pH of Weak Bases: Videos & Practice Problems

Weak bases, characterized as weak electrolytes, only partially dissociate in solution, necessitating the use of an ICE (Initial, Change, Equilibrium) chart to calculate equilibrium concentrations in molarity (M). The base ionization constant (K_b) is essential for determining these equilibrium amounts. To assess the extent of ionization, the percent ionization formula is used:

Percent Ionization=[OH-] at equilibrium/Initial concentration of weak base×100

This calculation reveals that weak bases ionize less than 100%, unlike strong bases, which ionize completely. Understanding this concept is crucial for predicting the behavior of weak bases in aqueous solutions and their ionization efficiency.

ICE Charts of Weak Bases

Weak bases are classified as weak electrolytes, meaning they only partially dissociate into ions when dissolved in water. To analyze the behavior of weak bases in solution, we utilize an ICE chart, which stands for Initial, Change, and Equilibrium. This chart helps in calculating the equilibrium concentrations of the species involved in the reaction.

In the context of an ICE chart, the concentrations are expressed in molarity (M), which is defined as moles of solute per liter of solution. For weak bases, we also consider the base association constant, denoted as K_b, which quantifies the strength of the base in terms of its ability to accept protons.

When working with weak bases, it is essential to remember that due to their weak nature, the ICE chart is a crucial tool for determining the exact equilibrium concentrations in a given chemical process. By setting up the initial concentrations, accounting for the changes that occur during the reaction, and calculating the final equilibrium concentrations, one can effectively analyze the behavior of weak bases in aqueous solutions.

Hydroxide Ion Concentration Example

To calculate the hydroxide ion concentration in a 0.55 M potassium fluoride solution at 25 degrees Celsius, we start by recognizing that potassium fluoride (KF) dissociates into potassium ions (K⁺) and fluoride ions (F^-). Since potassium is a main group metal, it does not contribute to acidity, making it neutral. However, the fluoride ion acts as a weak base because it is the conjugate base of hydrofluoric acid (HF), which has an acid dissociation constant (K_a) of 3.5 × 10^-4.

Next, we set up an ICE (Initial, Change, Equilibrium) chart for the reaction of F^- with water, where water acts as the acid. The reaction can be represented as:

F^- + H₂O ⇌ HF + OH^-

In the ICE chart, we start with an initial concentration of 0.55 M for F^- and 0 for HF and OH^-. The change in concentration will be -x for F^- and +x for both HF and OH^-. Thus, at equilibrium, the concentrations will be:

• [F^-] = 0.55 - x
• [HF] = x
• [OH^-] = x

To find the base dissociation constant (K_b), we use the relationship between K_a and K_w (the ion product of water):

K_w = K_a × K_b

Rearranging gives us:

K_b = K_w / K_a = (1.0 × 10^-14) / (3.5 × 10^-4) = 2.857 × 10^-11

Using the 500 approximation method, we compare the initial concentration of the weak base (0.55 M) to K_b. The ratio is:

0.55 / (2.857 × 10^-11) = 1.925 × 10¹⁰,

which is much greater than 500. This allows us to ignore the -x in the equilibrium expression.

The equilibrium expression for K_b is:

K_b = [HF][OH^-] / [F^-]

Substituting the equilibrium concentrations gives:

2.857 × 10^-11 = (x)(x) / (0.55)

Cross-multiplying leads to:

x² = 2.857 × 10^-11 × 0.55 = 1.57135 × 10^-11

Taking the square root of both sides, we find:

x = 3.96 × 10^-6 M.

This value represents the hydroxide ion concentration at equilibrium. Therefore, the final answer for the hydroxide ion concentration in the solution is:

3.96 × 10^-6 M.

Calculating pH of Weak Bases Example

To calculate the pH of a weak base solution, such as ethyl amine, we first need to determine the equilibrium concentration of hydroxide ions. This is achieved using an ICE (Initial, Change, Equilibrium) chart. For a 0.12 M solution of ethyl amine, which has a base dissociation constant (K_B) of 5.6 × 10^-4, we start by writing the equilibrium reaction:

C₂H₅NH₂ + H₂O ⇌ C₂H₅NH₃⁺ + OH^-

In the ICE chart, the initial concentration of ethyl amine is 0.12 M, while the initial concentrations of the products (ethyl ammonium ion and hydroxide ion) are 0. The change in concentration for the reactants is -x, and for the products, it is +x. Thus, the equilibrium concentrations can be expressed as:

Ethyl amine: 0.12 - x

Ethyl ammonium ion: x

Hydroxide ion: x

Next, we set up the equilibrium constant expression:

K_B = \(\frac{[C_2H_5NH_3^+][OH^-]}{[C_2H_5NH_2]}\) = \(\frac{x \cdot x}{0.12 - x}\) = \(\frac{x^2}{0.12 - x}\)

To simplify calculations, we can use the 500 approximation method. We calculate the ratio of the initial concentration of the weak base to its K_B value:

\(\frac{0.12}{5.6 \times 10^{-4}} = 214.3\)

Since this value is less than 500, we cannot ignore the -x term, and we must use the quadratic formula to solve for x. Rearranging the equation gives:

x² + 5.6 × 10^-4x - 6.72 × 10^-5 = 0

Using the quadratic formula:

x = \(\frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\)

Substituting a = 1, b = 5.6 × 10^-4, and c = -6.72 × 10^-5 into the formula yields two potential solutions for x. After calculating, we find:

x ≈ 0.00792 M (valid) and x ≈ -0.00848 M (not valid, as concentrations cannot be negative).

Now that we have the hydroxide ion concentration (0.00792 M), we can find the pOH:

pOH = -log[OH^-] = -log(0.00792) ≈ 2.10

Finally, we can calculate the pH using the relationship:

pH + pOH = 14

pH = 14 - pOH = 14 - 2.10 = 11.90

Thus, the pH of the 0.12 M ethyl amine solution is approximately 11.90. Remember, when determining pH from a weak base, always check the equilibrium concentrations to ensure they are positive.

Calculating Percent Ionization of Weak Bases

Understanding the concept of percent ionization or percent dissociation is crucial when studying weak bases, which are classified as weak electrolytes. Unlike strong bases that fully ionize in solution, weak bases only partially dissociate into ions, resulting in less than 100% ionization. This distinction is essential for accurately calculating the extent of ionization in weak bases.

To determine the percent ionization of a weak base, the following formula is employed:

\[\text{Percent Ionization} = \left( \frac{[\text{OH}^-]_{eq}}{[\text{Base}]_{initial}} \right) \times 100\]

In this equation, \([\text{OH}^-]_{eq}\) represents the concentration of hydroxide ions at equilibrium, while \([\text{Base}]_{initial}\) denotes the initial concentration of the weak base. By applying this formula, one can effectively calculate the percent ionization for any weak base, providing insight into its behavior in aqueous solutions.

Percent Ionization Example

To calculate the percent ionization of sodium hypoiodide (NaIO) when dissolved in solution, we start by recognizing that hypoiodic acid (HIO) is a weak acid, indicated by its dissociation constant (K_a) of 2.3 × 10⁻¹¹. The conjugate base, NaIO, will undergo hydrolysis in water, where it reacts to form hypoiodic acid and hydroxide ions:

NaIO + H₂O ⇌ HIO + OH⁻

Next, we need to determine the initial concentration of the hypoiodide ion. First, we convert the mass of sodium hypoiodide (73.2 grams) to moles using its molar mass (165.89 g/mol):

Number of moles = 73.2 g / 165.89 g/mol = 0.441 moles

Since the solution volume is 500 mL (0.500 L), we calculate the molarity (M) of the solution:

Molarity = moles / liters = 0.441 moles / 0.500 L = 0.882 M

We set up an ICE (Initial, Change, Equilibrium) table for the reaction, focusing on the hydroxide ion concentration. Initially, the concentration of hydroxide ions (OH⁻) is 0, and we denote the change in concentration of OH⁻ as x:

Initial: [NaIO] = 0.882 M, [HIO] = 0, [OH⁻] = 0

Change: [NaIO] = -x, [HIO] = +x, [OH⁻] = +x

Equilibrium: [NaIO] = 0.882 - x, [HIO] = x, [OH⁻] = x

To find K_b, we use the relationship K_a × K_b = K_w, where K_w = 1.0 × 10⁻¹⁴. Thus:

K_b = K_w / K_a = (1.0 × 10⁻¹⁴) / (2.3 × 10⁻¹¹) = 4.3 × 10⁻⁴

Using the approximation method, we check if the initial concentration divided by K_b is greater than 500:

0.882 M / (4.3 × 10⁻⁴) = 2051.2 (greater than 500)

Since this condition is satisfied, we can ignore the -x in our equilibrium expression:

K_b = [OH⁻][HIO] / [NaIO] = x² / (0.882)

Cross-multiplying gives:

x² = K_b × 0.882 = (4.3 × 10⁻⁴) × (0.882) = 3.7 × 10⁻⁴

Taking the square root of both sides, we find:

x = [OH⁻] = √(3.7 × 10⁻⁴) ≈ 0.01947 M

Finally, we calculate the percent ionization of the hypoiodide ion:

Percent Ionization = ([OH⁻] at equilibrium / Initial concentration of NaIO) × 100

Percent Ionization = (0.01947 M / 0.882 M) × 100 ≈ 2.21%

This value represents the percent ionization of the hypoiodide ion in the solution.

Determine the pH of a solution made by dissolving 6.1 g of sodium cyanide, NaCN, in enough water to make a 500.0 mL of solution. (MW of NaCN = 49.01 g/mol). The K_a value of HCN is 4.9 × 10⁻¹⁰.

• A. 2.648
• B. 13.389
• C. 5.294
• D. 11.352

Answer: (D)

An unknown weak base has an initial concentration of 0.750 M with a pH of 8.03. Calculate its equilibrium base constant. 

• A. 9.35 × 10⁻⁹
• B. 1.53 × 10⁻¹²
• C. 6.54 × 10⁻³
• D. 1.07 × 10⁻⁶

Answer: (B)

Here’s what students ask on this topic:

How to find the pH of a weak base?

To find the pH of a weak base, you'll need to follow these steps:

1. Identify the weak base and its concentration in the solution. Let's say the base is B and its concentration is _[B].
2. Write down the equilibrium expression for the base dissociation: B + H₂O ⇌ BH⁺ + OH^-.
3. Use the base dissociation constant (K_b) for the weak base, which can be found in tables or literature. The K_b expression is K_b = ^[BH+][OH-]/_[B].
4. Set up an ICE table (Initial, Change, Equilibrium) to calculate the changes in concentrations of the reactants and products at equilibrium.
5. Assuming x is the change in concentration of OH^- ions at equilibrium, the K_b expression becomes K_b = ^x2/_{[B] - x}. Since weak bases only partially dissociate, x is much smaller than [B], allowing the approximation [B] - x ≈ [B].
6. Solve for x, which represents the [OH^-] at equilibrium.
7. Calculate the pOH and then use the relationship pH + pOH = 14 to find the pH.

What pH is a weak base?

A weak base is a base that does not fully dissociate into its ions in an aqueous solution. As a result, weak bases have a pH that is greater than 7 but less than 14. The exact pH of a weak base solution depends on the base's concentration and its dissociation constant (K_b). Typically, weak bases have a pH ranging from about 7.1 to just below 11. Examples of weak bases include ammonia (NH₃), with a pH around 11 when in a standard 0.1 M solution, and methylamine (CH₃NH₂). It's important to note that the pH can vary significantly with concentration and temperature. Weak bases partially accept protons, resulting in an equilibrium between the base and its conjugate acid in solution, which is why they do not achieve the higher pH levels of strong bases, which fully dissociate.

What is a weak base on the pH scale?

A weak base is a substance that does not fully ionize in solution, meaning it does not completely dissociate into its ions in water. On the pH scale, which ranges from 0 to 14, a weak base typically results in a pH value above 7 but below 14. The exact pH value will depend on the concentration of the base and its dissociation constant (_Kb). Weak bases partially accept protons from water, leading to the formation of the hydroxide ion (^OH-) and the corresponding conjugate acid of the base. Because they do not fully ionize, the solution will have a lower concentration of hydroxide ions compared to a strong base at the same concentration, resulting in a less alkaline pH. Examples of weak bases include ammonia (_NH3), methylamine (_CH3NH₂), and ethylamine (_C2H₅NH₂). The pH of a weak base solution is often found using the Henderson-Hasselbalch equation or by calculating the hydroxide ion concentration and then using the pOH to find the pH.