Problem 97 - Chemistry The Central Science In Si Units

Question

(a) For each of the following reactions, predict the sign of \(\Delta H^{\circ}\) and \(\Delta S^{\circ}\) without doing any calculations. (b) Based on your general chemical knowledge, predict which of these reactions will have \(K>1\) at \(25^{\circ} \mathrm{C} .(\mathbf{c})\) In each case, indicate whether \(K\) should increase or decrease with increasing temperature. (i) \(2 \mathrm{Fe}(s)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{FeO}(s)\) (ii) \(\mathrm{Cl}_{2}(g) \rightleftharpoons 2 \mathrm{Cl}(g)\) (iii) \(\mathrm{NH}_{4} \mathrm{Cl}(s) \rightleftharpoons \mathrm{NH}_{3}(g)+\mathrm{HCl}(g)\) (iv) \(\mathrm{CO}_{2}(g)+\mathrm{CaO}(s) \rightleftharpoons \mathrm{CaCO}_{3}(s)\)

Step-by-Step Solution

Answer

(i) \(\Delta H^{\circ}<0\), \(\Delta S^{\circ}<0\), \(K>1\) (decreases with \(T\)); (ii) \(\Delta H^{\circ}>0\), \(\Delta S^{\circ}>0\), \(K<1\) (increases with \(T\)); (iii) \(\Delta H^{\circ}>0\), \(\Delta S^{\circ}>0\), \(K<1\) (increases with \(T\)); (iv) \(\Delta H^{\circ}<0\), \(\Delta S^{\circ}<0\), \(K>1\) (decreases with \(T\)).

Step 1: Analyzing Reaction (i)

The reaction \(2 \mathrm{Fe}(s)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{FeO}(s)\) is a combination reaction forming an ionic compound. Since new bonds are formed, exothermic behavior is expected, so \(\Delta H^{\circ} < 0\). The reaction involves gas molecules being consumed, leading to a decrease in randomness, so \(\Delta S^{\circ} < 0\). An exothermic reaction with a decrease in entropy can have \(K > 1\), favoring the formation of the product at lower temperatures. As temperature increases, \(K\) decreases due to the exothermic nature.

Step 2: Analyzing Reaction (ii)

The reaction \(\mathrm{Cl}_{2}(g) \rightleftharpoons 2 \mathrm{Cl}(g)\) is a bond-breaking reaction that requires energy input, hence \(\Delta H^{\circ} > 0\). It involves the production of two moles of gas from one, increasing the system's disorder, so \(\Delta S^{\circ} > 0\). Despite requiring energy, the increase in entropy suggests \(K < 1\) at \(25^{\circ} \mathrm{C}\). However, \(K\) increases with temperature increase, as the reaction is endothermic.

Step 3: Analyzing Reaction (iii)

For \(\mathrm{NH}_{4} \mathrm{Cl}(s) \rightleftharpoons \mathrm{NH}_{3}(g)+\mathrm{HCl}(g)\), sublimation of solid to gases generally requires energy, indicating \(\Delta H^{\circ} > 0\). The reaction involves the formation of gases from a solid, increasing the entropy, so \(\Delta S^{\circ} > 0\). \(K < 1\) at \(25^{\circ} \mathrm{C}\) due to the endothermic nature, but \(K\) increases with temperature.

Step 4: Analyzing Reaction (iv)

The reaction \(\mathrm{CO}_{2}(g)+\mathrm{CaO}(s) \rightleftharpoons \mathrm{CaCO}_{3}(s)\) is a synthesis reaction forming a solid from a gas, usually exothermic, so \(\Delta H^{\circ} < 0\). The reaction results in decreased disorder, suggesting \(\Delta S^{\circ} < 0\). \(K > 1\) at \(25^{\circ} \mathrm{C}\) as the production of solid is favored, but \(K\) decreases as temperature increases due to the exothermic nature.

Key Concepts

Entropy

Entropy is a fundamental concept in thermodynamics that measures the degree of randomness or disorder in a system. It is denoted by the symbol \(S\). In chemistry, entropy changes, represented by \(\Delta S\), occur during chemical reactions and can indicate how the disorder of a system changes when reactants become products.

In a reaction where the number of gas molecules increases, like the conversion of \(\mathrm{Cl}_2(g)\) to \(2\mathrm{Cl}(g)\), entropy increases. This is because more particles are free to move, thus increasing randomness. On the other hand, in reactions where gases form more ordered states, such as when a gas reacts to form a solid, entropy decreases, as seen in the reaction \(\mathrm{CO}_2(g) + \mathrm{CaO}(s) \rightarrow \mathrm{CaCO}_3(s)\).

Understanding entropy helps predict whether a reaction is favorable. An increase in entropy \((\Delta S^{\circ} > 0)\) often means greater feasibility, especially at higher temperatures. However, entropy must be considered alongside enthalpy to determine the overall spontaneity of a reaction.

Enthalpy

Enthalpy is a measure of the total energy of a thermodynamic system, usually focused on heat changes during a reaction. It is represented by the symbol \(H\), and changes in enthalpy are denoted as \(\Delta H\).

Reactions can either release heat and be exothermic \((\Delta H^{\circ} < 0)\) or absorb heat and be endothermic \((\Delta H^{\circ} > 0)\). For example, reaction (i) \(2\mathrm{Fe}(s) + \mathrm{O}_2(g) \rightarrow 2\mathrm{FeO}(s)\) is exothermic since energy is released as new bonds are formed. Meanwhile, reaction (iii) \(\mathrm{NH}_4\mathrm{Cl}(s) \rightarrow \mathrm{NH}_3(g) + \mathrm{HCl}(g)\) is endothermic as energy is needed to sublimate the solid into gases.

The sign and magnitude of \(\Delta H\) help in determining the favorability of a reaction at different temperatures. Exothermic reactions, which release energy, are usually more spontaneous at lower temperatures, while endothermic reactions become more feasible as the temperature increases.

Chemical Equilibrium

Chemical equilibrium occurs when the rates of the forward and reverse reactions are equal, and the concentrations of reactants and products remain stable over time. This balance is described by the equilibrium constant \(K\).

For example, in the reaction \(2\mathrm{Fe}(s) + \mathrm{O}_2(g) \rightleftharpoons 2\mathrm{FeO}(s)\), the reaction is exothermic and has a lower entropy, leading to \(K > 1\) at room temperature, meaning the products are favored.

The value of \(K\) also varies with temperature changes due to the relationship between enthalpy and equilibrium, often described by the van 't Hoff equation. For exothermic reactions, \(K\) decreases with an increase in temperature because the reverse reaction becomes more favorable. Conversely, for endothermic reactions, such as the sublimation of \(\mathrm{NH}_4\mathrm{Cl}\), \(K\) increases with temperature, favoring product formation as the temperature is raised.

Understanding chemical equilibrium and its dependence on temperature is crucial for predicting how changes in conditions will affect the direction and extent of a chemical reaction.