Autoionization of Water and pH Calculate the \(\mathrm{pH}\) of each acid solution. Explain how the pH values you calculate demonstrate that the pH of an acid solution should carry as many digits to the right of the decimal place as the number of significant figures in the concentration of the solution. $$\begin{array}{l}{\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]=0.044 \mathrm{M}} \\ {\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]=0.045 \mathrm{M}} \\\ {\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]=0.046 \mathrm{M}}\end{array}$$

Understanding the pH scale is fundamental in chemistry. It serves as a measure to express the acidity or basicity of a solution. The pH scale is logarithmic, which means each whole pH value below 7 is ten times more acidic than the next higher value. For instance, a pH of 3 is ten times more acidic than a pH of 4.
The scale goes from 0 to 14, with 7 being neutral. Solutions with a pH less than 7 are acidic, while those with a pH greater than 7 are basic. Neutral solutions, like pure water, have a pH of exactly 7. A small change in pH can indicate a significant change in the hydronium ion concentration, which is why understanding pH is crucial for studying the properties of different substances.

Hydronium ions, represented as \(\mathrm{H}_3\mathrm{O}^+\), are the hallmark of an acidic solution and are responsible for its acidic properties. The concentration of these ions in a solution is a direct indicator of its acidity.
In chemistry, the concentration of hydronium ions is usually expressed in moles per liter (M). When we speak of a concentration of 0.045 M, for example, we mean that there are 0.045 moles of hydronium ions per liter of solution.
Calculating the pH of a solution requires knowing the concentration of hydronium ions because the pH is inversely related to this concentration. The formula used for calculating pH is \(\mathrm{pH} = -\log_{10}[\mathrm{H}_3\mathrm{O}^+]\). As the [H3O+] increases, the solution becomes more acidic and the pH value decreases.

Significant figures are essential in chemistry for expressing the precision of measurements. They tell us how exactly a value is known. For example, a concentration reported as 0.046 M has two significant figures, indicating the value is precise to the hundredths place.
It is important to maintain the correct number of significant figures throughout calculations to ensure accuracy and to not imply greater precision than is actually present. When calculating pH, the number of significant figures in the hydronium ion concentration determines the number of decimal places that should be in the pH value. If the concentration of \(\mathrm{H}_3\mathrm{O}^+\) in a solution is known to two significant figures, the calculated pH should be reported to two decimal places to maintain consistency in precision.

Water has a remarkable property called autoionization, where two water molecules react to produce a hydronium ion \(\mathrm{H}_3\mathrm{O}^+\) and a hydroxide ion \(\mathrm{OH}^-\). This equilibrium reaction is represented as: \(2\mathrm{H}_2\mathrm{O}(l) \rightleftharpoons \mathrm{H}_3\mathrm{O}^+(aq) + \mathrm{OH}^-(aq)\).
The autoionization of water is a key concept explaining why water can conduct electricity and also establishes the basis for the pH scale in pure water. At 25°C, the concentration of \(\mathrm{H}_3\mathrm{O}^+\) and \(\mathrm{OH}^-\) in pure water is \(1 \times 10^{-7} \mathrm{M}\), which gives a neutral pH of 7. In solutions where water is present, any change in the concentration of hydronium ions, due to the addition of acids or bases, can shift the equilibrium, thus changing the pH of the solution.