Consider the graph of Gibbs free energy G vs Extent of reaction. The number of statement/s from the following which are true with respect to points (a), (b) and (c) is _________
A. Reaction is spontaneous at (a) and (b)
B. Reaction is at equilibrium at point (b) and non-spontaneous at point (c)
C. Reaction is spontaneous at (a) and non-spontaneous at (c)
D. Reaction is non-spontaneous at (a) and (b)

Solution

Chemistry ma’am · 3 steps

Read the slope of the curve at each point: downhill is spontaneous, flat is equilibrium, uphill is not.

1. Slope decides. The slope of G against extent of reaction is Δᵣ G at that point. A negative slope means the forward reaction lowers G, so it is spontaneous. A zero slope is equilibrium, and a positive slope means the forward reaction is non-spontaneous.
2. Read the points. At (a) the curve falls steeply, so Δᵣ G < 0 and the reaction is spontaneous. At (b) the curve is at its minimum, so Δᵣ G = 0 and the reaction is at equilibrium. At (c) the curve rises, so Δᵣ G > 0 and the forward reaction is non-spontaneous.

   Statement	What it claims	Check against the graph	Verdict
   A	spontaneous at (a) and (b)	(b) is equilibrium, not spontaneous	false
   B	equilibrium at (b), non-spontaneous at (c)	minimum at (b), rising at (c)	true
   C	spontaneous at (a), non-spontaneous at (c)	falling at (a), rising at (c)	true
   D	non-spontaneous at (a) and (b)	(a) is spontaneous, (b) is equilibrium	false

3. So. Only statements B and C are true, so the answer is 2.

The common slip: 3. Calling (b) spontaneous because G is lowest there makes statement A look true and gives 3, not 2.

The idea to keep. On a G vs extent of reaction graph, look at the slope, not the height. The minimum is equilibrium, where Δᵣ G = 0. It is not the most spontaneous point.

Answer from the NTA final answer key. Solution by PrepWiser.