### Video Transcript

A dynamic equilibrium is
established between two reactants A and B according to the equation shown: A,
aqueous, is in equilibrium with two B, aqueous. Compound A has an initial
concentration of 0.8 moles per cubic decimeter that drops to 0.4 moles per cubic
decimeter once equilibrium is established. Which graph for this equilibrium is
correct?

Dynamic equilibrium is established
when the forward and reverse reactions occur at the same nonzero rate. When the forward and reverse
reactions have the same rate, the reactant and product concentrations will remain
constant even though both reactions are still occurring. Looking at the graphs, we can
determine when equilibrium is established by identifying the point in time where the
concentrations of A and B no longer change.

We are told in the question that
compound A has an initial concentration of 0.8 moles per cubic decimeter that drops
to 0.4 moles per cubic decimeter once equilibrium is established. Looking at the graphs, we can see
that only graphs (C) and (D) show compound A as having an initial concentration of
0.8 moles per cubic decimeter. So, we can eliminate graphs (A) and
(B). Graphs (C) and (D) also show that
the concentration of compound A is 0.4 moles per cubic decimeter once equilibrium is
established.

To determine which of these graphs
is correct, we’ll need to consider how the concentration of B changes over time. Looking at the balanced chemical
equation, we see that for every mole of A that reacts, two moles of B are
produced. Over the course of this reaction,
the concentration of A decreases by 0.4 moles per cubic decimeter. So, the concentration of B should
increase by twice as much. We should therefore expect that
compound B has an initial concentration of zero moles per cubic decimeter that
increases to 0.8 moles per cubic decimeter once equilibrium is established. This is shown in graph (D).

In conclusion, the graph for the
equilibrium between A and two B that is correct is the graph shown in answer choice
(D).