what is the Q of a rxn?

For slightly soluble materials (Ksp)we call it Qsp and it is the ion product of the ions.In fact, in my school days we called it ion-product and I still consider that a better name. Then we compare Qsp with Ksp to know if there is a ppt or not.

For equilibrium constants it is usually called Qrxn (reaction quotient which I consider a misnomer) and it is the same form as Keq BUT you use the concentrations in the problem and not those at equilibrium. Again, one compares Qrxn with Keq to determine which way the reaction will go to reach equilibrium. I can elaborate on these if necessary.

so it is during the reaction process

Not necessarily.

Suppose we have a ppt, AgCl, which has a value of Ksp = 1 x 10^-10 (that's a cloe number but I don't know the exact value).
Now we have a solution The is 0.1M in NaCl and we dump in AgNO3 that is 0.001M. Will a ppt form?
Qsp = (Ag^+)(Cl^-) = (0.001)(0.1) = 1E-4. This is larger than Ksp = 1E-10; therefore, a ppt of AgCl will occur.
On the other hand if NaCl = 1E-6M and AgNO3 = 1E-6M, then Qsp = (Ag^+)(Cl^-)= (1E-6)(1E-6) = 1E-12. That is smaller than Ksp = 1E-10 so no ppt of AgCl will form.
For a reaction of
2N2O5 ==> 2N2 + 5O2. I;ll make up a number for Keq of 1E-20 (a very small number).
Keq = (N2)^2(O2)^5/((N2O5)^2
N2O5 = 1M, N2 = 2M and O2 = 1M. Which way is equilibrium; i.e., will the reaction move to the left or to the right?
Qrxn = (N2)^2(O2)^5/(N2O5)^2
Qrxn = (2)^2((1)^5/(1)^2 = 4. That is larger than Keq = 1E-20 (by a bunch) so it will move to the left to reach equilibrium.

The "Q" of a reaction refers to the reaction quotient, which is a way to determine the relative concentrations of products and reactants in a chemical reaction at a given point in time. It is similar to the equilibrium constant (K), but it is calculated using the concentrations of reactants and products at any point in the reaction, rather than at equilibrium.

To calculate the reaction quotient (Q), you need to determine the concentrations (or partial pressures) of the reactants and products in the reaction. The Q is then determined by writing the expression for the chemical reaction and plugging in the concentrations of the species involved.

The general form of the Q expression for a reaction is:

Q = [C]^c [D]^d / [A]^a [B]^b

Where [A], [B], [C], and [D] represent the concentrations of the reactants and products, and the letters a, b, c, and d represent the stoichiometric coefficients in the balanced chemical equation.

By comparing the Q value to the equilibrium constant (K), you can determine whether the reaction is at equilibrium (Q = K) or is in a state of disequilibrium (Q ≠ K).