Question

Determine the pH of each solution. $$\begin{array}{l}{\text { a. } 0.0100 \mathrm{M} \mathrm{HClO}_{4}} \\\ {\text { b. } 0.115 \mathrm{M} \mathrm{HClO}_{4}} \\ {\text { c. } 0.045 \mathrm{M} \mathrm{Sr}(\mathrm{OH})_{2}} \\ {\text { d. } 0.0852 \mathrm{M} \mathrm{KCN}} \\ {\text { e. } 0.155 \mathrm{M} \mathrm{NH}_{4} \mathrm{Cl}}\end{array} $$

Short answer

pH of: a) 0.0100 M HClO4 = 2, b) 0.115 M HClO4 = 0.939, c) 0.045 M Sr(OH)2 = 12.946, d) 0.0852 M KCN is calculated using Kb and the ionic product of water, e) 0.155 M NH4Cl is calculated using Ka and the concentration of NH4+.

Step-by-step solution

Identify the nature of the compound and calculate the pH of 0.0100 M HClO4

For a strong acid such as HClO4, it fully dissociates in water. Therefore, the concentration of hydrogen ions, [H+], is equal to the concentration of the acid. Use the formula pH = -log[H+] to calculate the pH. So, pH of the solution is given by pH = -log(0.0100).

Calculate the pH of 0.115 M HClO4

Similar to Step 1, HClO4 is a strong acid and it fully dissociates. The pH is calculated by using the formula: pH = -log[H+] = -log(0.115).

Calculate the pH of 0.045 M Sr(OH)2

Sr(OH)2 is a strong base and dissociates fully in water. It releases two moles of hydroxide ions, [OH-], per mole of Sr(OH)2. The [OH-] concentration is 0.045 M * 2 = 0.090 M. Then, use the formula pOH = -log[OH-] to find pOH and then pH = 14 - pOH to find the pH.

Calculate the pH of 0.0852 M KCN

KCN is a salt that comes from a weak acid (HCN) and a strong base (KOH). In water, CN- will react with water to form HCN, increasing the OH- concentration. This can be approached by using the formula for Kb (Kb = Kw / Ka, where Kw = 10^-14 and Ka is the acid dissociation constant of HCN), and then calculating the concentration of OH- to finally find the pOH and pH.

Calculate the pH of 0.155 M NH4Cl

NH4Cl is a salt derived from NH3, a weak base, and HCl, a strong acid. In solution, NH4+ will donate a proton to water, increasing the hydronium ion concentration, [H3O+]. Use the Ka value for NH4+ (which is Kw / Kb of NH3) to find the concentration of [H3O+] and then calculate the pH using the formula pH = -log[H3O+].

Key concepts

Acid-Base Chemistry

Understanding acid-base chemistry is fundamental to calculating pH values in solutions. Acids are substances that donate protons (hydrogen ions, H+) when dissolved in water, whereas bases are substances that accept these protons. The strength of an acid or base is determined by its ability to dissociate in water. Strong acids and bases dissociate completely, while weak acids and bases do not.

For instance, HClO₄ is considered a strong acid and dissociates fully into H+ and ClO₄^- ions in solution. This full dissociation allows us to directly relate the concentration of the acid to the concentration of hydrogen ions, making the pH calculation straightforward. The fundamental formula for calculating pH is given by pH = -log[H+], where [H+] is the concentration of hydrogen ions in moles per liter. In the context of the given exercise, calculating the pH of a strong acid involved simply taking the negative logarithm of its concentration.

Strong and Weak Acids and Bases

The distinction between strong and weak acids and bases is crucial for accurate pH calculation. Strong acids, like HClO₄, and strong bases, such as Sr(OH)₂, dissociate completely in a solution, which simplifies calculation as the concentration of the acid or base equates to the concentration of H+ or OH- ions. The exercise demonstrated how Sr(OH)₂ releases two hydroxide ions for each formula unit dissolved, leading to a doubling of the molarity for pOH calculations.

On the other hand, weak acids and bases only partially dissociate, establishing an equilibrium between the undissociated and dissociated forms. The equilibrium constants for these reactions, Ka for acids and Kb for bases, indicate their strength and are valuable in calculations involving weak acids or bases, as seen with KCN and NH₄Cl in the provided solutions. The exercise highlighted using the relationship between Kw, Ka, and Kb to find the concentration of OH- or H3O+ ions for pH calculations.

pH and pOH Calculations

The concepts of pH and pOH are essential tools in quantifying the acidity or basicity of a solution. pH is a measure of the hydrogen ion concentration and is calculated using the formula pH = -log[H+]. For strong acids or bases, this calculation is straightforward as the ion concentration is equal to the original concentration of the acid or base.

Conversely, pOH measures the hydroxide ion concentration and is given by pOH = -log[OH-]. Once pOH is calculated for a basic solution, pH can be found using the formula pH = 14 - pOH, considering that at 25°C, the product of the hydrogen ion and hydroxide ion concentrations (Kw) is always 1x10^-14. This was utilized in the exercise to find the pH of strong and weak bases. The pH of weak acid or base solutions often requires a more complex approach involving equilibrium expressions and the corresponding Ka or Kb values, as the provided steps illustrated for KCN and NH₄Cl solutions.