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:

  1. 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.
  2. 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: $$ \text{Change in } [B] = 0 - 0.4 = 0.4 $$
  3. 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: $$ n = \frac{\text{Change in } [B]}{\text{Change in } [A]} = \frac{0.4}{0.2} = 2 $$
  4. Conclusion:

    • The value of $n$ is 2.

Hence, the correct option is B) 2.


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