Question

The following illustration displays the relative number of species when an acid, HA, is added to water. a. Is HA a weak or strong acid? How can you tell? b. Using the relative numbers given in the illustration, determine the value for \(K_{\mathrm{a}}\) and the percent dissociation of the acid. Assume the initial acid concentration is \(0.20 \mathrm{M}\).

Short answer

HA is a weak acid, based on the partial dissociation observed in the illustration. The value of Ka for HA is approximately \(2.0 \times 10^{-3}\), and the percent dissociation of the acid is 10%.

Step-by-step solution

Identify if HA is a weak or strong acid

From the illustration, we can see that when HA is added to water, it does not dissociate completely, and there are still molecules of HA remaining. Since strong acids completely dissociate in water, we can conclude that HA is a weak acid.

Determine the relative numbers from the illustration

Let's assume that x moles of HA dissociate. According to the illustration, when x moles of HA dissociate, we have: - HA: Initial concentration - x i.e. \(0.20 - x\) - H3O: x moles - A: x moles

Write the Ka expression for HA

The Ka expression for HA is given by: \[ K_{a} = \frac{[\mathrm{H}_{3}\mathrm{O}^{+}][\mathrm{A}^{-}]}{[\mathrm{HA}]}\]

Calculate the value of Ka

Substitute the values obtained in Step 2 into the Ka expression: \[ K_{a} = \frac{x \times x}{0.20 - x}\] Since x is very small compared to 0.20, we can approximate \(0.20 - x \approx 0.20\): \[ K_{a} \approx \frac{x^{2}}{0.20}\] We are given that x = 0.020, so we can plug this value into the equation to calculate the value of Ka: \[ K_{a} \approx \frac{(0.020)^{2}}{0.20} = 2.0 \times 10^{-3}\]

Calculate the percent dissociation

Percent dissociation is the proportion of the acid molecules that have dissociated, given by the formula: \[ \text{Percent dissociation} = \frac{\text{Amount dissociated}}{\text{Initial concentration}} \times 100\] Using the values from Step 2: \[ \text{Percent dissociation} = \frac{0.020}{0.20} \times 100 = 10\%\] So, the percent dissociation of the acid is 10%.

Key concepts

Weak Acid

A weak acid is a type of acid that does not completely dissociate into its ions in a solution. Unlike strong acids, which release all of their hydrogen ions, weak acids only partially dissociate. This partial dissociation is what characterizes weak acids and also means they have a higher pH compared to strong acids.

For example, acetic acid (CH3COOH) is a common weak acid found in vinegar. When added to water, a small portion of acetic acid molecules donate a proton (H+) to form the acetate ion (CH3COO-) and the hydronium ion (H3O+). Most of the acid remains in its molecular form because the process is not fully completed. The incomplete dissociation is crucial for determining various properties of the acid, including its acid dissociation constant (Ka) and percent dissociation.

Percent Dissociation

Percent dissociation is a measure of the strength of an acid or base, expressed as the percentage of a solute that is ionized in a solution. It is calculated by taking the amount of substance that has dissociated and dividing it by the initial concentration, then multiplying by 100. For weak acids, the percent dissociation is usually low, indicating that only a small fraction of the acid molecules dissociate.

For instance, if you start with a 0.20 M solution of a weak acid and after establishing an equilibrium, you have 0.020 M of its ions, the percent dissociation can be calculated as follows: \[ \text{Percent dissociation} = \frac{0.020}{0.20} \times 100 = 10\text{%} \]
This value provides a quick insight into the relative strength of the weak acid; the higher the percent dissociation, the stronger the weak acid behaves in the given environment.

Acid-Base Equilibrium

Acid-base equilibrium refers to the chemical balance that occurs when an acid and base react and form their respective conjugate base and conjugate acid. This balance is represented by the equilibrium constant expression. In the case of weak acids, the acid dissociation constant, or Ka, indicates the degree of dissociation at equilibrium. The higher the Ka value, the stronger the acid.

The equilibrium expression for a weak acid, HA, dissociating in water to produce H3O+ ions and A- ions is given by: \[ K_{a} = \frac{[\text{H3O}^{+}][\text{A}^{-}]}{[\text{HA}]} \]
Here, the square brackets denote the molarity of each species. Achieving equilibrium means that the rate of the forward reaction (acid losing a proton) is equal to the rate of the reverse reaction (conjugate base gaining a proton), leading to constant concentrations of the acid, its ions, and the hydronium ions in solution.

Molarity

Molarity, often denoted by M, is a unit of concentration used in chemistry to describe the amount of a substance in a given volume of solution. It is defined as moles of solute per liter of solution. This measurement is especially important when discussing acids and bases because it allows chemists to calculate the strengths and reactions of these substances in solution.

For example, if you dissolve one mole of a solute into one liter of solvent, you obtain a 1 M solution. When studying acid-base reactions, knowing the molarity of an acid, such as HA, helps scholars determine how much of the acid will dissociate into ions, thereby affecting the pH of the solution. The molar concentration of each species at equilibrium is used in the calculation of Ka values and, subsequently, in finding the percent dissociation, revealing the extent of the acid's dissociation in water.