Question

Follow the directions of Question 64. Consider two beakers: Beaker A has a weak acid \(\left(K_{\mathrm{a}}=1 \times 10^{-5}\right)\) Beaker B has HCl. The volume and molarity of each acid in the beakers are the same. Both acids are to be titrated with a \(0.1 \mathrm{M}\) solution of \(\mathrm{NaOH}\) (a) Before titration starts (at zero time), the pH of the solution in Beaker \(A\) is _________ the \(p H\) of the solution in Beaker B. (b) At half-neutralization (halfway to the equivalence point), the \(\mathrm{pH}\) of the solution in Beaker \(\mathrm{A}\) __________ the \(\mathrm{pH}\) of the solution in Beaker \(\mathrm{B}\). (c) When each solution has reached its equivalence point, the \(\mathrm{pH}\) of the solution in Beaker \(\mathrm{A} \) _________ the \(\mathrm{pH}\) of the solution in Beaker B. (d) At the equivalence point, the volume of \(\mathrm{NaOH}\) used to titrate HCl in Beaker B ________ the volume of \(\mathrm{NaOH}\) used to titrate the weak acid in Beaker A.

Short answer

Answer: Due to the limitations of the information provided and without the specific concentrations of both acids, it is not possible to directly compare the acidity of the solutions in Beaker A and Beaker B. However, we can still analyze the complexity of calculating the pH of a strong acid (HCl) versus a weak acid. Determining the stronger acid depends on their specific initial concentrations, not just their dissociation constants (Ka).

Step-by-step solution

Calculate the concentration of H+ in Beaker A

To calculate the concentration of H+ ions in Beaker A, we can use the Ka expression: Ka = [H+][A-]/[HA] Given Ka = 1 x 10^(-5), we can assume that the initial concentration of the weak acid is "c" and the dissociation is small (x). Therefore, we can rewrite the Ka expression as follows: 1 x 10^(-5) = (x)(x)/(c-x) Since x is drastically smaller than c, we can simplify the equation as follows: 1 x 10^(-5) = x^2/c

Calculate the concentration of H+ in Beaker B

As HCl is a strong acid, it will dissociate completely in water. Therefore, the concentration of H+ ions in Beaker B will be equal to the initial concentration of HCl. Let the initial concentration of HCl be [HCl]. Then, the concentration of H+ ions in Beaker B is [HCl].

Calculate the pH of both solutions

Now that we have the concentration of H+ ions for both solutions, we can calculate the pH using the pH formula: pH = -log[H+] For Beaker A: pH(A) = -log(x) For Beaker B: pH(B) = -log[HCl]

Compare the pH values

Comparing the pH values of both solutions will allow us to analyze the acidity of these solutions. The lower the pH value, the higher the acidity. If pH(A) < pH(B), then the solution in Beaker A is more acidic. If pH(A) > pH(B), then the solution in Beaker B is more acidic. If pH(A) = pH(B), both solutions have the same acidity.

Key concepts

pH Calculation

Calculating pH is a fundamental aspect of chemistry, involving the measurement of the acidity or alkalinity of a solution. The pH scale runs from 0 to 14, with 7 being neutral. Values below 7 indicate acidic solutions, while those above 7 denote basic or alkaline solutions.

In the context of the exercise, we need to calculate the pH for both a weak acid (in Beaker A) and a strong acid (in Beaker B). For the weak acid, the calculation involves a consideration of its acid dissociation constant (Ka), which is a measure of its ability to donate protons in solution.

To estimate the pH of the weak acid in Beaker A, we assume a small degree of dissociation and simplify the Ka expression to Ka \(= x^2/c\). Subsequently, with the calculated H+ concentration (x), we use the pH formula: \(\text{pH} = -\log[H+]\).

In contrast, strong acids like HCl in Beaker B disassociate completely, so their H+ concentration is equal to their original molarity. This allows for direct pH calculation without the need for the Ka expression. Once we have the concentrations, calculating their respective pH values is straightforward by applying the formula \(\text{pH} = -\log[H^+]\). This step is critical for determining the nature of the solution at the start of the titration process.

Weak Acid Dissociation

Weak acid dissociation refers to the incomplete separation of a weak acid into its ions in an aqueous solution. Unlike strong acids, which completely dissociate into their ions, weak acids partially ionize in water, resulting in an equilibrium between undissociated molecules and ions.

In the exercise, Beaker A contains a weak acid with a given Ka, a reflection of its ionization strength. The dissociation can be represented by the chemical equation HA \(\rightleftharpoons H^+ + A^-\), with the varying concentrations described by the expression \(K_{a} = \frac{[H^+][A^-]}{[HA]}\).

To calculate the degree of dissociation, we use an \(x\) to symbolize the amount of weak acid that ionizes, thus producing \(x\) moles of \(H^+\) and \(A^-\) ions. Since the dissociation is slight and \(x\) small, the initial concentration of \(HA\) can be approximated as unchanged (i.e., \(c - x \approx c\)).

Featuring this approximation, the \(K_{a}\) expression turns into \(K_{a} = \frac{x^2}{c}\), leading us to solve for \(x\), the concentration of the H+ ions, which plays a crucial role in when calculating pH. This concept is vital for understanding the initial acidity of our weak acid solution and setting the stage for the titration analysis.

Titration Equivalence Point

The equivalence point in a titration is the moment where the quantity of titrant added is exactly the same as the quantity of substance present in the sample. For acid-base titrations, this is the point at which the amount of acid equals the amount of base, and all the analyte (the acid in our case) has reacted with the titrant (the base).

In an acid-base titration, the equivalence point is often identified by a marked pH change and is usually accompanied by a color change if an indicator is used. For instance, in Beaker A, titrating the weak acid with \(NaOH\), the equivalence point pH will be greater than 7 due to the formation of the conjugate base of the weak acid, which slightly ionizes in water, making the solution slightly basic.

Conversely, the titration of a strong acid like HCl in Beaker B with \(NaOH\) results in an equivalence point pH of about 7, as the \(NaCl\) produced does not affect the pH of the solution.

This concept is crucial in predicting the outcome of the titration process in parts (b) and (c) of the exercise. Understanding the equivalence point helps in the selection of proper indicators for the titration and also in analyzing the titration curve, which shows the pH change over the volume of titrant added. The comparison of equivalence points between weak and strong acids in the exercise enhances the grasp of acid-base titration complexities.