Examples of ICE Table Calculations for Equilibrium Problems

📚 Quick Study Guide

• ⚖️ Equilibrium is the state where the rates of the forward and reverse reactions are equal, resulting in no net change in reactant and product concentrations.
• 🧊 An ICE table (Initial, Change, Equilibrium) is a tool used to calculate equilibrium concentrations.
• ✍️ Setting up an ICE Table:
  • 📝 Write the balanced chemical equation.
  • 🧪 Create a table with rows for Initial, Change, and Equilibrium concentrations.
  • 📊 Fill in the initial concentrations.
  • 📈 Use 'x' to represent the change in concentration.
  • 🎯 Calculate the equilibrium concentrations in terms of 'x'.
• ➗ The equilibrium constant, $K$, is the ratio of product concentrations to reactant concentrations at equilibrium, each raised to the power of its stoichiometric coefficient. $K = \frac{[Products]}{[Reactants]}$
• 💡Remember to use the quadratic formula if you cannot assume 'x' is small ($x < 5\%$ of the initial concentration). The quadratic formula is: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ for the equation $ax^2 + bx + c = 0$

Practice Quiz

1. Question 1: Consider the reaction: $N_2(g) + 3H_2(g) \rightleftharpoons 2NH_3(g)$. Initially, a reaction vessel contains 1.0 M $N_2$ and 2.0 M $H_2$. At equilibrium, the concentration of $NH_3$ is 0.8 M. What is the value of K?
   1. 0.30
   2. 0.68
   3. 1.78
   4. 2.15
2. Question 2: For the reaction $A(g) \rightleftharpoons B(g) + C(g)$, $K = 2$. Initially, only A is present at a concentration of 3.0 M. What is the equilibrium concentration of B?
   1. 0. 0 M
   2. 1. 0 M
   3. 2. 0 M
   4. 3. 0 M
3. Question 3: For the reaction $2SO_2(g) + O_2(g) \rightleftharpoons 2SO_3(g)$, the initial concentrations are $[SO_2] = 4.0 M$ and $[O_2] = 2.0 M$. At equilibrium, $[SO_3] = 3.0 M$. What is the equilibrium concentration of $O_2$?
   1. 0. 25 M
   2. 0. 50 M
   3. 0. 75 M
   4. 1. 50 M
4. Question 4: Consider the reaction: $H_2(g) + I_2(g) \rightleftharpoons 2HI(g)$. The value of K is 50. Initially, $[H_2] = 1.0 M$ and $[I_2] = 2.0 M$. What is the equilibrium concentration of HI?
   1. 0. 13 M
   2. 0. 26 M
   3. 0. 52 M
   4. 0. 74 M
5. Question 5: For the reaction $PCl_5(g) \rightleftharpoons PCl_3(g) + Cl_2(g)$, $K = 0.042$. Initially, $[PCl_5] = 1.0 M$. What is the equilibrium concentration of $Cl_2$?
   1. 0. 021 M
   2. 0. 205 M
   3. 0. 410 M
   4. 0. 958 M
6. Question 6: For the reaction $CO(g) + H_2O(g) \rightleftharpoons CO_2(g) + H_2(g)$, $K = 4$. Initially, $[CO] = 2.0 M$ and $[H_2O] = 2.0 M$. What is the equilibrium concentration of $CO_2$?
   1. 0. 67 M
   2. 0. 33 M
   3. 1. 67 M
   4. 2. 33 M
7. Question 7: Consider the reaction: $2NO(g) + Cl_2(g) \rightleftharpoons 2NOCl(g)$. Initially, a reaction vessel contains 2.0 M NO and 1.0 M $Cl_2$. At equilibrium, the concentration of $NOCl$ is 1.0 M. What is the value of K?
   1. 0. 29
   2. 0. 57
   3. 1. 14
   4. 2. 29