Interpret the given graph

The graph is of rate of formation of product versus time.

Let the rate be $r = \dfrac{d[Y]}{dt}$.

From the figure (as described by regions I, II, III), the rate behaves as follows:

• Region I: rate is approximately constant
• Region II: rate decreases with time
• Region III: rate again becomes approximately constant (very small / nearly zero)

Since for reaction $X \to Y$, $r = -\frac{d[X]}{dt} = \frac{d[Y]}{dt}$ the variation of rate with time reflects how rate depends on concentration as the reactant gets consumed.

Basic idea about order from rate–time graph

• For a zero-order reaction: $r = k$ so rate is constant with time until reactant is available.

• For a first-order reaction: $r = k[X]$ and since $[X]$ decreases exponentially with time, rate also decreases exponentially with time.

Thus:

• constant-rate region suggests zero order,
• decreasing-rate region suggests non-zero order, and specifically for a smooth exponential-like decrease, first order is consistent.

Examine each statement

(A) Overall order of this reaction is one.

This is false.

The graph shows different behavior in different regions, so the reaction does not have a single overall order of 1 over the entire time range.

(B) Order of this reaction can't be determined.

This is false.

From the graph, qualitative determination is possible:

• constant rate in some region $\Rightarrow$ zero order there,
• decreasing rate in region II $\Rightarrow$ not zero order; here it is interpreted as first order.

So order-related information can be inferred.

(C) In region I and III, the reaction is of first and zero order respectively.

This is false.

In region I, rate is constant, so that corresponds to zero order, not first order. Region III is also approximately constant, so zero order there is fine, but since region I is wrongly labeled first order, the statement is false.

(D) In region II, the reaction is of first order.

This is true.

In region II, rate decreases with time as concentration decreases, which is characteristic of first-order behavior.

(E) In region II, the order of reaction is in the range of 0.1 to 0.9.

This is false.

Region II is identified as first order, i.e. order $=1$, which is not in the interval $0.1$ to $0.9$.

Count correct statements

Only statement (D) is correct.

Hence, the number of correct statements is $\boxed{1}$

Comparison with stored answer

Stored correct answer = $1$.

Our derived answer also = $1$.

Therefore, the answer agrees with the stored answer.