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To understand pH calculation, we start with its basic definition. The pH of a solution is a measure of its acidity or basicity, represented as\[ pH = -\log [\text{H}_3\text{O}^+] \]where - \([\text{H}_3\text{O}^+]\) is the hydronium ion concentration. In our example, calculating the pH involves using the equilibrium concentration of hydronium ions from the dissociation reaction. Once we find \([\text{H}_3\text{O}^+] = x\) from the ICE table, we can plug this value into the formula to find the pH. Keep in mind that a lower pH indicates a more acidic solution, while a higher pH indicates a more basic solution. Generally, pH values range between 0 and 14.

The acid dissociation constant, denoted as \(K_a\), is key to understanding how strong or weak an acid is. It represents how well an acid ionizes in solution. For a typical acid dissociation reaction:\[ HA \rightleftharpoons H^+ + A^- \]The expression for \(K_a\) is:\[ K_a = \frac{[H^+][A^-]}{[HA]} \]Here, - \([H^+]\) and \([A^-]\) are the concentrations of the products, - \([HA]\) is the concentration of the undissociated acid. In the context of the given exercise, the original step by step solution details that for hydrated zinc ion dissociation in water, we utilize the following reaction:\[ \text{Zn} \left( \text{H}_2\text{O} \right)_6^{2+}(aq) + \text{H}_2\text{O}(l) \rightleftharpoons \text{Zn} \left( \text{H}_2\text{O} \right)_5\text{OH}^-(aq) + \text{H}_3\text{O}^+(aq) \] The \(K_a\) expression given for this reaction is:\[ K_a = \frac{[\text{Zn} \left( \text{H}_2\text{O} \right)_5\text{OH}^-][\text{H}_3\text{O}^+]}{[\text{Zn} \left( \text{H}_2\text{O} \right)_6^{2+}]} \]This highlights the relationship between the reactants and products in equilibrium, crucial for determining solutions' pH.

An ICE table is a structured method for organizing the concentrations of reactants and products during a chemical equilibrium process. ICE stands for Initial, Change, and Equilibrium:- **Initial:** Here, you list the initial concentrations before the reaction occurs. - Example: - \([\text{Zn} \left( \text{H}_2\text{O} \right)_6^{2+}] = 0.15 \, M\) - \([\text{H}_3\text{O}^+] = 0\) - **Change:** This stage illustrates how concentrations change as the reaction moves toward equilibrium. - In our equation, assume the change is noted by \(x\). - Change for reactants decreases, while products increase by the same \(x\). - **Equilibrium:** Shows the concentrations when the system has reached equilibrium. - We'll have: - \([\text{Zn} \left( \text{H}_2\text{O} \right)_6^{2+}] = 0.15 - x\) - \([\text{H}_3\text{O}^+] = x\)Using an ICE table enables students to visualize the shift in concentrations logically and compute the necessary values to find pH, aiding in comprehending the complex concept of equilibrium. ICE tables are incredibly useful for complex reactions like the one with zinc chloride, guiding through a step-by-step process.