Glossary

3.3 pH scale and calculations for strong and weak acids/bases

3 min read•july 22, 2024

is a crucial concept in chemistry, measuring the acidity or basicity of solutions. It's defined as the negative logarithm of hydronium ion concentration, ranging from 0 to 14. Understanding pH helps us grasp how acids and bases behave in various contexts.

Calculating pH for strong and weak acids and bases involves different approaches. Strong acids and bases completely dissociate, making pH calculations straightforward. Weak acids and bases partially dissociate, requiring the use of dissociation constants and equilibrium calculations to determine pH.

pH and the Concentration of Hydronium Ions

Definition and significance of pH

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  • pH logarithmic scale measures acidity or basicity of a solution
    • Ranges from 0 to 14 with 7 being neutral (pure water at 25℃)
    • Lower pH values indicate higher acidity (lemon juice, vinegar)
    • Higher pH values indicate higher basicity (baking soda, bleach)
  • pH defined as negative logarithm base 10 of hydronium ion concentration [H3O+][H_3O^+] in a solution
    • Mathematical expression: pH=−log⁡10[H3O+]pH = -\log_{10}[H_3O^+]
  • Concentration of hydronium ions [H3O+][H_3O^+] inversely related to pH
    • As [H3O+][H_3O^+] increases, pH decreases and solution becomes more acidic
    • As [H3O+][H_3O^+] decreases, pH increases and solution becomes more basic
  • In pure water at 25℃, [H3O+]=[OH−]=1×10−7[H_3O^+] = [OH^-] = 1 \times 10^{-7} M resulting in neutral pH of 7
    • Acidic solutions have [H3O+]>1×10−7[H_3O^+] > 1 \times 10^{-7} M and pH<7pH < 7
    • Basic solutions have [H3O+]<1×10−7[H_3O^+] < 1 \times 10^{-7} M and pH>7pH > 7

Calculating pH for Strong and Weak Acids and Bases

pH calculations for strong acids and bases

  • Strong acids and bases completely dissociate in aqueous solutions
    • For HA: HA(aq)+H2O(l)→H3O(aq)++A(aq)−HA_{(aq)} + H_2O_{(l)} \rightarrow H_3O^+_{(aq)} + A^-_{(aq)} (hydrochloric acid HCl, nitric acid HNO₃)
    • For strong base MOH: MOH(aq)→M(aq)++OH(aq)−MOH_{(aq)} \rightarrow M^+_{(aq)} + OH^-_{(aq)} ( NaOH, potassium hydroxide KOH)
  • For strong acids, [H3O+][H_3O^+] equals initial concentration of acid
    • Calculate pH using: pH=−log⁡10[H3O+]pH = -\log_{10}[H_3O^+]
  • For strong bases, [OH−][OH^-] equals initial concentration of base
    • Calculate using: pOH=−log⁡10[OH−]pOH = -\log_{10}[OH^-]
    • Convert pOH to pH using: [pH + pOH = 14](https://www.fiveableKeyTerm:pH_+_pOH_=_14)

pH determination for weak acids and bases

  • Weak acids and bases partially dissociate in aqueous solutions
    • For HA: HA(aq)+H2O(l)⇌H3O(aq)++A(aq)−HA_{(aq)} + H_2O_{(l)} \rightleftharpoons H_3O^+_{(aq)} + A^-_{(aq)} (acetic acid CH₃COOH, benzoic acid C₆H₅COOH)
    • For B: B(aq)+H2O(l)⇌BH(aq)++OH(aq)−B_{(aq)} + H_2O_{(l)} \rightleftharpoons BH^+_{(aq)} + OH^-_{(aq)} (ammonia NH₃, methylamine CH₃NH₂)
  • Acid dissociation constant Ka used to determine pH of weak acids
    • Ka=[H3O+][A−][HA]K_a = \frac{[H_3O^+][A^-]}{[HA]}
    • Assume [H3O+]=[A−][H_3O^+] = [A^-] and [HA]initial≈[HA]equilibrium[HA]_\text{initial} \approx [HA]_\text{equilibrium}
    • Solve for [H3O+][H_3O^+] using quadratic formula or approximation methods
    • Calculate pH using: pH=−log⁡10[H3O+]pH = -\log_{10}[H_3O^+]
  • Base dissociation constant Kb used to determine pH of weak bases
    • Kb=[BH+][OH−][B]K_b = \frac{[BH^+][OH^-]}{[B]}
    • Assume [BH+]=[OH−][BH^+] = [OH^-] and [B]initial≈[B]equilibrium[B]_\text{initial} \approx [B]_\text{equilibrium}
    • Solve for [OH−][OH^-] using quadratic formula or approximation methods
    • Calculate pOH using: pOH=−log⁡10[OH−]pOH = -\log_{10}[OH^-]
    • Convert pOH to pH using: pH+pOH=14pH + pOH = 14

Converting Between pH, pOH, [H+], and [OH-]

  • pH and pOH related by equation: pH+pOH=14pH + pOH = 14
    • If given pH, calculate pOH using: pOH=14−pHpOH = 14 - pH
    • If given pOH, calculate pH using: pH=14−pOHpH = 14 - pOH
  • [H3O+][H_3O^+] and [OH−][OH^-] related by ion product of water, Kw=[H3O+][OH−]=1×10−14K_w = [H_3O^+][OH^-] = 1 \times 10^{-14} at 25℃
    1. If given [H3O+][H_3O^+], calculate [OH−][OH^-] using: [OH−]=Kw[H3O+][OH^-] = \frac{K_w}{[H_3O^+]}
    2. If given [OH−][OH^-], calculate [H3O+][H_3O^+] using: [H3O+]=Kw[OH−][H_3O^+] = \frac{K_w}{[OH^-]}
  • To convert between pH and [H3O+][H_3O^+], use:
    • pH=−log⁡10[H3O+]pH = -\log_{10}[H_3O^+]
    • [H3O+]=10−pH[H_3O^+] = 10^{-pH}
  • To convert between pOH and [OH−][OH^-], use:
    • pOH=−log⁡10[OH−]pOH = -\log_{10}[OH^-]
    • [OH−]=10−pOH[OH^-] = 10^{-pOH}

Key Terms to Review (18)

Buffer capacity: Buffer capacity refers to the ability of a buffer solution to resist changes in pH when small amounts of acid or base are added. It is a measure of how well a buffer can maintain its pH level, which is essential in various chemical reactions and biological processes. The effectiveness of a buffer depends on its concentration and the ratio of acid to its conjugate base, influencing how much acid or base can be neutralized without significantly altering the pH.
Dilution: Dilution is the process of reducing the concentration of a solute in a solution, typically by adding more solvent. This adjustment can change the properties of a solution, including its pH, which is essential when preparing solutions for various chemical reactions or analyses. Understanding dilution is crucial in preparing for acid-base titrations and accurately measuring the pH of both strong and weak acids and bases.
Dissociation Constant (Ka): The dissociation constant, denoted as $$K_a$$, is a quantitative measure of the strength of an acid in solution, specifically indicating how well an acid donates protons to water. It reflects the equilibrium between the undissociated acid and its dissociated ions in a solution, playing a crucial role in determining the pH of weak acids and their behavior in chemical reactions.
Henderson-Hasselbalch Equation: The Henderson-Hasselbalch equation is a mathematical formula used to calculate the pH of a buffer solution based on the concentration of its acidic and basic components. It connects the pH of a solution to the pKa of the acid and the ratio of the concentrations of the conjugate base to the acid, making it a vital tool for understanding buffer systems, acid-base titrations, and equilibrium in various chemical reactions.
Hydrochloric acid (HCl): Hydrochloric acid is a strong, corrosive acid that is a solution of hydrogen chloride gas in water. It is widely used in various applications, including chemical synthesis and industrial processes, and is a key player in understanding acid-base behavior and strength in solutions.
Hydrogen Ion Concentration: Hydrogen ion concentration refers to the amount of hydrogen ions (H+) present in a solution, which directly influences the acidity or alkalinity of that solution. This concentration is crucial for understanding the pH scale, as the pH value is mathematically defined as the negative logarithm of the hydrogen ion concentration. A higher concentration of hydrogen ions results in a lower pH, indicating a more acidic solution, while a lower concentration leads to a higher pH and a more basic solution.
Ionization: Ionization is the process by which an atom or a molecule acquires a negative or positive charge by gaining or losing electrons, resulting in the formation of ions. This process is crucial for understanding the behavior of acids and bases in solution, as it influences the concentration of hydrogen ions (H$^+$) or hydroxide ions (OH$^-$), which directly impacts pH and chemical reactivity.
Litmus paper: Litmus paper is a type of pH indicator used to determine the acidity or basicity of a solution. It changes color in response to the pH level: turning red in acidic solutions (pH < 7) and blue in basic solutions (pH > 7). This simple yet effective tool allows for quick assessments of whether a solution is acidic or basic, which is crucial when working with strong and weak acids or bases.
PH: pH is a measure of the acidity or basicity of a solution, representing the negative logarithm of the hydrogen ion concentration. It provides a scale that ranges from 0 to 14, where lower values indicate acidic conditions, neutral is around 7, and higher values denote basic conditions. This concept is crucial in understanding chemical reactions, especially in buffer solutions and when calculating the strength of acids and bases.
PH + pOH = 14: The equation pH + pOH = 14 defines the relationship between the acidity and basicity of a solution at 25°C, indicating that the sum of the pH and pOH values is always equal to 14. This concept is essential in understanding how the concentration of hydrogen ions (H extsuperscript{+}) and hydroxide ions (OH extsuperscript{-}) interact in aqueous solutions. It serves as a foundation for calculating the pH or pOH when one of these values is known, which is crucial for evaluating strong and weak acids and bases.
PH = -log[h+]: The equation pH = -log[h+] expresses the relationship between the concentration of hydrogen ions in a solution and its pH value. It shows that as the concentration of hydrogen ions increases, the pH value decreases, indicating a more acidic solution. This mathematical expression is crucial for understanding acidity and basicity in both strong and weak acids and bases, allowing chemists to quantify how acidic or basic a solution is.
PH scale: The pH scale is a logarithmic scale used to measure the acidity or basicity of a solution, ranging from 0 to 14. A pH of 7 is considered neutral, while values below 7 indicate acidity and values above 7 indicate alkalinity. Understanding the pH scale is crucial for calculations involving strong and weak acids and bases, as it directly relates to the concentration of hydrogen ions in a solution.
POH: The pOH is a measure of the acidity or basicity of a solution, calculated using the formula $$pOH = -\log[OH^-]$$, where $$[OH^-]$$ represents the concentration of hydroxide ions in moles per liter. This term is crucial for understanding the relationship between hydroxide ions and the overall pH of a solution, allowing for calculations involving strong and weak bases as well as their equilibrium states in aqueous solutions.
Sodium Hydroxide: Sodium hydroxide (NaOH) is a strong alkaline compound commonly known as lye or caustic soda, and it plays a crucial role in various chemical processes. Its ability to completely dissociate in water makes it a strong base, significantly affecting pH levels in solutions. As a strong base, sodium hydroxide is essential for understanding acid-base strength and the calculations associated with pH levels of both strong and weak acids and bases.
Strong acid: A strong acid is a substance that completely dissociates into its ions in an aqueous solution, meaning it donates all of its protons (H+) to the solution. This complete ionization leads to a high concentration of hydrogen ions, resulting in a low pH value. Strong acids play a crucial role in various chemical processes, including titrations and understanding acid-base equilibrium.
Temperature: Temperature is a measure of the average kinetic energy of particles in a substance, which directly influences how substances interact and react with one another. It plays a crucial role in determining reaction rates, the spontaneity of reactions, equilibrium positions, and the behavior of acids and bases.
Weak acid: A weak acid is an acid that partially dissociates in solution, meaning that only a fraction of its molecules donate protons (H+) to the solution, resulting in a lower concentration of hydrogen ions compared to strong acids. This partial ionization affects the pH of the solution and influences how these acids behave in various chemical contexts, including titrations, calculations involving pH, and their classification based on strength and equilibrium constants.
Weak base: A weak base is a substance that partially ionizes in solution, resulting in a limited increase in hydroxide ion concentration. This incomplete ionization means that weak bases do not fully dissociate in water, leading to a lower pH than strong bases. Understanding weak bases is crucial for analyzing their behavior in acid-base reactions, calculating pH levels, and determining the strength of various acids and bases.
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