Dissociation is the process where compounds, known as electrolytes, break apart into their constituent ions when dissolved in a solvent, typically water. This process is fundamental to understanding the behavior of acids, bases, and salts in solution. Percent dissociation, often represented by the Greek letter alpha (\(\alpha\)), provides a quantitative measure of the extent of this separation. It indicates the fraction of the initial substance that has successfully ionized, linking directly to the inherent strength of an acid or base.
Defining Dissociation and the Percent Dissociation Formula
Electrolytes are categorized based on their dissociation behavior in an aqueous solution. Strong electrolytes, such as hydrochloric acid, dissociate nearly 100% into ions. Weak electrolytes, conversely, such as acetic acid, only partially dissociate, establishing an equilibrium between the intact molecule and its separated ions. Percent dissociation is a measure reserved for these weak substances to quantify their limited ionization.
The formula for calculating percent dissociation is a simple ratio of the amount of substance that has broken down to the initial amount present. It is expressed as the concentration of the dissociated species at equilibrium divided by the initial concentration of the solute, multiplied by 100%. This “amount” is typically measured in molarity. For a weak acid, this ratio compares the equilibrium concentration of the hydrogen ion (\([\text{H}^+]\)) to the starting concentration of the acid.
Calculating Dissociation Using Equilibrium Constants (\(K_a\) and \(K_b\))
For weak electrolytes, the amount of the compound that dissociates is governed by a reversible chemical reaction that reaches dynamic equilibrium. To determine the concentration of the dissociated ions, one must use the appropriate equilibrium constant. The Acid Dissociation Constant (\(K_a\)) and the Base Dissociation Constant (\(K_b\)) quantify the position of this equilibrium for weak acids and weak bases. A smaller \(K_a\) or \(K_b\) value indicates a weaker electrolyte, meaning less dissociation occurs.
This calculation requires setting up an equilibrium expression where the constant equals the product concentrations divided by the reactant concentration. A systematic method known as an ICE (Initial, Change, Equilibrium) table is employed to track concentrations. The ICE table uses a variable \(x\) to represent the unknown equilibrium concentration of the dissociated ions. The \(K_a\) or \(K_b\) value is the required input data to solve for \(x\), which represents the amount dissociated.
Step-by-Step Calculation Example for a Weak Acid
Consider calculating the percent dissociation of a \(0.10 \text{ M}\) solution of acetic acid (\(\text{CH}_3\text{COOH}\)), given its \(K_a\) is \(1.8 \times 10^{-5}\). The dissociation reaction is: \(\text{CH}_3\text{COOH} (\text{aq}) \rightleftharpoons \text{H}^+ (\text{aq}) + \text{CH}_3\text{COO}^- (\text{aq})\).
The first step involves setting up the ICE table based on the initial concentration and the stoichiometry of the reaction.
| Species | \(\text{CH}_3\text{COOH}\) | \(\text{H}^+\) | \(\text{CH}_3\text{COO}^-\) |
| :—: | :—: | :—: | :—: |
| Initial (I) | \(0.10 \text{ M}\) | \(0 \text{ M}\) | \(0 \text{ M}\) |
| Change (C) | \(-x\) | \(+x\) | \(+x\) |
| Equilibrium (E) | \(0.10 – x\) | \(x\) | \(x\) |
Next, the equilibrium concentrations are substituted into the \(K_a\) expression: \(K_a = \frac{[\text{H}^+][\text{CH}_3\text{COO}^-]}{[\text{CH}_3\text{COOH}]} = \frac{(x)(x)}{0.10 – x}\). Because the \(K_a\) value (\(1.8 \times 10^{-5}\)) is very small, \(x\) is assumed negligible compared to the initial concentration of \(0.10 \text{ M}\). This approximation simplifies the denominator to \(0.10\), resulting in the equation: \(1.8 \times 10^{-5} \approx \frac{x^2}{0.10}\). Solving for \(x\) yields \(x^2 = 1.8 \times 10^{-6}\).
Taking the square root determines the equilibrium concentration of the dissociated ion: \(x = [\text{H}^+] = 0.00134 \text{ M}\). This \(x\) value represents the amount dissociated in the percent dissociation formula. The final step is to insert this calculated value into the percent dissociation formula: \(\alpha = (\frac{[\text{H}^+]_{\text{eq}}}{[\text{CH}_3\text{COOH}]_{\text{initial}}}) \times 100\%\). The calculation is \((\frac{0.00134 \text{ M}}{0.10 \text{ M}}) \times 100\%\), which results in a percent dissociation of \(1.34\%\).
External Factors Influencing Percent Dissociation
The equilibrium constant (\(K_a\) or \(K_b\)) is a fixed value for a given substance at a specific temperature, but the actual percent dissociation of a weak electrolyte is affected by external conditions. One significant factor is the initial concentration of the weak electrolyte in the solution. The percent dissociation increases as the initial concentration decreases, which is known as the dilution effect. When a solution is diluted, the equilibrium shifts toward the side with more ions to counteract the stress of lower concentration, according to Le Chatelier’s Principle.
This shift means that for a more dilute solution, a larger fraction of the solute molecules will ionize, resulting in a higher percent dissociation. Temperature is another influence because dissociation reactions involve a transfer of heat. Since most dissociation processes are endothermic, increasing the temperature provides more energy to the system. This shifts the equilibrium to the product side, thereby increasing the concentration of dissociated ions and raising the percent dissociation. A change in temperature is the only factor that actually alters the numerical value of the equilibrium constants, \(K_a\) and \(K_b\).