The progress of the reaction A > n B with time t is shown in the figure. From this information, determine the value of n: A) 1 B) 2 C) 3 D) 4
Question
The progress of the reaction $A \rightarrow n B$ with time $t$ is shown in the figure.
From this information, determine the value of $n$:
 A) 1
 B) 2
 C) 3
 D) 4
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Answer
To determine the value of $n$ in the reaction $A \rightarrow nB$ using the graph provided, follow these steps:

Initial Observations:
 At time $t=0$, the concentration of $A$ is 0.6 and the concentration of $B$ is 0.
 At a later time $t$, the concentration of $A$ decreases to 0.4 and the concentration of $B$ increases to 0.4.

Changes in Concentrations:
 The change in concentration of $A$ from $t=0$ to $t=t$ is: $$ \text{Change in } [A] = 0.6  0.4 = 0.2 $$
 The change in concentration of $B$ from $t=0$ to $t=t$ is: $$ \text{Change in } [B] = 0  0.4 = 0.4 $$

Relationship Between Changes:
 According to the reaction $A \rightarrow nB$, the amount of $A$ that reacts is directly proportional to the amount of $B$ produced.
 If 0.2 moles of $A$ are converted, resulting in an increase of 0.4 moles of $B$, we can determine $n$ by: $$ 0.2 \text{ moles of } A \rightarrow 0.4 \text{ moles of } B $$
 Therefore, $n$ is given by: $$ n = \frac{\text{Change in } [B]}{\text{Change in } [A]} = \frac{0.4}{0.2} = 2 $$

Conclusion:
 The value of $n$ is 2.
Hence, the correct option is B) 2.
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