Calculate the \(\mathrm{pH}\) of each solution. (a) \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]=1.7 \times 10^{-8} \mathrm{M}\) (b) \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]=1.0 \times 10^{-7} \mathrm{M}\) (c) \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]=2.2 \times 10^{-6} \mathrm{M}\) (d) \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]=7.4 \times 10^{-4} \mathrm{M}\)

The pH scale is an essential tool in chemistry that measures the acidity or basicity of aqueous solutions. It extends from 0 to 14, with each value corresponding to a different level of acidity or alkalinity. Solutions with a pH less than 7 are considered acidic, while those with a pH greater than 7 are basic (or alkaline). A pH exactly at 7 indicates a neutral solution, such as pure water.

Understanding the pH scale is critical as it affects chemical reactions, biological processes, and environmental systems. The scale is logarithmic, which means each whole pH value below 7 is ten times more acidic than the next higher value. For example, a solution with a pH of 3 is ten times more acidic than one with a pH of 4. Similarly, each whole pH value above 7 is ten times more basic than the next lower value.

Acidity and basicity are fundamental concepts in chemistry, referring to the concentration of hydrogen ions (H⁺) and hydroxide ions (OH^-) in a solution. Acids are substances that increase the concentration of hydrogen ions when dissolved in water, leading to a lower pH. Common examples include citric acid and hydrochloric acid.

On the other hand, bases reduce the hydrogen ion concentration by either directly releasing hydroxide ions or absorbing hydrogen ions, resulting in a higher pH. Baking soda and bleach are everyday household bases. The balance between hydrogen ions and hydroxide ions determines a solution's pH level, directly impacting its chemical properties.

In the context of pH, it's necessary to consider the concentration of hydronium ions (H₃O⁺), rather than just hydrogen ions (H⁺). Hydronium ions are formed when hydrogen ions associate with water molecules. The concentration of these ions in a solution is expressed in molarity (M), which is moles per liter.

When calculating pH, the concentration of hydronium ions is crucial as it directly influences the acidity of the solution. Lower concentrations of hydronium ions, such as 1.7 x 10^-8 M, are indicative of less acidic or more neutral solutions, while higher concentrations, like 7.4 x 10^-4 M, represent more acidic solutions.

The relationship between hydronium ion concentration and pH is logarithmic. This means that pH is calculated as the negative logarithm, to the base 10, of the hydronium ion concentration (expressed in molarity). The logarithmic nature of the pH scale allows us to conveniently express a wide range of ion concentrations on a more manageable scale.

To calculate the pH, you'll use the formula: pH = -log₁₀ [H₃O⁺]. So, if you have a hydronium ion concentration of 1.0 x 10^-7 M, the pH is calculated as -log₁₀ (1.0 x 10^-7) which simplifies to 7. Logarithmic calculations can be tricky, so using a scientific calculator is recommended to obtain accurate results. Understanding how to perform these calculations is vital for interpreting and predicting the properties of chemical solutions.