pH Calculations Involving Weak Acids

Need help preparing for the General Chemistry section of the MCAT? MedSchoolCoach expert, Ken Tao, will teach everything you need to know about pH calculations of weak acids. Watch this video to get all the MCAT study tips you need to do well on this section of the exam!
Weak acids are weak electrolytes, only partially dissociating in an aqueous solution. Knowing this, we cannot make the assumption that the concentration of weak acid is equal to the concentration of hydronium in an acidic solution. The calculations for the pH of weakly acidic solutions are more involved than the calculations for strong acids, and require you to interpret acid-base equilibria.
Weak Acids
Weak acids dissociate to different degrees, depending on the identity of the weak acid. To give you an idea of acid strength, the MCAT will provide you with either the Ka or pKa of the acid. Given the concentration of weak acid and the Ka the acid, we can use an ICE table to set up an equilibrium expression and solve for hydronium concentration. Given a solution of 5 x 10-3 M acetic acid, which has a Ka of 1.8 x 10-5, what is the pH of the solution?
An ICE table organizes the initial concentrations and final concentrations of compounds participating in an acid-base reaction. In order to setup an ICE table, you need to create a column for every reactant and every product, as well as three rows in which you will track the concentrations of compounds from start to finish. Given the equilibria between acetic acid and acetate, we can begin to construct the horizontal and vertical labels of an ICE table. Next, we want to indicate the concentrations of compounds at the beginning and end of the reaction. For now, we have only been provided with the concentration of acetic acid, so we can write the initial concentration of acetic acid to be [CH3COOH] - a known value. Based on our reaction, for every 1 mole of acetic acid that ionizes, one mole of acetate and one mole of hydrogen ion are formed. On our ICE table, we can represent this statement in the “change” row, which is the change in concentration of compounds from the beginning to the end of the reaction. Because the change in concentration of acetic acid is equal and opposite to that of acetate and hydrogen ion, we can say that for every “X” moles of acetic acid broken down, “X” moles of acetate and hydrogen ion form. The equilibrium row tells us the concentration of compounds once the reaction has reached an equilibrium. In this case, the reaction started with acetate of concentration equal to [CH3COOH], so the final concentration of acetic acid will be “[CH3COOH] - X”. Since X moles of acetic acid are breaking down, X moles of acetate and hydrogen ion form. These are all recorded in the ICE table below.
The “equilibrium” row on the ICE table denotes the concentrations of products and reactants at reaction equilibria. Recall that the ratio of products to reactants is equal to the Ka of a reaction, which we were provided. Therefore, we can set the Ka of the reaction equal to the ratio of products to reactants for the given reaction, and substitute in the concentrations for each compound provided by the equilibrium row of the ICE table. Since we are interested in the pH of the solution, we are interested in the concentration of hydrogen ions at equilibrium, given by X. Knowing this, we can solve our equation for X. When we do this, we notice that X can be expressed in terms of the known quantities Ka and [CH3COOH]. Plugging these values in, we find that X = 3 x 10-4, which is the concentration of hydrogen ions in the solution.
To find the pH of the solution, we can take the negative log of hydronium concentration. However, given the difficulty of calculating -log[3 x 10-4] by hand, we can estimate the pH to be between -log[1 x 10-4], which equals 3, and -log[10 x 10-4], which equals 4. The pH can thus be expressed as 3 less than pH less than 4.
There is a shortcut for calculating the pH of a weakly acidic or basic solution. All of the steps for the calculation of the pH of this weakly acidic solution can be simplified into the single expression below. Anytime you are given the Ka and starting concentration of some weak acid, the shortcut equation can be used. All of the steps for calculating the pH of a weakly acidic solution are the same for calculating the pOH of a weakly basic solution. Therefore, the same shortcut can be used to find the pOH of a basic solution, albeit with the values for Kb and concentration of weak base.
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