- An Initial, Change, Equilibrium (ICE) table can help determine the final amount of each species after a chemical reaction.
- Strong acids/bases react completely in water, so all of the acid/base is shown reacting in the change row of an ICE table.
- The amounts of H3O+ or HO− in the equilibrium row of an ICE table can be used to calculate the pH or pOH respectively.
When adding an acid or base to water, we are often interested in knowing how acidic (or basic) the resulting solution is. The acidity is related to how much H3O+ is in the solution, so pH is often used to describe the acidity of a solution. Likewise, pOH can describe the basicity of a solution. A common approach to determining the pH (or pOH) of a solution after adding an acid or base to water involves using an ICE (initial, change, equilibrium) table. Here we will discuss how to use an ICE table to determine the pH/pOH of a solution made with a strong acid or strong base, but this approach is equally valid for other chemical reactions as well.
Whenever you are asked to solve for the pH or pOH of a solution following an acid-base reaction, follow the steps below:
- Write out the balanced chemical reaction at the top.
- Draw an ICE table below the chemical reaction by labelling initial (I), change (C), and equilibrium (E) rows. Fill in the initial amounts (in moles or concentration based on total volume) for each chemical species in the “I” row. You can ignore H2O, since its concentration is generally large enough to not change significantly during the course of the reaction and will not be needed in subsequent calculations.
- Fill in how much you expect the amount of each species to change in the “C” row. Usually, reactants are disappearing so will have negative values and products are appearing so will have positive values. Remember to take the stoichiometry of the reaction into account.
- Add the values in the column below each chemical species and fill in the sum in the equilibrium “E” row.
- Use the equilibrium concentration of H3O+ or HO− to solve for the pH or pOH.
Let’s apply these steps to solve for the pH after adding a strong acid to water. Suppose we were asked to determine the pH if 0.79 moles of HCl are added to 1.3 L of water. First, let's calculate the concentration of HCl to use as the initial amount in the ICE table:
It would also be okay to keep the amount of HCl in moles for the ICE table, but since we'll ultimately need the concentration of H3O+ to calculate the pH it's helpful to convert all amounts to concentrations from the beginning. Now, let’s construct the ICE table using steps 1-4 above, then determine the pH using step 5:
- Write out the reaction between HCl and water:
- Draw an ICE table and add initial amounts:
- This is a strong acid, so it all reacts with water:
- Add the amounts in each column to get the equilibrium concentrations:
- Use the equilibrium concentration of H3O+, 0.608 M, to calculate the pH:
Notice that we kept an additional significant figure for all intermediate calculations (three) to prevent rounding errors, but gave our final answer with two significant figures to match the data given in the question. This method may seem tedious when solving for the pH or pOH of a strong acid/base solution, and you are welcome to skip writing out the full ICE table once you are comfortable with how to solve these types of questions. However, the full ICE table approach will be helpful to write out as we attempt more complex questions in later sections.
Avoid this common error with significant figures when using logarithmic scales like pH
Typically, we would consider a value of 12.35 to have four significant figures, 1.72 to have three significant figures and 0.95 to have two significant figures. However, for logarithmic scales like pH, pOH, pKa, and pKb, only the numbers after the decimal place count as significant. For example, pH values of 12.35, 1.72, and 0.95 all have only two significant figures. To understand the reason for this, consider the value written in scientific notation with three significant figures. If we take the logarithm of this value,
, we get 3.554. The 3 before the decimal place accounts for the 103 component in scientific notation (which does not contribute to the number of significant figures). The 3.58 component of the number in scientific notation (which contributes all three significant figures) is accounted for after the decimal place (.554) when represented as a logarithm. That is, in logarithmic scales only the numbers after the decimal place contribute to the number of significant figures.
Try solving each of the examples below on your own before expanding to view the solutions.
View solution:
The total number of moles of HBr is:
The total volume of the solution is:
Thus, the concentration of HBr based on the total volume is:
Next, construct the ICE table:
From the ICE table, the equilibrium concentration of H3O+ is 0.154 M, so the pH of the diluted solution is
Example 2: What is the pOH of a 0.0589 M solution of NaOH?
View solution:
The amount of NaOH is already given as a concentration based on total volume, so we can start with the ICE table:
The H2O above the arrow in the reaction shows that NaOH is dissociating when dissolved in water. From the ICE table, the equilibrium concentration of HO− is 0.0589 M, so the pOH of this solution is
Example 3: What is the pOH when 0.79 moles of HCl are added to 1.3 L of water at 298 K?
View solution:
This question is almost identical to the example in the text above, except that we're asked to calculate the pOH instead of the pH. As shown in the ICE table in the text above, the equilibrium concentration of H3O+ is 0.608 M and the pH of this solution is . At 298 K,
and so the pOH is given by
Interactive: