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The pH of a solution is a measure of its acidity or basicity and is calculated from the concentration of hydrogen ions \([H^+]\). When dealing with weak acids like propanoic acid, it鈥檚 essential to first find the equilibrium concentration of \([H^+]\).
Once you have it, you use the formula \( ext{pH} = -\log[H^+]\). For our specific example:
\[\text{pH} = -\log(0.0036)\]
This results in a pH of approximately 2.44, indicating an acidic solution. The negative logarithm in the formula gives you the power of 10, making it a simple yet efficient way to express the hydrogen ion concentration.

An ICE table is a systematic way to organize data for reactions in equilibrium. Here, 'I' stands for initial concentration, 'C' for change in concentration, and 'E' for equilibrium concentration.
This tool helps in visualizing how concentrations shift as a chemical reaction proceeds toward equilibrium.

• Initial Concentration (I): Start with 0.100 M for propanoic acid and 0 M for products (H鈦� and C鈧僅鈧匫鈧傗伝).
• Change (C): As the reaction proceeds, the amount of acid decreases by \-x\ M, while both H鈦� and C鈧僅鈧匫鈧傗伝 increase by \+x\ M.
• Equilibrium (E): Use the expressions \(0.100 - x\) for the acid, and x for the ions.

This concise table simplifies complex equilibrium problems helping you to define the unknowns clearly.

The acid dissociation constant, \(K_a\), tells us how well an acid can donate a proton. It鈥檚 essential in calculating equilibrium concentrations. For propanoic acid, the expression is:
\[K_a = \frac{[H^+][C鈧僅鈧匫鈧俕-]}{[HC鈧僅鈧匫鈧俔}\]
With \(K_a = 1.3 \times 10^{-5}\). By substituting the equilibrium concentrations (from the ICE table), we can write:
\[1.3 \times 10^{-5} = \frac{x^2}{0.100 - x}\]
Simplifying often assumes \(x \approx 0.0036\), as x is small compared to the initial acid concentration (a valid approximation for weak acids), converting the equation to:
\[1.3 \times 10^{-5} \approx \frac{x^2}{0.100}\]
This simplifies to solve for \(x\), the concentration of H鈦� at equilibrium.

Percent dissociation shows how much of the initial acid dissociates into ions, an important aspect to consider in equilibrium studies. Use the formula:
\[\text{Percent Dissociation} = \frac{[H^+]_{\text{equilibrium}}}{[HC鈧僅鈧匫鈧俔_{\text{initial}}} \times 100\%\]
For propanoic acid, this becomes:
\[\frac{0.0036}{0.100} \times 100\% \approx 3.6\%\]
This low percentage confirms that propanoic acid is indeed a weak acid, as only a small fraction dissociates in solution. This calculation helps in comparing the strength of different acids and is a crucial part of equilibrium analysis.