91Ó°ÊÓ

When dealing with acids, understanding the concept of pH is essential. The pH scale is a measure of acidity or basicity in a solution. It's a logarithmic scale that runs from 0 to 14.
In our example, pH is determined from the concentration of hydronium ions (\[\text{H}_3\text{O}^+\]). The formula to calculate pH is:

• \[\text{pH} = -\log{[\text{H}_3\text{O}^+]}\]

This means that a higher concentration of \[\text{H}_3\text{O}^+\] results in a lower pH, indicating a stronger acidic solution.
For instance, in the solution with \[\text{HIO}_3\] that dissociates to form \[\text{H}_3\text{O}^+\], we calculated \[\text{H}_3\text{O}^+\] to be 0.0405 M. Plugging this into the formula gives us a pH of approximately 1.39. This describes a strongly acidic environment, as pH values below 7 indicate acidity. Short recap:

• Acids have pH values less than 7.
• The more hydronium ions, the lower the pH value.

Acid-base equilibrium describes the balance between the concentrations of acids and bases in a solution. When acids dissolve in water, they dissociate, releasing ions that establish equilibrium in the solution.
For the reaction \[\text{HIO}_3 + \text{H}_2\text{O} \rightleftharpoons \text{H}_3\text{O}^+ + \text{IO}_3^-\], the molecule \[\text{HIO}_3\] releases hydronium ions (\[\text{H}_3\text{O}^+\]) and iodate ions (\[\text{IO}_3^-\]).
This balance is described by the acid dissociation constant (\[K_a\]):

• \[K_a = \frac{[\text{H}_3\text{O}^+][\text{IO}_3^-]}{[\text{HIO}_3]}\]

The value of \[K_a\] provides insight into the strength of an acid. A higher \[K_a\] indicates a stronger acid as it shows a greater extent of dissociation. In our exercise, \[K_a\] is given as\[1.7 \times 10^{-1}\], signifying significant dissociation, which supports the low pH found.
Key points:

• Equilibrium implies the rate of acid dissociation equals the rate of association back into the acid form.
• Changes in concentration affect the equilibrium, driven by Le Chatelier's Principle.

The quadratic formula is a handy tool in chemistry, especially when dealing with equilibrium problems that involve squared terms. This comes into play when the acid dissociates, and the equilibrium expression involves a term squared.
In our solution for \[\text{HIO}_3\] dissociation, we derived the equation:

• \[1.7 \times 10^{-1} = \frac{x^2}{0.0500 - x}\]

This leads to the quadratic form:

• \[x^2 + 1.7x - 0.085 = 0\]

Using the quadratic formula to solve: \[x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\] helps us find possible values for \[x\], the concentration at equilibrium. Using values \[a = 1\], \[b = 1.7\], and \[c = -0.085\], we found \[x\approx 0.0405\].
This is used to determine concentrations of equilibrium species. It is crucial when the simplification of assumptions (like neglecting \[x\] in the denominator) can't be applied.
Highlight:

• The quadratic formula provides solutions in scenarios where the concentration changes are significant and assumptions aren't valid.
• Understanding its use helps solve complex equilibrium problems in chemistry.