Problem 70 - Chemistry The Molecular Science

Question

The equilibrium constant \(K_{\mathrm{c}}\) for this reaction is 0.16 at \(25^{\circ} \mathrm{C},\) and the standard reaction enthalpy is \(16.1 \mathrm{~kJ}\). $$ 2 \mathrm{NOBr}(\mathrm{g}) \rightleftharpoons 2 \mathrm{NO}(\mathrm{g})+\mathrm{Br}_{2}(\ell) $$ Predict the effect of each of these changes on the position of the equilibrium; that is, state which way the equilibrium will shift (left, right, or no change) when each of these changes is made for a constant-volume system. (a) Adding more \(\mathrm{Br}_{2}\) (b) Removing some \(\mathrm{NOBr}\) c). Lowering the temnerature

Step-by-Step Solution

Answer

Equilibrium shifts left for adding \( \mathrm{Br}_{2} \), removing \( \mathrm{NOBr} \), and lowering the temperature.

Step 1: Analyze the Effect of Adding More \( \mathrm{Br}_{2} \)

According to Le Chatelier's principle, if more \( \mathrm{Br}_{2} \) is added, the system will try to counteract this change by shifting the equilibrium to the left to consume the excess \( \mathrm{Br}_{2} \). Thus, the equilibrium will shift towards the reactants.

Step 2: Analyze the Effect of Removing Some \( \mathrm{NOBr} \)

Removing \( \mathrm{NOBr} \) decreases the concentration of reactants. According to Le Chatelier's principle, the equilibrium will shift to the left to replace the removed \( \mathrm{NOBr} \), meaning it will favor the formation of more reactants.

Step 3: Analyze the Effect of Lowering the Temperature

The reaction is endothermic, with a standard reaction enthalpy \( \Delta H = 16.1 \, \mathrm{kJ/mol} \). Lowering the temperature favors the exothermic direction (reverse reaction), so the equilibrium will shift to the left, favoring the formation of more \( \mathrm{NOBr} \).

Key Concepts

Chemical Equilibrium

In chemistry, equilibrium refers to a state where both reactants and products maintain constant concentrations over time. Consider this like a balance in which neither side is changing because the reactions moving forward and backward occur at the same rate.
This concept is key in understanding reactions that do not go to completion, but instead reach a balance, termed as dynamic equilibrium.
Interestingly, even though the concentration remains constant, reactions are still active, continuously converting between reactants and products.

• This continuous activity indicates no real standstill but a dynamic state of balance.

By this understanding, the equilibrium position can be altered by manipulating conditions like concentration and temperature. Importantly, Le Chatelier's Principle helps predict how changes impact the equilibrium.

• When conditions are altered, the system adjusts to counteract the change, striving to restore equilibrium.

Endothermic Reaction

An endothermic reaction is one that absorbs heat from its surroundings. As the reaction progresses, energy in the form of heat is taken in, which is necessary to drive the reaction forward.
This particular property of reactions informs us about how they are affected by temperature changes.
For the reaction involving NOBr, this process involves a reaction enthalpy (\( \Delta H\) of 16.1 kJ), indicating it requires heat to proceed towards completing the products NO and Br₂.

• This means the reaction naturally moves forward with added heat, as it helps overcome the energy barrier.

When temperature alters, reactions exhibit the temperature-induced shifts. Lowering the temperature actually shifts the equilibrium opposite to the direction requiring heat, which in the case of endothermic reactions means favoring the reverse reaction.

• Thus, reducing temperature tends to move the reaction back to produce more reactants.

Equilibrium Constant

The equilibrium constant, denoted as \( K_{\mathrm{c}}\), is a reflection of the ratio of the concentration of products to reactants at equilibrium for a given reaction. This measurement allows chemists to quantify how far a reaction proceeds before reaching equilibrium.

• A high \( K_{\mathrm{c}}\) value signifies a reaction that favors product formation, while a low value suggests a tendency to favor reactants.

In the case of the NOBr reaction, the given equilibrium constant of 0.16 implies a notable preference for reactants under the outlined conditions. The equilibrium constant is sensitive to temperature changes, but remains unaffected by concentration or pressure alterations if the reaction involves gases.
This means while concentrations of involved substances change, \( K_{\mathrm{c}}\) remains a steadfast parameter unless the temperature changes, providing a reliable measure of reaction dynamics at constant temperature.