pH of Weak Acids: Videos & Practice Problems

Hydronium Ion Concentration Example

To calculate the hydronium ion concentration for a 0.30 M solution of hydrocyanic acid (HCN), we first recognize that HCN is a weak acid, indicated by its acid dissociation constant (Ka) of \(4.9 \times 10^{-10}\), which is less than 1. This means it does not fully dissociate in solution.

We begin by setting up an ICE (Initial, Change, Equilibrium) table to analyze the dissociation of HCN in water. The dissociation reaction can be represented as:

\[ \text{HCN} + \text{H}_2\text{O} \rightleftharpoons \text{H}_3\text{O}^+ + \text{CN}^- \]

In the ICE table, we denote the initial concentration of HCN as 0.30 M, while the initial concentrations of the products, hydronium ions (\(H_3O^+\)) and cyanide ions (\(CN^-\)), are both 0. The changes in concentration as the reaction reaches equilibrium are represented as follows:

Initial:
\[\text{[HCN]} = 0.30, \quad \text{[H}_3\text{O}^+] = 0, \quad \text{[CN}^-] = 0\]

Change:
\[\text{[HCN]} = -x, \quad \text{[H}_3\text{O}^+] = +x, \quad \text{[CN}^-] = +x\]

At equilibrium, the concentrations are:

Equilibrium:
\[\text{[HCN]} = 0.30 - x, \quad \text{[H}_3\text{O}^+] = x, \quad \text{[CN}^-] = x\]

Next, we can express the equilibrium constant expression for the dissociation of HCN:

\[ K_a = \frac{[\text{H}_3\text{O}^+][\text{CN}^-]}{[\text{HCN}]} \]

Substituting the equilibrium concentrations into the expression gives:

\[ 4.9 \times 10^{-10} = \frac{x^2}{0.30 - x} \]

To simplify the calculation, we can apply the 500 approximation method. This method allows us to ignore the \(-x\) in the denominator if the ratio of the initial concentration to \(K_a\) is greater than 500. Here, we calculate:

\[ \frac{0.30}{4.9 \times 10^{-10}} \approx 6.12 \times 10^8 \] (which is indeed greater than 500)

Thus, we can simplify our equation to:

\[ 4.9 \times 10^{-10} = \frac{x^2}{0.30} \]

Cross-multiplying gives:

\[ x^2 = 4.9 \times 10^{-10} \times 0.30 = 1.47 \times 10^{-10} \]

Taking the square root of both sides yields:

\[ x = \sqrt{1.47 \times 10^{-10}} \approx 1.2 \times 10^{-5} \, \text{M} \]

Since \(x\) represents the concentration of hydronium ions at equilibrium, we conclude that the hydronium ion concentration for the 0.30 M solution of hydrocyanic acid is:

\[ [H_3O^+] = 1.2 \times 10^{-5} \, \text{M} \]

Calculating Percent Ionization of Weak Acids

Percent ionization, also known as percent dissociation, is a crucial concept in understanding the behavior of weak acids in aqueous solutions. It quantifies the extent to which a weak acid can ionize, reflecting its strength as an electrolyte. Unlike strong acids, which fully ionize (100%) in solution, weak acids only partially ionize, resulting in a percentage that is less than 100%.

To calculate the percent ionization of a weak acid, the following formula is used:

\[\text{Percent Ionization} = \left( \frac{[\text{H}_3\text{O}^+]}{[\text{HA}]_0} \right) \times 100\]

In this equation, \([\text{H}_3\text{O}^+]\) represents the equilibrium concentration of hydronium ions, while \([\text{HA}]_0\) denotes the initial concentration of the weak acid before any ionization occurs. To find the equilibrium concentration of hydronium ions, one can either be provided with this value or calculate it using an ICE (Initial, Change, Equilibrium) chart, which helps track the changes in concentration throughout the ionization process.

Understanding percent ionization is essential for predicting the behavior of weak acids in various chemical contexts, as it provides insight into their reactivity and strength in solution.

Percent Dissociation Example

To calculate the percent dissociation of acetic acid, we start with its initial concentration, which is given as 4.10 × 10⁻¹ M (or 0.410 M). Acetic acid is a weak acid, indicated by its acid dissociation constant (K_a) value of 1.8 × 10⁻⁵, which is less than 1. This means that it does not fully dissociate in solution.

We can set up an ICE (Initial, Change, Equilibrium) chart to analyze the dissociation of acetic acid (CH₃COOH) in water:

Species	Initial (M)	Change (M)	Equilibrium (M)
CH3COOH	0.410	−x	0.410 − x
H3O+	0	+x	x
CH3COO−	0	+x	x

Next, we can write the expression for the acid dissociation constant:

K_a = \(\frac{[H_3O^+][CH_3COO^-]}{[CH_3COOH]}\)

Substituting the equilibrium concentrations into the expression gives us:

1.8 × 10⁻⁵ = \(\frac{x \cdot x}{0.410 - x}\)

To simplify the calculation, we can use the 500 approximation method. This method states that if the ratio of the initial concentration to K_a is greater than 500, we can ignore the term "−x" in the denominator. Here, we calculate:

\(\frac{0.410}{1.8 \times 10^{-5}} \approx 22,777.8\), which is indeed greater than 500.

Thus, we can simplify our equation to:

1.8 × 10⁻⁵ = \(\frac{x^2}{0.410}\)

Cross-multiplying gives:

x² = 1.8 × 10⁻⁵ × 0.410 = 7.38 × 10⁻⁶

Taking the square root of both sides, we find:

x = 2.717 × 10⁻³ M

This value of x represents the concentration of H₃O⁺ at equilibrium. To find the percent dissociation, we use the formula:

Percent Dissociation = \(\frac{[H_3O^+]}{[CH_3COOH]_{initial}} \times 100\)

Substituting the values we have:

Percent Dissociation = \(\frac{2.717 \times 10^{-3}}{0.410} \times 100 \approx 0.66\%\)

This indicates that approximately 0.66% of the acetic acid dissociates in solution, which is consistent with the behavior of weak acids.

An unknown weak acid has an initial concentration of 0.55 M. What is the pH of the solution if the weak acid also has a pK_a of 5.79?

• A. 0.60
• B. 6.05
• C. 3.02
• D. 5.75

Answer: (C)

Here's what students ask on this topic:

What is the role of an ICE chart in calculating the pH of weak acids?

An ICE chart, which stands for Initial, Change, Equilibrium, is essential for calculating the pH of weak acids because these acids only partially dissociate in aqueous solutions. The chart helps organize the concentrations of the acid and its ions at different stages: the initial concentration before dissociation, the change in concentration as the acid dissociates, and the equilibrium concentration after dissociation. Since weak acids do not fully ionize, the ICE chart allows you to calculate the equilibrium concentrations of hydronium ions (_H3O⁺) and the remaining acid. These values are necessary to determine the pH, which is related to the hydronium ion concentration. The acid dissociation constant, K_a, is used alongside the ICE chart to solve for unknown concentrations, making it a critical tool in weak acid pH calculations.

How do you calculate the percent ionization of a weak acid?

Percent ionization of a weak acid indicates the fraction of the acid that dissociates into ions in solution. It is calculated using the formula: $\mathrm{Percent Ionization}=\frac{\mathrm{[H₃O⁺]_equilibrium}}{\mathrm{[HA]_initial}}\times 100$. Here, $\mathrm{[H₃O⁺]}$ is the hydronium ion concentration at equilibrium, and $\mathrm{[HA]}$ is the initial concentration of the weak acid. To find the equilibrium hydronium concentration, you often use an ICE chart or it may be provided. Since weak acids only partially ionize, the percent ionization is always less than 100%, reflecting their weaker acidic nature compared to strong acids.

Why do weak acids require the use of the acid dissociation constant (Ka) in pH calculations?

The acid dissociation constant, K_a, quantifies the strength of a weak acid by expressing the equilibrium constant for its dissociation into ions. Because weak acids do not fully ionize, K_a helps determine the extent of ionization in solution. In pH calculations, K_a is used with an ICE chart to relate the initial concentration of the acid to the equilibrium concentrations of the acid and hydronium ions. This relationship allows you to solve for the hydronium ion concentration, which is necessary to calculate the pH. Without K_a, it would be impossible to accurately determine how much the weak acid dissociates, making it a crucial parameter in understanding and calculating the pH of weak acid solutions.

How does the partial ionization of weak acids affect their pH compared to strong acids?

Weak acids partially ionize in aqueous solutions, meaning only a fraction of the acid molecules release protons (^H+) to form hydronium ions (_H3O⁺). This partial ionization results in a lower concentration of hydronium ions compared to strong acids, which ionize completely. Consequently, weak acids have higher pH values (less acidic) than strong acids at the same concentration. The degree of ionization is quantified by the acid dissociation constant (K_a) and can be calculated using an ICE chart. Understanding this difference is important because it explains why weak acids do not produce as many hydronium ions and thus have a less pronounced effect on the pH of a solution.

What units are used in an ICE chart when calculating the pH of weak acids?

In an ICE chart used for weak acid pH calculations, concentrations are expressed in molarity (M), which is moles of solute per liter of solution. This unit is essential because the acid dissociation constant (K_a) and equilibrium expressions are based on molar concentrations. The ICE chart tracks the initial molarity of the weak acid, the change in molarity as the acid dissociates, and the equilibrium molarity of all species involved, including the hydronium ion concentration. Using molarity ensures consistency and accuracy in calculating the pH, which depends on the hydronium ion concentration at equilibrium.