The ideal pH for a public swimming pool is considered by...

The ideal pH for a public swimming pool is considered by many to be pH 7.5 . Outside the range of $\mathrm{pH} 7.2-7.8$, exposed eyes will become bloodshot and other adverse effects may be evident. Calculate the following a. The $\left[\mathrm{H}_3 \mathrm{O}^{+}\right]$value of pH 7.5 b. The $\left[\mathrm{H}_3 \mathrm{O}^{+}\right]$value of pH 8.5 c. The multiple difference there is in $\left[\mathrm{H}_3 \mathrm{O}^{+}\right]$between pH 7.5 and pH 8.5 $$ \frac{\left[\mathrm{H}_3 \mathrm{O}^{+}\right] \mathrm{pH} 7.5}{\left[\mathrm{H}_3 \mathrm{O}^{+}\right] \mathrm{pH} 8.5} $$

The ideal pH for a public swimming pool is considered by many to be pH 7.5 . Outside the range of $\mathrm{pH} 7.2-7.8$, exposed eyes will become bloodshot and other adverse effects may be evident. Calculate the following
a. The $\left[\mathrm{H}_3 \mathrm{O}^{+}\right]$value of pH 7.5
b. The $\left[\mathrm{H}_3 \mathrm{O}^{+}\right]$value of pH 8.5
c. The multiple difference there is in $\left[\mathrm{H}_3 \mathrm{O}^{+}\right]$between pH 7.5 and pH 8.5

$$
\frac{\left[\mathrm{H}_3 \mathrm{O}^{+}\right] \mathrm{pH} 7.5}{\left[\mathrm{H}_3 \mathrm{O}^{+}\right] \mathrm{pH} 8.5}
$$

Key Concepts

pH Scale

The pH scale is a measure of the acidity or basicity of an aqueous solution, defined as the negative logarithm (base 10) of the hydronium ion concentration in the solution. This logarithmic scale compresses a wide range of hydrogen ion concentrations into a manageable scale, typically from 0 (highly acidic) to 14 (highly basic).

Hydronium Ion Concentration

Hydronium ion concentration, indicated as [H3O+], represents the amount of hydrogen ions in solution. It is a critical quantity in acid-base chemistry because it directly influences the pH of the solution and thus its chemical reactivity and biological compatibility.

Logarithmic Relationship Between pH and [H3O+]

The relationship between pH and hydronium ion concentration is given by the equation pH = -log[H3O+]. This implies that each unit change in pH corresponds to a tenfold change in the hydronium ion concentration. Understanding this relationship is vital when comparing the acidity of different solutions.

Ratio of Hydronium Ion Concentrations

When comparing the hydronium ion concentrations of two solutions at different pH values, the logarithmic nature of the pH scale means that a difference of one pH unit corresponds to a tenfold difference in concentration. Thus, calculating the ratio of [H3O+] for solutions at different pH values involves using exponential relationships to determine the factor by which one concentration exceeds the other.

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