Ice Box Calculations By: Clifford Beaton

Introduction An ice box is a table that is used for equilibrium calculations when we are given starting concentrations for chemicals. The starting concentrations have to be changed to equilibrium concentrations before they can be used in an equilibrium expression. The I stands for initial, the C for change and the E for equilibrium. An ice box looks like this: Molarity H + Cl - HCl I nitial 1.0M 0.5M 0M C hange -0.3M +0.3M E quilibrium 0.7M 0.2M 0.3M

Example 1 A 10.0L bulb is filled with 4.0 mol of NO (g), 2.0 mol of O 2(g). The gases then reached equilibrium according to the equation 2NO (g) + O 2(g) ↔ 2NO 2(g). At Equilibrium, the bulb only contained 2.8 mol of NO (g). Calculate the K eq for this reaction. Since we aren’t given all of the equilibrium concentrations, we need to use an ice box. First we calculate the initial concentrations and fill them into the ice box. Since we weren’t given a concentration for the product, we assume it starts at 0M. Then with the one given equilibrium concentration, we find the change in concentrations. The concentrations change according to the mol ratio in the balanced equation, so O 2 will change half as much as NO. Generally, reactants are used up and products are produced so the reactants will have negative changes and the products will have positive ones. Then we calculate the K eq. K eq = (0.12) 2 /(0.28) 2 (0.14) = 1.3 Since the K eq is greater than one, the products are favoured. If it was less than one the reactants would be favoured. NO O 2 NO 2 0.4M 0.2M 0M M 0.14M 0.12M

Example 2 You can also use variables to represent the change in concentrations in an ice box. You know you need to use variables if the starting concentrations are given but no equilibrium concentrations are given. For the following reaction, find all equilibrium concentrations if you started off with 0.5M of H 2 and 0.5M of I 2 0.5M and K eq = 32. H 2(g) + I 2(g) ↔ 2HI (g) You start by setting up your equilibrium expression. 32 = (2x) 2 /(0.5-x) 2 Solve for x and you get x = Then you go back to the equilibrium concentrations and plug in x to get 0.13M for H 2 and I 2 and 0.74M for HI. H 2 I 2 HI 0.5M 0M -x +2x 0.5-x 2x

Example 3 Sometimes when using variables, it doesn’t work out so that you can take the square root of every term in the equilibrium expression. For these questions you would need to use the quadratic formula: x = -b ± √(b 2 -4ac) 2a Find all equilibrium concentrations for the following reaction if you begin with 0.2M of PCl 5 and the equilibrium constant is 1.3. PCl 5(g) ↔ PCl 3(g) + Cl 2(g) Again you set up you equilibrium expression. 1.3 = (x) 2 /(0.2-x) This equilibrium expression is a quadratic so you need the quadratic formula to solve for x. Once you solve, you get x = and x = x = gives you negative concentrations so you need to discard it which leaves x = as your answer. Plug it back into the equilibrium concentrations and you get 0.024M for PCl 5 and 0.176M for PCl 3 and Cl 2. PCl 5 PCl 3 Cl 2 0.2M 0M -x +x 0.2-x x x

Ice Boxes for Acids and Bases Ice boxes are often needed for finding the ionization constants for acids or bases. You can use ice boxes to calculate the pH or ionization percentage of an acid. Example: An unknown acid HX has a concentration of 10M and its K a = Find its pH. For this example, you would need the quadratic formula to solve for x but in some cases you can disregard the –x in the ice box. The rule is: if the molarity of the acid divided by the K a is greater than 1000, you can drop the –x because it does not make a significant difference in the calculation. If the number is less than 1000, you need to keep the –x and use the quadratic equation to solve for x. HX H + X - 10M 0M -x +x 10-x x x

Remember Ice boxes are used often for equilibrium calculations and ionization constants for acids and bases. You know you need an ice box when: 1) You are given starting concentrations instead of equilibrium calculations. 2) You are dealing with ionization constants for weak acids or bases (K a or K b ) The ICE in ice box stands for I nitial, C hange, E quilibrium. Only equilibrium concentrations are used in an equilibrium expression. Always make sure the chemical equation is balanced before you find the changes in concentrations because they are related to the mol ratio.

THE END Information provided by Mr. Therrien’s Chemistry 12 booklet. + = HCl H + Cl - I1M0M C E0.5