Genchem 15.4

Equilibrium Concept

• Definition of Equilibrium

  • When the rates of the forward reaction become equal to the rate of the reverse reaction, dynamic equilibrium occurs.

  • At equilibrium, the reaction will proceed back and forth indefinitely unless affected by external factors.

Predicting Direction of Reactions with Reaction Quotient

• Introduction to Reaction Quotient (Q)

  • Used to determine if a reaction is at equilibrium or in progress.

  • Defined similarly to equilibrium constant (K) with the formula:

  • $Q=\frac{[products]^{coefficients}}{[reactants]^{coefficients}}$

  • Concentrations used in q can be from any point during the reaction.

• Comparison of q and K

  • To understand the direction of the reaction:

  • If Q<K Forward reaction occurs (toward products).

  • If Q>K Reverse reaction occurs (toward reactants).

  • If $Q=K$ → System is at equilibrium.

Solving Equilibrium Concentration Problems

Initial Setup

• Problems involving equilibrium concentrations when given initial concentrations and equilibrium constant (K) are fundamentally calculated using an ICE chart.

  • ICE chart structure includes:

  • Initial concentrations,

  • Changes represented by x,

  • Equilibrium concentrations.

Example Problem Overview

• A sample problem is presented involving a reaction between hydrogen gas (H₂) and iodine gas (I₂):

  • Chemical reaction: $H<em>{2(g)} + I</em>{2(g)} \rightleftharpoons 2HI_{(g)}$

• Initial concentrations given in moles, to be converted to molarity since the volume is one liter.

Step-by-step Calculation

1. Initial Concentrations:

   • H₂ = 1 mol (1 M),

   • I₂ = 2 mol (2 M),

   • HI = 0.

2. Equilibrium Constant (K):

   • Given $K_{c} = 50.5$.

3. Set Up ICE Chart:

   • Initial:

     • H₂: 1 M,

     • I₂: 2 M,

     • HI: 0 M.

   • Change as follows:

     • H₂: -x,

     • I₂: -x,

     • HI: +2x.

   • Equilibrium:

     • H₂: $1 - x$,

     • I₂: $2 - x$,

     • HI: $2x$.

4. K Expression:

   • $K<em>{c} = \frac{[HI]^2}{[H</em>2][I_2]}$ import

   • Substitute equilibrium concentrations:

   • $50.5 = \frac{(2x)^2}{(1-x)(2-x)}$.

   • Simplify to find:

   • $50.5 = \frac{4x^2}{(1-x)(2-x)}$.

5. Algebraic Rearrangement:

   • Multiply both sides by the denominator to eliminate fractions.

   • Rearranging leads to a quadratic equation:

   • $4x^2 - (50.5)(2 - 3x + x^2) = 0$.

6. Quadratic Formula Use:

   • Standard form: $ax^2 + bx + c = 0$,

   • Coefficients derived from the rearranged equation: $a = 46.5, b = -151.5, c = 101$.

   • Solve using: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$.

7. Calculating x:

   • Calculate numerical values,

   • Positive roots considered as valid solutions.

8. Find Equilibrium Concentrations:

   • Calculate:

     • H₂ at equilibrium = $1 - x$,

     • I₂ at equilibrium = $2 - x$,

     • HI at equilibrium = $2x$.

Summary of Procedure for Different Problems

• Identifying if your starting values for x, y, etc., lead to valid equilibrium concentrations is crucial.

• Understand how to differentiate between problems where equilibrium concentrations are given versus when K and initial concentrations are provided.

• Always ensure clarity in calculations to avoid errors, especially when using the quadratic formula,

• Recognize that only valid physical concentrations (i.e., positive values) will be meaningful in a reaction context.

Upcoming Topics and Advancements

• Prepare to explore the concepts of pressure equilibrium with associated problems as they relate to gas reactions.

• Consider implications of temperature adjustments on K values across different reactions and the necessity of leveraging the correct constants in calculations.