For propanoic acid \(\left(\mathrm{HC}_{3} \mathrm{H}_{5} \mathrm{O}_{2}, K_{\mathrm{a}}=1.3 \times 10^{-5}\right)\), determine the concentration of all species present, the \(\mathrm{pH}\), and the percent dissociation of a \(0.100-M\) solution.

The acid dissociation constant (Ka) is a quantitative measure of an acid's strength. More specifically, it represents the equilibrium constant for the dissociation of an acid into its conjugate base and a proton (H+). In the case of propanoic acid \( HC_3H_5O_2 \) with a Ka value of \(1.3 \times 10^{-5}\), we understand that it is a weak acid as it does not dissociate completely in solution.

For the dissociation reaction \( HC_3H_5O_2 \longleftrightarrow H^+ + C_3H_5O_2^- \), Ka is defined by the equation \( K_a = \frac{[H^+][C_3H_5O_2^-]}{[HC_3H_5O_2]} \), where the concentrations are those at equilibrium. To find the degree of dissociation, we solve for \( x \) where \(x \) represents the concentration of dissociated ions at equilibrium. Intuitively, a stronger acid would have a higher Ka value, signaling higher dissociation, whereas a weaker acid like propanoic has a lower Ka, implying less dissociation.

The pH of a solution is a logarithmic measure of the concentration of hydrogen ions (H+) present. The formula for pH is \( pH = -\log[H+] \). Through this calculation, we can determine the acidity or basicity of the solution. A lower pH value indicates a more acidic solution, while a higher pH indicates a more basic or alkaline solution.

In the context of propanoic acid's dissociation, the concentration of H+ ions at equilibrium, found as \( x \) in the earlier steps, can be plugged into the pH formula. This allows us to conclude the pH of the propanoic acid solution to be approximately 2.94, reflecting its acidic nature. Understanding pH is crucial for predicting the behavior of substances in different chemical environments and is a fundamental aspect of chemistry.

Percent dissociation offers insight into the extent of an acid's ionization in a given solution. It is calculated by the formula: \( \text{Percent dissociation} = \frac{\text{Concentration of dissociated acid}}{\text{Initial concentration of acid}} \times 100% \). This percentage reveals the portion of the original acid that has dissociated into ions.

For a 0.100 M solution of propanoic acid with an \(x\) value representing the dissociated amount of \(1.14 \times 10^{-3}M\), the percent dissociation can be calculated. The approximate percent dissociation for propanoic acid in this case is 1.14%, indicating a relatively low level of dissociation, as one would expect from a weak acid.

Equilibrium concentration refers to the concentration of reactants and products in a reaction at the state of equilibrium. This state occurs when the rate of the forward reaction equals the rate of the reverse reaction. For propanoic acid, the dissociation reaction achieves equilibrium when the concentration of un-dissociated acid, the hydrogen ions, and the conjugate base no longer change with time.

By setting up an ICE (initial, change, equilibrium) table and solving for \( x \) as done in our example, we derived the equilibrium concentrations for HC3H5O2, H+, and C3H5O2-. Understanding and calculating these values is important as they dictate the behavior and properties of the solution, including its reactivity, pH, and buffer capacity.