ABSTRACT

The relation between rate constant k₁ and absolute temperature T for graphite, anthracite, and coal floated with only frother was investigated using combined theoretical and empirical approaches. It was determined that the relation between lnk₁ and 1/T is curvilinear and requires a polynomial of a second degree for a sufficient approximation of the experimental data points. Therefore, the well-known Arrhenius empirical formula for chemical reactions, predicting a linear relation, cannot be used for relating lnk₁ and 1/T. Available in literature thermodynamic and kinetic considerations show that for chemical reactions and equilibrium processes the relation between the first order rate constant k₁ and absolute temperature T is lnk₁ = lnk₋₁-ΔH^o /RT +ΔS^o/R, where ΔH^o is standard enthalpy change, ΔS^o standard entropy change, R gas constant and k₋₁ is the rate constant of the reverse reaction, in our case the disintegration of the bubble-particle aggregate. Assuming that the performed batch flotation tests for a long time of flotation provide an equilibrium quantity called ultimate or maximum recovery, the values of enthalpy and entropy as well as reverse process rate constant k₋₁ were determined. It was found that k₁ depended on two constants (ΔH^o and ΔS^o) and two variables (1/T and k₋₁ = f(1/T)).

摘要

使用理论和经验相结合的方法研究了仅用起泡剂漂浮的石墨、无烟煤和煤的速率常数k ₁与绝对温度T之间的关系。已确定 ln k ₁和 1/ T之间的关系是曲线的，并且需要二次多项式才能充分近似实验数据点。因此，著名的化学反应阿伦尼乌斯经验公式，预测线性关系，不能用于关联 ln k ₁和 1/ T. 文献中的热力学和动力学考虑表明，对于化学反应和平衡过程，一级速率常数k ₁与绝对温度T之间的关系为 ln k ₁  = ln k _-1 -ΔH ^o /R T +ΔS ^o /R，其中 ΔH ^o是标准焓变，ΔS ^o是标准熵变，R 气体常数和k _-1是逆反应的速率常数，在我们的例子中是气泡-粒子聚集体的分解。假设对长时间浮选进行的批量浮选测试提供了称为最终或最大回收率的平衡量，确定了焓和熵的值以及逆过程速率常数k _-1。发现k ₁取决于两个常数（ΔH ^o和ΔS ^o）和两个变量（1/ T和k _-1  = f(1/ T )）。