Question

Without using a calculator, determine the \(\mathrm{pH}\) and \(\mathrm{pOH}\) of each solution. Rank the solutions from most acidic to most basic. a. \(1.0 \times 10^{-2} \mathrm{M} \mathrm{HCl}\) b. \(1.0 \times 10^{-4} \mathrm{M} \mathrm{HCl}\) c. \(1.0 \times 10^{-2} \mathrm{M} \mathrm{NaOH}\) d. \(1.0 \times 10^{-4} \mathrm{M} \mathrm{NaOH}\)

Short answer

pH and pOH values are: a (pH = 2, pOH = 12), b (pH = 4, pOH = 10), c (pH = 12, pOH = 2), d (pH = 10, pOH = 4). Most acidic to most basic: a > b > d > c.

Step-by-step solution

Determine the pH of the HCl solutions

Since HCl is a strong acid, it completely dissociates in water. The pH is calculated using the formula \( pH = -\log[H^+] \). For a, the concentration of HCl is \( 1.0 \times 10^{-2} \) M, so \( pH = -\log(1.0 \times 10^{-2}) = 2 \). For b, the concentration is \( 1.0 \times 10^{-4} \) M, so \( pH = -\log(1.0 \times 10^{-4}) = 4 \) .

Determine the pH of the NaOH solutions

NaOH is a strong base that completely dissociates into \( Na^+ \) and \( OH^- \) ions. The \( pOH \) is given by \( pOH = -\log[OH^-] \). For c, the concentration of NaOH is \( 1.0 \times 10^{-2} \) M, so \( pOH = -\log(1.0 \times 10^{-2}) = 2 \) and \( pH = 14 - pOH = 12 \). For d, the concentration is \( 1.0 \times 10^{-4} \) M, so \( pOH = -\log(1.0 \times 10^{-4}) = 4 \) and \( pH = 14 - pOH = 10 \) .

Determine the pOH of all solutions

The pOH can be determined from the pH value using the relationship \( pOH = 14 - pH \). For HCl solutions a and b, where pH is 2 and 4, the corresponding pOH values are 12 and 10, respectively. For NaOH solutions c and d, we've already calculated the pH to be 12 and 10, so the corresponding pOH will be 2 and 4, respectively.

Rank the solutions from most acidic to most basic

Most acidic solutions have the lowest pH values. Here, solution a has a pH of 2, b has a pH of 4, d has a pH of 10, and c has a pH of 12. Thus, the order from most acidic to most basic is: a (pH = 2) > b (pH = 4) > d (pH = 10) > c (pH = 12).

Key concepts

pH Scale

The pH scale is a measure of how acidic or basic a solution is. It ranges from 0 to 14, with lower values representing high acidity and higher values representing high basicity. A pH of 7 is considered neutral, which is the pH of pure water at 25°C. Solutions with a pH less than 7 are acidic, while those with a pH greater than 7 are basic. The pH scale is logarithmic, which means that each whole pH value below 7 is ten times more acidic than the next higher value. In the textbook exercise, for instance, a solution with a pH of 2 is 100 times more acidic than a solution with a pH of 4 because the difference is 2 pH units.

Understanding the pH scale is crucial for many scientific disciplines, including chemistry, biology, and environmental science. It helps predict the behavior of substances in different environments, and it's essential for managing the conditions required for various chemical reactions and biological processes.

Strong Acids and Bases

Strong acids, like HCl, and strong bases, such as NaOH, are substances that completely dissociate into their ions in aqueous solutions. This complete dissociation is what makes them strong; it ensures that all of the original molecules contribute to the acidity or basicity of the solution. Unlike weak acids and bases, which only partially dissociate, strong acids and bases give a clear and definite change in pH when dissolved.

For instance, HCl (hydrochloric acid) is a strong acid that dissociates completely into hydrogen ions (\(H^+\)) and chloride ions (\(Cl^-\)). Similarly, NaOH (sodium hydroxide) is a strong base that dissociates into sodium ions (\(Na^+\)) and hydroxide ions (\(OH^-\)). Because of their complete dissociation, the concentration of the acid or base directly translates into the concentration of hydroxide or hydrogen ions, which is then used to calculate the pH or pOH of the solution.

Concentration of HCl and NaOH

The concentration of a solute in a solution is a measure of how much of that solute is present in a given volume of solvent. It is commonly expressed in molarity (M), which is the number of moles of solute per liter of solution. In the case of our textbook exercise, HCl and NaOH have concentrations in the order of magnitude of \(10^{-2}\) M and \(10^{-4}\) M.

For strong acids like HCl, the concentration essentially equals the concentration of \(H^+\) ions because each molecule of HCl contributes one \(H^+\) ion. For strong bases like NaOH, the concentration is equal to the concentration of \(OH^-\) ions, as each molecule provides one \(OH^-\) ion. The molarity of a solution directly influences its pH or pOH; a higher molarity of an acid leads to a lower pH (more acidic), while a higher molarity of a base leads to a higher pH (more basic).

pH and pOH Relationship

There is a constant relationship between pH and pOH that is governed by the ion product constant for water (\(K_w\)) at a given temperature. At 25°C, which is the standard lab temperature, \(K_w\) is \(1.0 \times 10^{-14}\). The relationship between pH and pOH is given by the equation \( pH + pOH = 14 \).

When you know the pH of a solution, you can compute the pOH, and vice versa, using this relationship. For instance, if you have an acidic solution with a pH of 2, its pOH is 12, meaning that the solution has a very low concentration of \(OH^-\) ions and a high concentration of \(H^+\) ions. This relationship is vital because it allows for the calculation of the hydroxide ion concentration from the known hydrogen ion concentration, thus helping in understanding the solution's overall neutrality, acidity, or basicity.