Question

Would you expect the \(\mathrm{pH}\) of \(0.010 \mathrm{M}\) acetic acid to be higher or lower than \(2.0\) ?

Short answer

The pH of a 0.010M acetic acid solution is slightly above 2.0.

Step-by-step solution

Determine the Ionization of Acetic Acid

As a weak acid, acetic acid ( \(CH_3COOH\) ) partially ionizes in water: \( CH_3COOH \rightleftharpoons H^+ + CH_3COO^- \). Now since we know the concentration of the acetic acid. We can apply the ionization constant \(Ka\) for acetic acid. Because we're talking about a weak acid, we should note that not all of the \( CH_3COOH \) molecules ionize, only a small portion do, so the \( H_3O^+ \) ( or \(H^+\)) concentration is significantly less than \(0.010 M\).

Use the Ionization Constant to Find Hydronium Ion Concentration

Now we have to use the ionization constant (\( Ka \)) for acetic acid, which is \(1.8 * 10^{-5}\) at 25 degrees Celsius. We know that \( Ka = [CH_3COO-][H3O^+] / [CH_3COOH] \). Assuming x much of the acetic acid molecules ionize, we can say that the ion concentration is x. So, \( Ka = x^2/0.010 \). Solving this equation for x gives us the concentration of the hydronium ions.

Calculate the pH Value

Having the H3O+ ion concentration, the pH is calculated as the negative log of the H3O+ ion concentration: \( pH = -\log[H_3O^+] \). Use this formula to calculate the pH.

Key concepts

Weak Acid Ionization

Understanding weak acid ionization is pivotal when studying chemistry, especially in the context of pH calculation. Acetic acid, denoted as CH₃COOH, is a classic example of a weak acid that only partially ionizes in water. This ionization is represented by the reversible chemical equation:
\( CH_3COOH \rightleftharpoons H^+ + CH_3COO^- \).
When acetic acid ionizes, it releases hydrogen ions (H+) and acetate ions (CH₃COO⁻). The important thing to remember here is that not all molecules of acetic acid will disassociate; instead, a dynamic equilibrium is established between the ionized and non-ionized forms of the acid. In a solution of 0.010 M acetic acid, the concentration of ionized acetic acid will be significantly less than the initial concentration, because weak acids have limited ionization in water.

Ionization Constant (Ka)

To quantify the extent of ionization for weak acids, we use the ionization constant (\(Ka\)). This value is unique for each weak acid and indicates the strength of the acid's tendency to donate protons in an aqueous solution.
The relationship of the acid dissociation in solution can be expressed with the formula: \( Ka = \frac{[CH_3COO^-][H^+]}{[CH_3COOH]} \), where the concentrations of the products (ionized form) are in the numerator and the concentration of the reactant (non-ionized form) is in the denominator. For acetic acid, the value of Ka is typically around 1.8 x 10⁻⁵ at 25 degrees Celsius. This low value reflects the weak acid's characteristic of being only partially ionized in solution. When calculating ion concentrations, given the concentrations of other species in the equation, we can reformulate the equilibrium expression to solve for the unknown ionization level.

Hydronium Ion Concentration

The concentration of hydronium ions (\(H_3O^+\)), sometimes referred to as hydrogen ions (\(H^+\)), is a direct indicator of the acidity of a solution. For weak acids like acetic acid, calculating the concentration of hydronium ions requires an understanding of the extent of the acid's ionization as well as the ionization constant, Ka.
Assuming the variable 'x' represents the extent to which the acid ionizes (i.e., the concentration of the acid that ionizes to form hydronium ions), we can use the equilibrium expression \( Ka = \frac{x^2}{0.010 - x} \) to solve for 'x'. The assumption that \( Ka \approx \frac{x^2}{0.010} \) holds true when the degree of ionization is very small compared to the initial concentration of the acid, simplifying our calculations. Calculating 'x' allows us to determine the hydronium ion concentration, which is crucial for the calculation of pH.

pH Calculation

The pH of a solution is a logarithmic scale used to quantify the acidity or basicity of an aqueous solution. It is calculated as the negative base-10 logarithm of the hydronium ion concentration. The formula is \( pH = -\text{log}[H_3O^+] \).
In the context of a 0.010 M acetic acid solution, after determining the concentration of hydronium ions with the ionization constant and the initial concentration of the acid, we can plug that value into the aforementioned pH formula. Since we deal with weak acid ionization, the resulting pH will not be as low as for strong acids, translating to a pH value above 2. The precise pH value depends on the exact concentration of hydronium ions, which is calculated from 'x', as defined in the earlier steps for the ionization of acetic acid. To sum up, the pH provides a convenient and powerful way to convey the acid strength and behavior in solution.