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 one between barium hydroxide and ammonium thiocyanate, can be favorable if it is accompanied by a sufficient increase in entropy (disorder). In this case, the reaction produces more particles (barium thiocyanate, ammonia, and water), which leads to an increase in entropy. This increase in disorder compensates for the heat absorbed by the reaction, allowing it to proceed spontaneously and be considered favorable.

Step-by-step solution

Define an Endothermic Reaction

An endothermic reaction is a chemical reaction that absorbs heat from its surroundings. This means the enthalpy change, ΔH, of the reaction is positive (ΔH > 0). The reaction between barium hydroxide and ammonium thiocyanate is an example of an endothermic reaction.

Introduce the Concept of Spontaneity

A spontaneous reaction is a chemical reaction that proceeds on its own without any outside energy input. Whether a reaction is spontaneous or not depends on a combination of factors, including enthalpy (ΔH) and entropy (ΔS). To determine if a reaction is spontaneous, we can calculate the Gibbs free energy (ΔG) using the following equation: ΔG = ΔH - TΔS where T is the temperature in Kelvin.

Explain the Relationship between ΔH, ΔS, and ΔG

If ΔG is negative (ΔG < 0), then the reaction is spontaneous and considered favorable. If ΔG is positive (ΔG > 0), the reaction is not spontaneous and is considered unfavorable. The relationship between ΔH, ΔS, and ΔG helps us understand how changes in enthalpy and entropy can affect the spontaneity of a reaction: - If ΔH is negative (exothermic) and ΔS is positive (increasing disorder), the reaction will always be spontaneous (ΔG < 0). - If ΔH is positive (endothermic) and ΔS is negative (decreasing disorder), the reaction will never be spontaneous (ΔG > 0). - If both ΔH and ΔS are positive, the reaction can be spontaneous at high temperatures (ΔG < 0). - If both ΔH and ΔS are negative, the reaction can be spontaneous at low temperatures (ΔG < 0).

Apply the Concept of Spontaneity to the Reaction of Barium Hydroxide and Ammonium Thiocyanate

From the problem description, we know that the reaction of barium hydroxide and ammonium thiocyanate is a favorable endothermic reaction (ΔH > 0). Based on our knowledge of the relationship between ΔH, ΔS, and ΔG, it is clear that the reaction must have a positive entropy change (ΔS > 0) to compensate for the positive enthalpy change — namely, the reaction should involve an increase in disorder. In this case, the reaction involves the formation of more particles, since barium thiocyanate, ammonia, and water are formed from barium hydroxide and ammonium thiocyanate. This leads to an increase in entropy, making the overall reaction sufficiently favorable to proceed spontaneously despite the endothermic nature of the reaction. In conclusion, an endothermic reaction can be favorable if it is accompanied by a sufficient increase in entropy. For the reaction between barium hydroxide and ammonium thiocyanate, the increase in disorder (due to the formation of more particles) compensates for the absorption of heat, allowing the reaction to proceed spontaneously.