Problem 67 - Chemistry The Science in Context

Question

The value of the equilibrium constant of a reaction decreases with increasing temperature. Is the reaction endothermic or exothermic?

Step-by-Step Solution

Answer

Answer: The reaction is endothermic.

Step 1: Van't Hoff Equation

The Van't Hoff equation is given by: \[ \frac{d \ln K}{dT} = \frac{\Delta H}{RT^2} \] Where: d ln K/dT: the derivative of ln K with respect to temperature ΔH: the change in enthalpy of the reaction R: the universal gas constant (8.314 J mol⁻¹ K⁻¹) T: temperature in Kelvin

Step 2: Determine the Sign of ΔH

Given that the value of the equilibrium constant, K, decreases with increasing temperature, we can infer the following: - If the reaction is endothermic, ΔH will be positive (heat is absorbed) and the value of d ln K/dT will be negative. - If the reaction is exothermic, ΔH will be negative (heat is released) and the value of d ln K/dT will be positive.

Step 3: Conclusion

From the given information, we found that the value of the equilibrium constant, K, decreases with increasing temperature. Based on the Van't Hoff equation, this is only possible for endothermic reactions where ΔH is positive. Therefore, the reaction is endothermic.

Key Concepts

Equilibrium Constant

In the realm of chemical reactions, the equilibrium constant (\( K \) ) serves as a critical gauge that quantifies the extent to which a reaction occurs at a particular temperature. It is a measure of the balance between the reactants and products in a reversible chemical reaction when the reaction has reached a state of dynamic equilibrium. At this juncture, the rate of the forward reaction equals the rate of the reverse reaction, implying no net change in the concentration of reactants and products over time.

It's important to note that the value of the equilibrium constant is dependent on temperature. An increase in temperature can shift the position of equilibrium, thus altering the value of the constant itself. If the value of the equilibrium constant decreases with an increase in temperature, we infer that the forward reaction is favored at lower temperatures. Conversely, if the value of the constant increases with rising temperature, the equilibrium shifts to favor production of the products, hinting at a reaction that releases energy. Understanding this dependence is crucial when predicting the direction in which a reaction will proceed when subjected to thermal changes.

Endothermic Reaction

An endothermic reaction is one that absorbs energy from its surroundings in the form of heat. This type of reaction typically results in a temperature drop in the immediate environment as the system requires energy to drive the reaction forward. It's like a sponge soaking up water, except the sponge is the reaction and the water is heat energy! Chemically, the energy absorbed is used to break the bonds of reactants, which is a prerequisite for the formation of new bonds in the product molecules.

Determining whether a reaction is endothermic can often be deduced from the temperature dependency of the equilibrium constant. If the equilibrium constant decreases with an increase in temperature, it hints that the reaction is endothermic. In the context of the Van't Hoff equation, this translates to a positive enthalpy change (\( \text{ΔH} > 0 \) ), indicating that heat is absorbed from the environment into the system during the reaction.

Enthalpy Change

Enthalpy change (\( \text{ΔH} \) ) is a term that represents the amount of energy absorbed or released during a chemical reaction at constant pressure. In a nutshell, it tells us whether the reaction is soaking up heat energy (endothermic) or giving it off (exothermic). It's a central concept in thermochemistry and is dictated by the nature and arrangement of constituent atoms and the strength of the bonds being broken and formed.

When you see a positive enthalpy change (\( \text{ΔH} > 0 \) ), it's time to think of a heat pack that warms your hands by absorbing heat—an endothermic process. On the flip side, a negative enthalpy change (\( \text{ΔH} < 0 \) ) is reminiscent of an instant cold pack used for injuries, which releases energy to the surroundings—an exothermic process. The magnitude of enthalpy change guides chemists in predicting how a reaction behaves thermodynamically and can shed light on the reaction’s potential applications, from industrial synthesis to everyday products.

Exothermic Reaction

When we talk about an exothermic reaction, we're referring to a process that releases energy, primarily in the form of heat, to its surroundings. It's akin to lighting a bonfire on a cold night—the fire releases heat, warming anyone nearby. The release of energy in these reactions typically results from the formation of new bonds, which is a more energetically favorable state than the reactants. Consequently, the enthalpy change is negative (\( \text{ΔH} < 0 \) ), symbolizing the exodus of energy from the system to the ambiance.

In an exothermic reaction, the value of the equilibrium constant increases with a rise in temperature if the reaction is being driven in the reverse direction. This is because the added heat energy is effectively 'absorbed' by the reverse reaction. Exothermic processes are commonly harnessed for their thermal output, finding their place in domestic heating, combustion engines, and many other applications where heat is a valuable commodity.