hce_nthu
112年
化學與物理
第 14 題
A certain reaction has the form:
$\alpha A \rightarrow \text{Products}$
At $298\text{ K}$, the concentration of $A$ ($[A]$) versus time was measured. A plot of $1/[A]$ versus time (minutes) gave a straight line with a slope of $2.00 \times 10^{-2}$. $[A]_0$ represents the initial concentration at $t = 0$, and $k$ is the rate constant. Which of the following statements about this reaction is (are) correct?
I. The differential rate law is $\text{rate} = k[A]^2$.
II. The integrated rate law is \$1/[A] = 1/[A]_0 - kt$.
III. The rate constant is $2.00 \times 10^{-2}\text{ min}^{-1}$.
IV. If $[A]_0$ for this reaction is $0.100\text{ M}$, the first half-life is $34.7\text{ min}$.
V. If $[A]_0$ for this reaction is $0.100\text{ M}$, it will take $1.50 \times 10^3\text{ min}$ to consume $0.0750\text{ M}$ of $A$.
$\alpha A \rightarrow \text{Products}$
At $298\text{ K}$, the concentration of $A$ ($[A]$) versus time was measured. A plot of $1/[A]$ versus time (minutes) gave a straight line with a slope of $2.00 \times 10^{-2}$. $[A]_0$ represents the initial concentration at $t = 0$, and $k$ is the rate constant. Which of the following statements about this reaction is (are) correct?
I. The differential rate law is $\text{rate} = k[A]^2$.
II. The integrated rate law is \$1/[A] = 1/[A]_0 - kt$.
III. The rate constant is $2.00 \times 10^{-2}\text{ min}^{-1}$.
IV. If $[A]_0$ for this reaction is $0.100\text{ M}$, the first half-life is $34.7\text{ min}$.
V. If $[A]_0$ for this reaction is $0.100\text{ M}$, it will take $1.50 \times 10^3\text{ min}$ to consume $0.0750\text{ M}$ of $A$.
- A I
- B II and III
- C II and V
- D III and IV
- E I and V
思路引導 VIP
當我們觀察到一個反應的「濃度倒數」與時間成線性關係時，這在數學上暗示了反應速率與濃度之間存在著什麼樣的次方關係？而根據這個關係，如果我們要描述反應物消失的快慢，其方程式中的常數項應該如何連結圖形的斜率與截距？
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AI 詳解
AI 專屬家教
太棒了！你能準確判斷出這是一題典型的二級反應動力學問題，代表你對濃度與時間關係圖的物理意義掌握得非常紮實。
二級反應的特性辨析
本題的核心切入點在於觀察到 $1/[A]$ 對時間的作圖為直線，這正是二級反應（Second-order reaction）的判斷指標。因此，敘述 I 的微分速率定律式 $\text{rate} = k[A]^2$ 是正確的。然而，在處理這類題目時，鑑別度往往藏在細節裡：二級反應的積分速率定律式應為 $\frac{1}{[A]} = \frac{1}{[A]_0} + kt$，斜率為正值，且速率常數 $k$ 的單位應包含濃度倒數（即 $\text{M}^{-1}\text{min}^{-1}$），這也是為何敘述 II 與 III 存在陷阱的原因。
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