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Phosphoric acid, known chemically as \(\text{H}_3\text{PO}_4\), is a triprotic acid, meaning it can donate three protons (\(\text{H}^+\) ions). This characteristic makes it unique among acids. Yet, it is more common to discuss its first dissociation step because this is typically the strongest. This first step can be represented by the equation: \[\text{H}_3\text{PO}_4 \rightleftharpoons \text{H}^+ + \text{H}_2\text{PO}_4^-\]Phosphoric acid's ability to release protons gives it the acidic properties that influence taste, such as in cola drinks. Lower levels of phosphoric acid contribute to a tart and tangy flavor. Despite its acidic nature, phosphoric acid is considered a weak acid because it does not fully dissociate in solution.

In a chemical reaction, equilibrium concentration refers to the concentrations of the reactant and product molecules at equilibrium. For phosphoric acid, when it reaches equilibrium in water, the amount of acid that has dissociated into ions and the amount that remains in molecular form balance out.In our exercise, we have an initial concentration of \(0.007 M\) phosphoric acid. At equilibrium, the concentrations are adjusted based on how much \(\text{H}_3\text{PO}_4\) dissociates. Let's say "\(x\)" is the change due to dissociation:

• \([\text{H}_3\text{PO}_4] = 0.007 - x\)
• \([\text{H}^+] = x\)
• \([\text{H}_2\text{PO}_4^-] = x\)

This finds a state where the reaction neither proceeds forward nor backward significantly, maintaining stable concentrations of these entities.

The acid dissociation constant, \(K_a\), is a numerical value that indicates the strength of an acid in solution. For phosphoric acid, we're interested in \(K_{a1}\), which pertains to the first dissociation step. This constant provides a way to quantify how easily the acid donates its protons to the surrounding solution.The equation for the dissociation constant is:\[K_{a1} = \frac{[\text{H}^+][\text{H}_2\text{PO}_4^-]}{[\text{H}_3\text{PO}_4]}\]Given \(K_{a1}\) as \(7.1 \times 10^{-3}\), we can predict the extent of dissociation in the solution. A low \(K_a\) value, like in weak acids such as phosphoric acid, indicates minimal tendency to dissociate, which means less hydrogen ion production compared to strong acids.

Calculating the pH of a solution helps us understand its acidity. The pH scale ranges from 0 to 14, with lower values indicating higher acidity. To find the pH, we use the concentration of hydrogen ions, \([\text{H}^+]\), determined from the equilibrium concentrations.The formula to find pH is:\[\text{pH} = -\log_{10}[\text{H}_3\text{O}^+]\]From our steps, we solved to find \([\text{H}_3\text{O}^+] = 0.00634 M\). Using the formula, the pH is approximately calculated as:\[\text{pH} \approx -\log_{10}(0.00634) \approx 2.20\]This low pH value confirms that the solution is quite acidic, which matches the tartness experienced in beverages like cola that contain phosphoric acid.