Math Problem Statement

What are the equilibrium concentrations in a 0.25 M NH₃ solution for the reaction NH₃(aq) + H₂O(l) ⇌ NH₄⁺(aq) + OH⁻(aq), with Kc = 1.8 × 10⁻⁵?

Solution

The image you've uploaded contains a problem about calculating equilibrium concentrations for the reaction involving ammonia (NH3NH_3) and water, where the equilibrium constant Kc=1.8×105K_c = 1.8 \times 10^{-5}. You need to use the ICE (Initial, Change, Equilibrium) table method to find the equilibrium concentrations for this reaction.

Here's the general approach:

1. Write the balanced chemical equation:

NH3(aq)+H2O(l)NH4+(aq)+OH(aq)NH_3 (aq) + H_2O (l) \rightleftharpoons NH_4^+ (aq) + OH^- (aq)

2. Set up the ICE table:

  • I (Initial): You start with 0.25 M of NH3NH_3 and no NH4+NH_4^+ or OHOH^-.
  • C (Change): As the reaction proceeds to equilibrium, some of the NH3NH_3 will dissociate, producing NH4+NH_4^+ and OHOH^-.
  • E (Equilibrium): At equilibrium, you'll have the concentrations of NH3NH_3, NH4+NH_4^+, and OHOH^-.

The equilibrium expression based on the reaction is:

[ K_c = \frac{[NH_4^+][OH^-]}{[NH_3]} ]

Now, let's go step-by-step to fill the table.

  1. I (Initial):

    • [NH3]=0.25M[NH_3] = 0.25 \, M
    • [NH4+]=0[NH_4^+] = 0
    • [OH]=0[OH^-] = 0
  2. C (Change):

    • Let xx represent the concentration of NH3NH_3 that dissociates. Hence:
      • The change for NH3NH_3 will be x-x.
      • The change for both NH4+NH_4^+ and OHOH^- will be +x+x.
  3. E (Equilibrium):

    • [NH3]=0.25x[NH_3] = 0.25 - x
    • [NH4+]=x[NH_4^+] = x
    • [OH]=x[OH^-] = x

Substitute these into the equilibrium expression:

Kc=xx0.25x=1.8×105K_c = \frac{x \cdot x}{0.25 - x} = 1.8 \times 10^{-5}

Now, you can solve this equation to find xx, and then determine the equilibrium concentrations for each species.

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Math Problem Analysis

Mathematical Concepts

Equilibrium Chemistry
ICE Tables
Quadratic Equations

Formulas

Kc = [NH₄⁺][OH⁻] / [NH₃]
x (concentration change)

Theorems

Le Chatelier's Principle

Suitable Grade Level

Grades 10-12