Question

The acid-base chemistry reaction of barium hydroxide \(\left(\mathrm{Ba}(\mathrm{OH})_{2}\right)\) with ammonium thiocyanate \(\left(\mathrm{NH}_{4} \mathrm{SCN}\right)\) in water creates barium thiocyanate, ammonia, and water. The reaction is highly favorable, but is also so endothermic that the solutions cools to such an extent that a layer of frost forms on the reaction vessel. Explain how an endothermic reaction can be favorable.

Short answer

Answer: An endothermic reaction, like the reaction between barium hydroxide and ammonium thiocyanate, can be favorable due to the significant positive entropy change in the reaction, which indicates an increase in disorder. At high temperatures, the positive entropy change is large enough to offset the endothermic energy absorption, resulting in a negative Gibbs free energy value, making the reaction spontaneous and favorable.

Step-by-step solution

Understand Endothermic and Exothermic Reactions

In chemical reactions, energy is either absorbed or released. When energy is absorbed from the surroundings, the reaction is called endothermic. On the other hand, when energy is released to the surroundings, the reaction is called exothermic. In an endothermic reaction, the overall energy of the products is higher than the energy of the reactants. This means that energy is required for the reaction to occur and heat is absorbed by the reaction. In contrast, in an exothermic reaction, the overall energy of the products is lower than the energy of the reactants, meaning heat is released by the reaction.

What Makes a Reaction Favorable

A reaction is considered favorable if it proceeds spontaneously under certain conditions. The spontaneity of a reaction is determined by several factors, including the change in Gibbs free energy (\(\Delta G\)), which is a measure of the thermodynamic potential of a system. A reaction is spontaneous and favorable if \(\Delta G\) is negative. The change in Gibbs free energy is connected with enthalpy (\(\Delta H\)) and entropy (\(\Delta S\)) changes in the reaction according to the formula: $$\Delta G = \Delta H - T\Delta S$$ where \(T\) represents the temperature.

Connecting Endothermic Reactions and Favorability

In endothermic reactions, \(\Delta H\) is positive because heat is absorbed by the reaction. However, this does not mean that the reaction cannot be favorable. The entropy change, \(\Delta S\), is a measure of the increase or decrease in the disorder of a system. If the entropy change is positive, indicating an increase in the disorder of the system, the reaction can be favorable at high temperatures. This is because a large, positive value of \(T\Delta S\) can overcompensate for the positive \(\Delta H\), resulting in a negative value for \(\Delta G\).

Explain the Favorability of the Given Endothermic Reaction

The acid-base reaction between barium hydroxide \(\left( \mathrm{Ba}(\mathrm{OH})_{2} \right)\) and ammonium thiocyanate \(\left( \mathrm{NH}_{4}\mathrm{SCN} \right)\) is an endothermic reaction, which means it absorbs heat from its surroundings. Despite being endothermic, this reaction is highly favorable. This is because the entropy change (\(\Delta S\)) in the reaction is positive, which indicates an increase in disorder. At high temperatures, the positive entropy change can be significant enough to offset the endothermic energy absorption. Thus, a large positive \(T\Delta S\) value compensates for the positive \(\delta H\), resulting in a negative \(\Delta G\) value, making the reaction spontaneous and favorable. The consumption of large amounts of heat from the surroundings to support the endothermic reaction leads to a noticeable decrease in temperature, causing frost to form on the reaction vessel.