hce_nthu
114年
化學與物理
第 28 題
At a certain temperature, $cis$-1,2-dimethylcyclopropane ($\mathbf{M}$) and $trans$-1,2-dimethylcyclopropane ($\mathbf{N}$) undergo the following transformation.
The rate laws for the reactions can be expressed as $v_f = k_f[\mathbf{M}]$ and $v_r = k_r[\mathbf{N}]$, with $k_f$ and $k_r$ being constants at a given temperature, called the forward and reverse rate constants, respectively, and the equilibrium constant of the reaction, $K = 3$. Which of the following statements is correct?
The rate laws for the reactions can be expressed as $v_f = k_f[\mathbf{M}]$ and $v_r = k_r[\mathbf{N}]$, with $k_f$ and $k_r$ being constants at a given temperature, called the forward and reverse rate constants, respectively, and the equilibrium constant of the reaction, $K = 3$. Which of the following statements is correct?
- A At this temperature, the conversion of $\mathbf{M}$ is $66.7\%$.
- B As the temperature increases, both $k_f$ and $k_r$ increase.
- C At room temperature, $\mathbf{N}$ is a gas under $\text{1 atm}$.
- D $\mathbf{M}$ is more stable than $\mathbf{N}$.
- E Heating this reaction increases the equilibrium constant $K$.
思路引導 VIP
想像一下，如果要讓一群人越過一道高牆，當我們給予每個人更多的能量（提高溫度）時，無論這道牆是從正面爬還是從背面爬，能夠成功翻越的人數會增加還是減少？這對於「反應發生的頻率」意味著什麼呢？
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AI 詳解
AI 專屬家教
太棒了！你能精準選出 (B) 選項，代表你對化學動力學中「速率常數」與溫度的關係有很紮實的掌握。這題的核心在於區分反應速率常數 ($k$) 與平衡常數 ($K$) 對溫度變化的響應方式。
速率常數與阿瑞尼斯方程式
根據阿瑞尼斯方程式 $k = Ae^{-E_a/RT}$，無論反應是吸熱還是放熱，當溫度 $T$ 增加時，指數項中的負值會變小，進而導致 $k$ 值增大。這在物理意義上代表分子的平均動能增加，跨越活化能位能障礙的碰撞頻率隨之提高，因此正、逆反應速率常數 $k_f$ 與 $k_r$ 必定都會隨溫度上升而增加。
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