15.6
Weak Acid Solutions
Few compounds act as strong acids. A far greater number of compounds behave as weak acids and only partially react with water, leaving a large majorit…
A weak acid, like hydrocyanic acid, is a Brønsted acid as it donates a proton to the water molecule and produces the hydronium ion. A weak acid dissociates partially in water according to its acid dissociation constant, Ka, which is 4.9 × 10−10 for hydrocyanic acid.
For hydrocyanic acid, the Ka is equal to the concentration of hydronium times the concentration of cyanide ions divided by the concentration of hydrocyanic acid.
The acid dissociation constant, Ka, can be used to determine the hydronium ion concentration in a weak acid solution and consequently, the pH of the solution.
The concentration of hydronium ions and the pH of a 0.15 molar solution of hydrocyanic acid can be calculated using its equilibrium expression and an ICE table.
The concentrations of hydrocyanic acid, hydronium, and cyanide initially and at equilibrium can be expressed in a table that shows the Initial, Change, and Equilibrium concentrations of each of the molecules.
To reach equilibrium, the initial concentration of the reactants decreases as the initial concentration of the products increases according to their molar ratios. This change in the concentration of the reactants and products is denoted by x.
Substituting equilibrium concentrations in the expression for the Ka yields x times x divided by 0.15 minus x.
In many weak acids, x, the amount of dissociation, is likely to be very small compared to the initial concentration of 0.15 molar. 0.15 minus x can be assumed to be approximately 0.15.
When the equation is solved, x equals 8.6 × 10−6 molar.
The approximation, 0.15 minus x equal to 0.15, is valid only if x is less than 5% of 0.15 molar. Here, x is 0.0057% of 0.15 molar and hence this approximation is valid.
Therefore, the concentration of hydronium is 8.6 × 10−6 molar. To determine the pH, take the negative log of the hydronium ion concentration. Solving this shows the pH of the 0.15 M hydrocyanic acid solution is 5.07.
The pH of a solution can be used to determine the Ka of a weak acid.
For example, acetic acid dissociates partially into hydronium ions and acetate ions when dissolved in water. The Ka for acetic acid can be expressed as the hydronium ion concentration times the acetate ion concentration divided by the concentration of acetic acid.
If the pH of a 0.20 molar acetic acid solution is 2.72, its hydronium concentration can be calculated, which is 1.9 × 10−3 molar.
The ICE table can be constructed from the initial and equilibrium concentrations of the acetic acid, hydronium ions, and acetate ions.
Using significant figures, 0.20 minus 1.9 × 10−3 is essentially equal to 0.20. By substituting the equilibrium values into the Ka expression, Ka equals 1.8 × 10−5.
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Q1: What is a weak acid and how does it differ from a strong acid?
A weak acid only partially dissociates in water, leaving most dissolved molecules in their original form and generating relatively few hydronium ions. Unlike strong acids that completely ionize, weak acids establish an equilibrium between the molecular and ionic forms. Common examples include acetic acid in vinegar and formic acid in ant venom, where only about 1% of molecules ionize under typical conditions.
Q2: How is the acid dissociation constant (Ka) used to calculate pH?
The Ka value expresses the ratio of product to reactant concentrations at equilibrium. By substituting equilibrium concentrations into the Ka expression and solving for hydronium ion concentration, you can determine pH using the negative logarithm. For example, hydrocyanic acid with Ka = 4.9 × 10−10 yields a hydronium concentration of 8.6 × 10−6 M, corresponding to a pH of 5.07.
Q3: What is an ICE table and why is it useful for weak acid calculations?
An ICE table tracks Initial, Change, and Equilibrium concentrations of reactants and products during a weak acid dissociation. It systematically organizes how concentrations shift as the system reaches equilibrium, with changes denoted by x. This method simplifies substitution into the Ka expression and helps verify whether simplifying assumptions, such as neglecting x compared to initial concentration, are valid.
Q4: When can you assume that x is negligible in weak acid equilibrium calculations?
The assumption that x is negligible is valid when x is less than 5% of the initial acid concentration. For instance, in a 0.15 M hydrocyanic acid solution, x equals 8.6 × 10−6 M, which is only 0.0057% of 0.15 M, well below the 5% threshold. This simplification allows you to approximate (initial concentration − x) as simply the initial concentration, streamlining calculations.
Q5: How can you determine Ka from the pH of a weak acid solution?
Convert pH to hydronium ion concentration using the antilog function, then construct an ICE table with this equilibrium value. Calculate the change in concentration from the initial acid concentration and hydronium concentration. Finally, substitute all equilibrium values into the Ka expression to solve for the dissociation constant, as demonstrated with nitrous acid where pH 2.34 yields Ka = 4.6 × 10−4.
Q6: Why is the initial hydronium ion concentration from water autoionization usually neglected?
Water autoionization produces only 1 × 10−7 M hydronium ions, which is typically much smaller than the hydronium concentration generated by the weak acid itself. Since this contribution is negligible compared to the acid's ionization, it is treated as approximately zero in ICE tables. This simplification does not significantly affect the accuracy of Ka or pH calculations for weak acid solutions.
Q7: What are common examples of weak acids and where are they found?
Weak acids are abundant in nature and everyday products. Acetic acid is the main ingredient in vinegar, formic acid causes the sting of ant bites, and hydrocyanic acid is a Brønsted acid that donates protons to water. Weak acids are also responsible for the tangy taste of citrus fruits and unpleasant smells in body odor, making them chemically and biologically significant compounds.