim bidmei terumah" - they are sold to kohanim at the price of Terumah. The entire mixture is now forbidden to a non-kohen, since it does not contain a hundred times its amount of chullin, and therefore the owner of the mixture may sell all of it to a kohen. The kohen eats it, and the seller collects the going price of Terumah.
In practice, the going price of Terumah is generally lower than the price of a non-Terumah product. If a regular bin of grain costs, for the sake of discussion, ten dollars, then Terumah grain traded among kohanim will sell for less than that, say nine dollars a bin. The reason is not only the different supply and demand curves among kohanim, since many kohanim receive Terumah; even if they were equal, a kohen would ordinarily prefer to buy chullin over Terumah. Why? Because chullin is not exposed to becoming tamei and thereby disqualified from being eaten, whereas Terumah is always at risk of becoming tamei inadvertently and never being eaten at all. Because of this drawback, no kohen in his right mind would pay the price of chullin for Terumah, and therefore the going price of Terumah products is lower than that of comparable products.
Whatever the going rate may be, he is entitled to collect that full price from the kohen, "chutz mi'demei osah se'ah" - the owner of the mixture may not charge the kohen for the Terumah component that fell in, since that Terumah is the property of the tribe and belongs to the kohanim. He was obligated to give it to them, and he does not collect from them for what is rightfully theirs.
For example: one basket of Terumah fell into ten baskets of chullin, and everything is tahor. Now he must sell the kohen all eleven units, but charge for only ten. If a basket of ordinary grain sells for ten dollars, and Terumah grain for nine, he cannot collect ninety-nine dollars, because one out of the eleven rightfully belongs to the family of kohanim as Terumah. So he collects only ninety dollars from the kohen for eleven units of the medumah mixture, and the kohen eats all of it in taharah.
"Im le'maaser rishon naflah - yikra shem li'terumas maaser":
Maaser rishon is the gift given to the Levi, and the obligation to separate terumas maaser from it - one tenth - still rests upon it. Suppose the Levi has a vessel containing ten units of maaser rishon wheat, and a unit of Terumah fell in. He now has eleven units of grain, and he cannot give them to the kohen as they are, since there is still a separate mitzvah to tithe the maaser rishon.
First approach: The Levi designates and declares: "One of the ten units of maaser in this mixture shall be terumas maaser for the mixture." Now he has eleven units before him: one Terumah gedolah, one terumas maaser, and nine maaser rishon. He will sell them all to the kohen, but charge for only nine, since the other two units belong to the kohen in any case.
Second approach (which does not disagree, but is simply another way to do it): The Levi may prefer not to sell the mixture to the kohen at the discounted price of Terumah. For on the nine units of maaser rishon he will collect only nine dollars per unit - eighty-one dollars, instead of the ninety dollars he would have received had they been sold as ordinary grain. He will therefore bring another ninety units of maaser rishon that he has from other sources, set them alongside the vessel containing the mixture, and say: "One of the ten units of maaser rishon in the mixture shall be terumas maaser for the remaining nine, and the other nine shall be terumas maaser for the ninety units I have brought." In this way he places his entire terumas maaser obligation inside the mixture alone. Now all eleven units are either Terumah gedolah or terumas maaser, and he gives them to the kohen for free and the kohen eats them as they are; while the Levi does not need to sell anything at a discount, and keeps all ninety se'ah for himself - losing nothing financially.
Maaser sheni and hekdesh - "harei elu yipadu":
If the Terumah fell into a container of maaser sheni, there is no possibility of giving it to the kohen, since maaser sheni too would have to be eaten in Jerusalem and in taharah, and all its various restrictions rest upon it. However, there is an option to redeem the sanctity of the maaser sheni onto a coin or coins, take them up to Jerusalem, and buy fresh food items there with them. In this way the sanctity is transferred from the maaser sheni to the coins and the maaser is deconsecrated - that is redemption. Therefore, before selling the mixture to the kohen at the price of the chullin component, he must first transfer that maaser sheni onto a coin.
The same law applies when the Terumah fell into hekdesh. Hekdesh means that a person consecrated his property to become the property of the Beis HaMikdash, and we are speaking here of bedek habayis, that is, a monetary gift. This is an external sanctity: the grain given to the Beis HaMikdash is not holy in and of itself, and the sanctity is not part of the essence of the substance, but rather it is imbued with sanctity because it is the gift and property of the Beis HaMikdash. For this reason there is the option of transferring the sanctity from the hekdesh onto something else, such as money. (Had it been intrinsically holy, like something consecrated to be offered as a korban, it could not be redeemed.)
In practice: he had ten units of flour and he said, "This flour shall be a gift to the Beis HaMikdash," and before he gave it, a unit of Terumah fell into it. Now he has eleven units before him - ten of hekdesh and one of Terumah - and he cannot give them to the kohen, since a kohen does not eat hekdesh. First he redeems it, saying: "Wherever the ten units of hekdesh are located in this mixture, their sanctity shall be redeemed and transferred onto a coin of equal value." Then he sells all eleven units to the kohen at the price of ten units of Terumah, and the money onto which he redeemed the hekdesh he uses to give to the Beis HaMikdash.
"V'im temei'im hayu" - when the chullin are tamei and the Terumah is tahor:
The final case: the unit of Terumah that fell into fewer than a hundred units of chullin and created the medumah mixture was tahor, while the chullin it fell into were tamei. Here the mixture can and must be given to the kohen, and it may be sold to him at the price of the non-Terumah component. But there is a separate issue here: the kohen may not render the Terumah tamei and cannot allow it to become tamei.
The tamei chullin do not render the Terumah tamei on their own. Even through direct contact - for foods, including Terumah, to become tamei, they first require hechsher, that is, preparation to receive tumah. This is done by wetting the food with one of the seven liquids that enable this, provided the wetting is not against his will (the requirement of 'nicha lei'). As long as the Terumah has not been wetted, it is immune from becoming tamei. The pitfall arises in preparing bread: the kohen grinds the Terumah together with the chullin and adds water to knead the dough, and at that moment, once it has been wetted, the Terumah becomes capable of receiving tumah, and through its contact with the tamei chullin it becomes tamei - and that is not good.
The mnemonic for the seven liquids is: "yad shachat dam" (read as "a hand slaughters blood"). It has no meaning beyond serving as a mnemonic:
Yud - yayin, wine.
Dalet - devash, honey (bee honey).
Shin - shemen, oil (olive oil).
Ches - chalav, milk.
Tes - tal, dew.
Dalet - dam, blood.
Mem - mayim, water.
Only these seven liquids make food susceptible to tumah. Ordinary fruit juices, such as apple juice, do not: grain that became wet with apple juice has not been rendered susceptible and is not ready to receive tumah.
There is another law one needs to know regarding the transfer of tumah: for food to transfer tumah, it must be of the required measure, which is the volume of an egg. Less than an egg's volume of food, even if it is tamei and comes into direct contact with other food, does not transfer its tumah. This is a separate law in its own right.
Therefore the Mishnah says that when the chullin were tamei - and the same law applies to first tithe, second tithe and hekdesh, in which one must follow everything stated above - the kohen must do what is necessary so that his Terumah will not become tamei when he eats the mixture. And how does he do this?
"nekudim" - according to the Bartenura, nekudim means dry: since it never became wet, there is no possibility of transferring tumah. Others say that nekudim means very small portions of dough, whose size is limited so that the dough will not contain an egg's volume of tamei chullin.
"kelayos" - roasted and dry, like puffed wheat (known in Israel as "shalva"). Through roasting, the wheat becomes edible and tasty, but it is completely dry, and for that reason there is no possibility that it will become tamei and transfer the tumah of the chullin to the pure Terumah.
"o yaloshu b'mei feiros" - when the kohen prepares dough composed of the tamei chullin flour and the pure Terumah flour, he should not add ordinary water, which makes food susceptible to tumah, but should knead it with fruit juice: apple juice, berry juice or pomegranate juice. Bread made from such a mixture does not receive tumah, and there is no transfer of tumah in it.
"o yechalek es ha'isos ad shelo yehei b'makom echad k'beitzah" - he should distribute the mixed flour, which contains pure Terumah and tamei chullin, among other containers of flour, so that no single portion contains an egg's volume of tamei flour. Since no one place holds the measure of an egg, there is no source of tumah that can transfer tumah to the Terumah.
In summary: tamei Terumah that fell into less than one hundred parts of chullin - the mixture is left until it rots, a decree lest the kohen keep it as a source of fuel and come to eat it, and there is no difference whether it fell into chullin, into first tithe, into second tithe or into hekdesh. If the Terumah was pure - the mixture is sold to kohanim at the price of Terumah, except for the value of that one se'ah, which is the property of the tribe; and if it fell into first tithe, he designates it as terumas maaser, and if into second tithe or hekdesh, he must first redeem them. And if the chullin were tamei, the kohen takes one of four approaches: nekudim, kelayos, kneading with fruit juice, or dividing the doughs so that no one place contains an egg's volume. In this way the Terumah remains in its purity, and this is the end of the matter.