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CIE A-Level Chemistry Study Notes

25.1.2 pH and Acidity Constants

Understanding pH and acidity constants is essential in A-level Chemistry, particularly for grasping the nuances of acid-base chemistry. This section explores the mathematical definitions and practical applications of pH, Ka, pKa, and Kw, equipping students with the knowledge to distinguish between strong and weak acids and bases.

Introduction to pH

pH, a critical concept in chemistry, is a scale used to specify the acidity or alkalinity of an aqueous solution. It is defined as the negative logarithm (base 10) of the hydrogen ion concentration:

(pH=log10(H+))( \text{pH} = -\log_{10} (H^+) )

On a scale of 0 to 14, lower values represent more acidic solutions, and higher values indicate more alkaline solutions. Neutral solutions, like pure water, have a pH of 7.

Ph scale with examples mentioned

Image courtesy of brgfx on freepik

Understanding Acidity Constants (Ka and pKa)

Ka - Acid Dissociation Constant

The acid dissociation constant (Ka) quantifies the strength of an acid in solution. It is the equilibrium constant for an acid's dissociation into a hydrogen ion and its conjugate base:

(HAH++A)( \text{HA} \rightleftharpoons \text{H}^+ + \text{A}^- )

The expression for Ka is:

(Ka=(H+)(A)(HA))( \text{Ka} = \frac{(\text{H}^+)(\text{A}^-)}{(\text{HA})} )

Higher Ka values indicate stronger acids, as they dissociate more in solution.

pKa - The Logarithmic Scale

pKa offers a more user-friendly way to express acid strength. It is the negative logarithm of Ka:

(pKa=log10Ka)( \text{pKa} = -\log_{10} \text{Ka} )

Lower pKa values signify stronger acids. This logarithmic scale is particularly useful in comparing the strengths of different acids.

Diagram showing Ka - acid Dissociation Constant using ethanoic acid (a weak acid) as an example.

Image courtesy of Nagwa

Kw - The Ion Product of Water

Kw, the ion product of water, represents the equilibrium constant for the self-ionisation of water:

(Kw=(H+)(OH))( \text{Kw} = (\text{H}^+)(\text{OH}^-) )

Typically, at 25°C, Kw equals (1.0×1014)(1.0 \times 10^{-14}). This constant plays a pivotal role in understanding the relationship between (H+) and (OH−) in solutions.

Kw, or the ion product constant of water.

Image courtesy of Odette-rasmussen

Calculating pH

Strong Acids and Bases

Strong acids and bases dissociate completely in solution. For example, calculating the pH of a 0.1 M solution of hydrochloric acid (a strong acid) involves directly determining the concentration of hydrogen ions:

(pH=log10(0.1)=1)( \text{pH} = -\log_{10} (0.1) = 1 )

For strong bases, one calculates the pOH first and then derives the pH using the relationship pH + pOH = 14.

Weak Acids and Bases

Weak acids and bases only partially dissociate in solution, making their pH calculations more complex. Here, the equilibrium concentration of hydrogen ions is determined using the acid's Ka value.

To calculate the pH of a weak acid like acetic acid, one must use an ICE table to find the equilibrium concentrations of all species and then apply the pH formula.

Applications in Chemistry

The understanding of pH, Ka, pKa, and Kw is crucial in various chemical contexts:

  • Titration: In acid-base titrations, calculating the pH at various points is crucial for determining the equivalence point.
  • Buffer Solutions: Designing buffer solutions requires knowledge of pH and acidity constants to maintain stable pH levels.
  • Biological Systems: Many biological processes are pH-dependent, and understanding these concepts is key to grasping biochemical reactions.

Advanced Topics in pH and Acidity Constants

The Role of Temperature

The value of Kw, and thus pH, can vary with temperature. Students should understand how changes in temperature can affect the ion product of water and the resulting pH of a solution.

The Concept of pOH

pOH, analogous to pH, is another important concept. It represents the alkalinity of a solution and is particularly useful in calculations involving bases.

A diagram showing pH and pOH scale.

Image courtesy of A Step

Henderson-Hasselbalch Equation

This equation is vital for understanding buffer solutions and their pH. It relates the pH of a solution to the pKa and the concentrations of the acid and its conjugate base:

(pH=pKa+log10((A)(HA)))( \text{pH} = \text{pKa} + \log_{10} \left( \frac{(\text{A}^-)}{(\text{HA})} \right) )

Limitations of the pH Scale

While the pH scale typically ranges from 0 to 14, it can exceed these limits in extremely acidic or basic solutions. This is an important consideration in high-level chemistry.

Conclusion

A thorough grasp of pH and acidity constants is fundamental for A-level Chemistry students. This knowledge not only aids in comprehending acid-base reactions but also provides a foundation for practical applications in various fields of chemistry and biology. Understanding these concepts facilitates a deeper appreciation of the chemical world and its intricacies.

FAQ

The pH of pure water is affected by temperature due to changes in the ion product of water (Kw). At 25°C, Kw is 1.0 × 10⁻¹⁴, and since the concentrations of hydrogen (H⁺) and hydroxide ions (OH⁻) are equal in pure water, the pH is 7. However, as temperature increases, Kw increases due to the enhanced dissociation of water molecules into hydrogen and hydroxide ions. This increased ionisation results in a higher concentration of both ions, but since the pH is dependent on the hydrogen ion concentration, the pH of pure water decreases (becomes more acidic) as temperature rises. Conversely, at lower temperatures, Kw decreases, leading to lower concentrations of these ions and a higher pH (more alkaline). This temperature dependency of pH is essential in processes where temperature control is critical, such as in biological systems and chemical reactions. It underscores the importance of considering environmental conditions when measuring and interpreting pH values, as the standard pH of 7 for neutrality is strictly true only at 25°C.

The pH scale, commonly ranged from 0 to 14, is based on the concentration of hydrogen ions in neutral water at 25°C, where the pH is 7 (neutral), and the concentrations of hydrogen (H⁺) and hydroxide ions (OH⁻) are both 1 × 10⁻⁷ M. However, in highly concentrated acidic or basic solutions, the hydrogen ion concentration can exceed 1 M (pH < 0) or the hydroxide ion concentration can exceed 1 M (pH > 14). This occurs because the pH scale is logarithmic and not limited to fixed endpoints. In extremely acidic solutions, a high concentration of hydrogen ions causes the pH to drop below 0. Conversely, in highly basic solutions, the low concentration of hydrogen ions (or high concentration of hydroxide ions) pushes the pH above 14. These extreme pH values are significant in industrial chemistry, where strong acids or bases are often used. They also challenge the traditional notion of the pH scale, highlighting its relative nature and dependence on specific conditions, particularly the solvent and temperature.

Yes, the pH of a solution can be negative, although this occurs under extreme conditions. The pH scale is commonly thought to range from 0 to 14, but these are not absolute limits. pH is defined as the negative logarithm of the hydrogen ion concentration. In highly acidic solutions, where the hydrogen ion concentration exceeds 1 Molar (M), the pH becomes negative. This situation arises with very strong acids, like concentrated sulfuric acid or hydrochloric acid, in high concentrations. For instance, a 1 M solution of a strong acid has a pH of 0, but a 10 M solution of the same acid would have a pH of -1. These extreme pH values are more theoretical and are rarely encountered in everyday situations. They are mainly of interest in industrial applications involving strong acids and in certain theoretical and experimental chemistry contexts. Understanding that pH can be negative helps in comprehending the logarithmic nature of the pH scale and the behaviour of highly acidic solutions.

The pKa value of an acid is a crucial indicator of its strength. It is the negative logarithm of the acid dissociation constant (Ka), which measures how readily an acid donates its proton to a base. A lower pKa value means a higher Ka, indicating a stronger acid that dissociates more completely in solution. This is because a lower pKa reflects a greater tendency of the acid to lose its proton. Understanding pKa values is vital in predicting the behaviour of acids in various chemical reactions, including synthesis and titration. In organic chemistry, the pKa values help predict the direction of proton transfer reactions, which are fundamental to understanding reaction mechanisms. In biochemistry, the pKa values of amino acids determine the ionisation state of proteins, affecting their structure and function. Therefore, pKa is not just a numerical value; it is a key concept that helps chemists understand and predict the behaviour of acidic substances in a wide range of chemical contexts.

The presence of a common ion in a solution of a weak acid affects its pH through the common ion effect. This phenomenon occurs when an ion that is a part of the weak acid's equilibrium (like the conjugate base) is added to the solution from another source. For instance, if acetate ions are added to an acetic acid solution, they shift the equilibrium position of the acetic acid dissociation reaction to the left (according to Le Chatelier's Principle), reducing the concentration of hydrogen ions and increasing the pH. This effect is crucial in understanding buffer solutions and their resistance to pH changes. The equilibrium expression for the weak acid is altered by the increased concentration of the common ion, resulting in a lower degree of ionisation of the acid. This principle is used in many practical applications, including controlling pH in industrial processes and biological systems, where maintaining a stable pH is essential.

Practice Questions

Calculate the pH of a 0.025 M solution of hydrochloric acid (HCl), a strong acid. Then, determine the pH after adding 0.010 moles of sodium hydroxide (NaOH) to 1 litre of the original HCl solution.

Hydrochloric acid is a strong acid and dissociates completely in water. The pH of the 0.025 M HCl solution is calculated using the formula pH = -log(H+). The (H+) is equal to the concentration of HCl, which is 0.025 M. Thus, pH = -log(0.025) ≈ 1.60. When NaOH is added, it neutralises some of the HCl. The number of moles of HCl initially present is 0.025 moles (0.025 M × 1 L). After adding 0.010 moles of NaOH, 0.015 moles of HCl remain unneutralised in 1 L, making the concentration 0.015 M. The new pH is -log(0.015) ≈ 1.82.

Given a 0.10 M solution of acetic acid (CH3COOH) with a Ka of 1.8 × 10^-5, calculate the pH of the solution.

To calculate the pH of a weak acid like acetic acid, we need to set up an equilibrium expression using its Ka value. The dissociation of acetic acid in water can be represented as CH3COOH ⇌ H+ + CH3COO-. Let x be the concentration of H+ at equilibrium. The ICE table shows the initial concentration of CH3COOH is 0.10 M, and at equilibrium, it is 0.10 - x. The equilibrium expression is Ka = (H+)(CH3COO-)/(CH3COOH). Substituting the values, we get 1.8 × 10^-5 = x^2/(0.10 - x). Assuming x << 0.10, we simplify to 1.8 × 10^-5 = x^2/0.10. Solving for x gives x ≈ 1.34 × 10^-3 M. Therefore, pH = -log(1.34 × 10^-3) ≈ 2.87.

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