Equilibrium

Equilibrium Part 1: Topics 7.1 to 7.6

Learning Targets

• Define Equilibrium

  • In terms of forward and reverse reaction rates.

  • In terms of amounts of products and reactants.

  • As a dynamic state.

• Interpret Graphs of concentration/partial pressures vs. time to determine when equilibrium is established.

Essential Questions

1. When has a reaction reached EQUILIBRIUM?

2. Why do we say a system at equilibrium is dynamic, not static?

3. What is the definition of equilibrium in terms of rates of reaction?

4. What is happening with the forward reaction and reverse reaction rates? Why?

   • Example: $N<em>2O</em>4(g) \rightleftharpoons 2NO_2(g)$

Equilibrium Dynamics

• Equilibrium Defined: A reaction reaches equilibrium when the rates of the forward and reverse reactions are equal. At this state, the concentrations of reactants and products remain constant.

• Dynamic State: Equilibrium is described as dynamic rather than static because although the concentrations of reactants and products remain constant, the reactions between them continue to occur.

  • Forward and reverse reactions are happening incessantly but at equal rates, hence no net change in concentration.

Examples and Discussions

Concentration Changes in Reactions

5. For the reaction $N<em>2(g) + 3H</em>2(g) \rightleftharpoons 2NH_3(g)$:

   • a. Why does ammonia’s concentration increase over time?

   • As the reaction proceeds, more $NH<em>3$ is formed from $N</em>2$ and $H_2$, due to the forward reaction.

   • b. Why do the hydrogen and nitrogen concentrations decrease over time?

   • The reactants $N<em>2$ and $H</em>2$ are being consumed to produce $NH_3$, leading to their gradual decline.

   • c. Based on the graph, what chemical species were introduced into the vessel?

   • d. What do the slopes and equilibrium concentration lines of the species tell us about the reaction?

Equilibrium Expressions

Writing Equilibrium Expressions

• Learning Targets:

  • Write equilibrium expressions for $K<em>c$, $K</em>p$, and $K_{eq}$.

  • Use Hess’s Law with equilibrium constants:

  • The $K$ value for the reverse reaction is the reciprocal of the $K$ value of the forward reaction:
    $K<em>{reverse} = \frac{1}{K</em>{forward}}$.

  • When you multiply the reaction by a factor of $n$, you raise the $K$ value to the $n$th power: $K_{new} = K^{n}$.

  • When adding reactions together, multiply their $K$ values to get the $K$ value of the new reaction:
    $K<em>{total} = K</em>1 \cdot K_2$.

Law of Mass Action

6. How do you write the equilibrium constant expression?

   • a. What do the coefficients become?

     • Coefficients become the exponents in the equilibrium expression.

   • b. What does a chemical species in brackets mean?

     • Brackets indicate concentration (in molarity) of the species.

   • c. What chemical species have concentrations?

     • Only gaseous and aqueous species have concentrations that are considered in equilibrium expressions.

   • d. If $K$ depends on concentrations of products and reactants, what do we EXCLUDE from the equilibrium expression?

     • Solids and liquids are excluded because their concentrations do not change significantly.

   • e. Why exclude them?

     • Their activity is constant and does not impact the equilibrium position.

   • f. Homogeneous equilibria involve the same phase (e.g., $N<em>2(g) + 3H</em>2(g) \rightleftharpoons 2NH_3(g)$, $HCN(aq) \rightleftharpoons H^+(aq) + CN^-(aq)$).

   • g. Heterogeneous equilibria involve more than one phase (e.g., $2KClO<em>3(s) \rightleftharpoons 2KCl(s) + 3O</em>2(g)$, $2H<em>2O(l) \rightleftharpoons 2H</em>2(g) + O_2(g)$).

Relationship of K Values

7. If you reverse a reaction, what is the $K$ value for the reversed reaction?

   • It is the reciprocal of the original $K$ value.

8. If you multiply a reaction by an $n$ factor, what happens to the $K$ value?

   • The $K$ value is raised to the $n$th power.

9. If you multiply a reaction by 2, what is the new $K$ value for the doubled reaction?

   • The new $K$ value will be $K^2$.

10. How is $K$ of a net reaction calculated from two other reactions?

    • Combine the $K$ values of the individual reactions according to Hess’s Law.

Concept Check: Equilibrium Constant Calculation

Given Reactions

• Overall Reaction: $2HF(aq) + C<em>2O</em>4^{2-}(aq) \rightleftharpoons 2F^-(aq) + H<em>2C</em>2O_4(aq)$

• Reactions Provided:

  • $HF(aq) \rightleftharpoons H^+(aq) + F^-(aq) \, (K_c = 6.8 \times 10^{-4})$

  • $H<em>2C</em>2O<em>4(aq) \rightleftharpoons 2 H^+(aq) + C</em>2O<em>4^{2-}(aq) \, (K</em>c = 3.8 \times 10^{-6})$

• K values are the same even with different starting concentrations.

• Equilibrium concentrations establish the K value at the specific temperature.

  • Example: Regardless of starting with $N<em>2$ and $H</em>2$ or with $NH_3$, equilibrium concentrations will result in the same relative amounts of all three substances.

• K is constant at a given temperature, independent of initial concentrations.

  • Even with varying initial amounts, it returns to a consistent set of equilibrium concentrations.

Comparing Kc and Kp

10. What is the difference between $K<em>c$ and $K</em>p$?

    • $K<em>c$ is based on molar concentrations, while $K</em>p$ is based on partial pressures of gases.

Example Exercises

Exercise 1

• Write the $K<em>p$ and $K</em>c$ expressions for the reaction: $N<em>2(g) + 3H</em>2(g) \rightleftharpoons 2NH_3(g)$

Exercise 2

• Calculate the equilibrium constant, $K<em>p$, for the reaction: $N</em>2(g) + 3H<em>2(g) \rightleftharpoons 2NH</em>3(g)$

  • Use given equilibrium pressures at a certain temperature.

Relation of Kp and Kc

10. What is the equation that ties $K<em>p$ and $K</em>c$ together?

    • $K<em>p = K</em>c(RT)^{∆n}$, where $∆n$ is the change in the number of moles of gas products minus those of reactants.

    • a. What is $∆n$ in this equation?

    • $∆n = (moles \, of \, products) - (moles \, of \, reactants)$

    • b. What happens if $∆n = 0?</strong></p></li><li><p>The$Kp$and$Kc values are equal because the term $(RT)^{∆n}$ becomes 1.

Exercise 3

• Calculate the K$value for the reaction using the$K_p$value from Exercise 2, temperature at 35°C.</strong></p></li></ul><h4 id="74939d40-7f2b-4783-80cb-2bd8a806db3c" data-toc-id="74939d40-7f2b-4783-80cb-2bd8a806db3c" collapsed="false" seolevelmigrated="true">Interpretation of K Values</h4><h5 id="cf595237-4daf-4371-878a-d8a50b69bbaf" data-toc-id="cf595237-4daf-4371-878a-d8a50b69bbaf" collapsed="false" seolevelmigrated="true">Learning Objectives</h5><ul><li><p><strong>Interpret the magnitude of$K$</strong>:</p><ul><li><p>If$K > 1$:</p></li><li><p>The forward reaction is favored at this temperature.</p></li><li><p>More products than reactants at equilibrium.</p></li><li><p>If$K < 1$:</p></li><li><p>The reverse reaction is favored.</p></li><li><p>More reactants than products at equilibrium.</p></li><li><p>If$K = 1$:</p></li><li><p>Both forward and reverse reactions are equally favored.</p></li><li><p>If$K$is a very large number:</p></li><li><p>The reaction effectively goes to completion at that temperature.</p></li></ul></li></ul><h5 id="f19cc2be-0e2a-40d5-bd1a-d079cacda3d4" data-toc-id="f19cc2be-0e2a-40d5-bd1a-d079cacda3d4" collapsed="false" seolevelmigrated="true">Values of K Analysis</h5><ol start="11"><li><p><strong>What do values of K tell us?</strong></p><ul><li><p><strong>a. If$K >> 1$</strong>: Reaction is complete; products predominately at equilibrium.</p></li><li><p><strong>b. If$K << 1$</strong>: Reaction favors reactants; reactants predominately at equilibrium.</p></li><li><p><strong>c. If$K$is a large value (much greater than 1) the reaction proceeds significantly towards products.</strong></p></li><li><p><strong>d. If$K$is a small value (much smaller than 1) the reaction favors reactants predominantly.</strong></p></li><li><p><strong>e. If$K = 1 (a rare occurrence): The equilibrium concentrations of reactants and products are relatively equal.

Reaction Quotient, Q

Learning Targets

• Define the Reaction Quotient, Q:

  • $Q$ is equal to the same expression as $K$, but is evaluated under non-equilibrium conditions.

• Calculate $Q$ to determine which direction the reaction must move to reach equilibrium:

  • If Q > K, the reaction shifts left (to reactants) to reach equilibrium.

  • If Q < K, the reaction shifts right (to products) to reach equilibrium.

  • If $Q = K$, the system is already at equilibrium.

Characteristics of Q

• Reactants and products are at their equilibrium concentrations when $Q$ is evaluated at equilibrium.

• Used when all concentrations are not at equilibrium – apply the law of mass action using current concentrations instead.

Concept Check

Equilibrium Mixture Scenario

• Given an equilibrium mixture in a closed vessel reacting according to:

  • $H<em>2O(g) + CO(g) \rightleftharpoons H</em>2(g) + CO_2(g)$

  • If more $H_2O(g)$ is added, is $QK$, or $Q=K$?

  • Reaction proceeds right to reestablish equilibrium, adjusting concentrations accordingly.

  • If more $H_2(g)$ is added, what is the effect on $Q$?

  • Reaction proceeds left to reestablish equilibrium and balance concentrations post-disturbance.