Calculate the \(\mathrm{pH}\) of the following. a. \(5 \times 10^{-4} \mathrm{MHCl}\) d. \(3 \times 10^{-2}\) M KOH b. \(7 \times 10^{-5} M\) NaOH e. \(0.04 \mathrm{m} M \mathrm{HCl}\) c. \(2 \mu M\) HCl f. \(6 \times 10^{-9}\) M HCl

The science of acids and bases plays a critical role in understanding chemical reactions and biological processes. At the core of this topic is the concept of acid-base equilibrium, a state where the concentrations of acids (H⁺ ions) and bases (OH^- ions) in a solution are stable.

To dive deeper into this equilibrium, we consider the ionization of acids and bases in water. Strong acids like HCl completely dissociate in water, contributing to an increase in H⁺ ion concentration. On the other hand, strong bases such as NaOH and KOH completely dissociate to yield OH^- ions. The dissociation plays a pivotal role in determining the acidity or basicity of a solution.

This equilibrium is quantified by the equilibrium constant for water, known as the ion-product constant (K_w), which at 25°C is equal to 1.0 x 10^-14. Understanding this constant helps us link the concentrations of H⁺ and OH^- ions in a solution. It's essential to make these concepts clear because they lay the groundwork for pH calculations and subsequent problem-solving.

When solving problems involving pH, it's important to understand molar concentration, a measure of the amount of a substance in a given volume of solution. It's represented by Molarity (M) and calculated as moles of solute per liter of solution.

In the context of our exercise, concentration is given directly for each substance, for instance,• 5 x 10^-4 M HCl refers to 5 x 10^-4 moles of HCl in one liter of solution.

This concept is crucial because the acid or base's molarity is directly used to determine the pH or pOH of the solution. For example, a 2 μM HCl solution indicates a highly dilute solution and consequently, a pH value closer to neutral. Remember that the unit μM stands for micromolar, which is equal to 10^-6 M, and mM stands for millimolar, equal to 10^-3 M. Correctly interpreting these units and converting them if necessary is imperative for accurate pH calculations.

The pH and pOH relationship is a central concept in understanding the acidity or basicity of solutions. pH stands for the 'power of hydrogen' and gives a measure of the acidity of a solution, while pOH gives a measure of its basicity.

The pH and pOH scales are inversely related and follow a simple mathematical relationship:
• pH + pOH = 14
This relationship is valid at 25°C, which is considered standard temperature for these calculations. In the given exercises, after calculating the [OH^-] for basic solutions, we can find the pOH by taking the negative logarithm base 10 of the [OH^-]. Then, by subtracting the pOH from 14, we get the pH of the solution. For example, if we have a pOH of 2, the pH would be 14 - 2 = 12, indicating a basic solution. Understanding the pH and pOH relationship is vital for effectively interpreting the results of acid-base reactions and making educated predictions about the behavior of solutions.