CHAPTER 14. Gibbs–Helmholtz Equation: Practical Applications in Thermochemistry
CHAPTER 14. Gibbs–Helmholtz Equation: Practical Applications in Thermochemistry
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第 14 章吉布斯·亥姆霍兹方程：热化学中的实际应用
DOI：
10.1039/9781839164095-00393
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Verevkin
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ΔrGo m= ΔrHo m - TΔrSo m= - RTln Kp（14.1）其中ΔrGo m为化学反应自由能的变化，ΔrHo m为反应焓，ΔrSo m为化学反应熵的变化。负号（< 0）提供一般可行性的定性指示。此外，气相热力学平衡常数Kp的大小（在任何感兴趣的温度T下）提供了对期望产物的可能产率的定量见解（例如，Kp bbb10的产率非常接近99%）。通常，热力学计算首先在参考温度T= 298 k下进行，使用反应参与者的标准摩尔等压热容Co pm，可以借助基尔霍夫定律推导出在任何期望温度下反应的可行性。根据公式eqn(14.1)，对生成焓和反应参与者熵的了解对于可行性分析是必不可少的。预测有机分子的熵和热容无疑是一项具有挑战性的任务。原则上，如果它们的结构、转动惯量和振动频率已知，则可以借助量子化学（QC）或统计力学可靠地计算它们。从eqn（14.1）可以明显看出，与焓项（通常单位为kJ mol−1）相比，熵预测（通常单位为jk−1 mol−1）的不准确性可以被认为不那么明显。然而，相比之下，反应参与者的标准摩尔生成焓ΔfHo m的预测或实验测定要困难得多，因为该性质对化合物的纯度非常敏感。例如，用于燃烧实验的样品中少量杂质（甚至小于0.05%）可以使测量的生成焓误差20-30 kJ mol−1。在这种情况下，开发不同的方法来验证实验焓，以从吉布斯-亥姆霍兹方程得到正确的可行性预测是必不可少的。这些包括经典的经验结构-性质关系和现代QC计算。例如，对r-取代苯酰胺、r-取代苯甲酸和r-取代苯的化学族的热力学性质进行了构性分析，揭示了所研究的化学族之间的焓具有一般的线性关系。这些线性相关性可以用于建立每个化学系列可用的实验结果的内部一致性。在过去的十年中，高水平的复合QC方法成为获得理论ΔfHo m （g, 298 k）值的有价值的工具2,3，所谓的“化学精度”为4-5 kJ mol−1。这些QC方法在时间和计算能力方面差别很大。QC计算目前正在成功地进行，以获得中小分子的ΔfHo m (g)值。在我们看来，这是QC和
ΔrGo m= ΔrHo m− TΔrSo m=− RTln Kp (14.1) where ΔrGo m is the change in the free energy of a chemical reaction, ΔrHo m is the reaction enthalpy and ΔrSo m is the change in the entropy of a chemical reaction. The negative sign (< 0) provides a qualitative indication of the general feasibility. Moreover, the magnitude of the gas-phase thermodynamic equilibrium constant Kp (at any temperature of interest T) provides quantitative insight into the possible yield of the desired product (eg for Kp> 10 the yield is very close to 99%). As a rule, thermodynamic calculations are initially carried out at the reference temperature T= 298 k. Using the standard molar isobaric heat capacities Co pm of reaction participants, the feasibility of the reaction at any desired temperature can be derived with the aid of kirchhoff's law. According to eqn (14.1), knowledge of enthalpies of formation and entropies of reaction participants is indispensable for the feasibility analysis. predicting the entropies and heat capacities of organic molecules is undoubtedly a challenging task. in principle, they can be reliably calculated with the help of quantum chemistry (QC) or using statistical mechanics if their structures, moments of inertia and vibrational frequencies are known. From eqn (14.1), it is obvious that the inaccuracy of the entropy predictions (calculated in the usual units J k− 1 mol− 1) compared with the enthalpic term (calculated in the usual units kJ mol− 1) can be regarded as less pronounced. in contrast, however, the prediction or experimental determinations of the standard molar enthalpies of formation, ΔfHo m, of the reaction participants are much more difficult owing to the very high sensitivity of this property to the purity of the compound. For example, a small amount of an impurity (even less than 0.05%) in the sample used for combustion experiments can falsify the measured enthalpy of formation by 20–30 kJ mol− 1. in this context, the development of different methods for validating experimental enthalpies for a correct feasibility prognosis from the gibbs–helmholtz equation is essential. These include classic empirical structure–property relationships and modern QC calculations. For example, the structure–property analysis of thermodynamic properties in chemical families of r-substituted benzamides, r-substituted benzoic acids and r-substituted benzenes revealed 1 some general linear interrelations for the enthalpies between the chemical families under study. These linear correlations can serve for the establishment of the internal consistency of experimental results available for each chemical series. in the past decade, high-level composite QC methods become a valuable tool 2, 3 for obtaining theoretical ΔfHo m (g, 298 k) values with a so-called “chemical accuracy” of 4–5 kJ mol− 1. These QC methods differ considerably in terms of time and computing power. QC calculations are currently being carried out successfully to obtain ΔfHo m (g) values for small-and medium-sized molecules. in our opinion, a judicious combination of QC and