For a certain reaction #2A + B rightleftharpoons C + 3D#, #K_(eq) = 4.2 xx 10^3#, which of the following is true?

The reaction lies to the right side because of the following:

The expression of the equilibrium constant #K# is:

#K=(["Products"])/(["Reactants"])#

Since #K>1# this means that the #["Products"]# is greater than the #["Reactants"]# and thus there is more products than reactants, and therefore, the equilibrium lies to the right.

Here is a video that I recently made about this topic:

Chemical Equilibrium | Reaction Quotient & Application of a Large K.

The equilibrium constant for this reaction is:

#"K"_(eq) = \frac(["products"])(["reactants"]) = \frac([C][D]^3)([A]^2[B]) = 4.2xx10^3#

#"K"_(eq) > 1#, thus #["products"] > ["reactants"]#, and the equilibrium lies to the "right" (a), or the "products" side.

(b) We cannot say what the rate of reaction is, because that's a kinetic description of a reaction whose kinetic quantities are unstated. We only know the equilibrium constant, which is a thermodynamic quantity. #DeltaG^@ = -RTlnK_(eq)#.

(c) This is backwards. If you had more reactants than products, then #0 < "K"_(eq) < 1#, since #["reactants"] < ["products"]#.

(d) This is only true if #"K"_(eq) = 1#, i.e. #["reactants"] = ["products"]#.