Question

Calculate \(K_{\mathrm{a}}\) 's for the following acids: (a) Citric acid, \(\mathrm{pK}_{\mathrm{a}}=3.14\) (b) Tartaric acid, \(\mathrm{pK}_{\mathrm{a}}=2.98\)

Short answer

Citric acid: \( K_a \approx 7.24 \times 10^{-4} \); Tartaric acid: \( K_a \approx 1.05 \times 10^{-3} \).

Step-by-step solution

Understand the Relationship

The relationship between the acid dissociation constant \( K_a \) and the \( \mathrm{pK}_a \) value is given by the formula: \( \mathrm{pK}_a = -\log_{10}(K_a) \). We will use this relationship to find the \( K_a \) values.

Rearrange the Formula

To find \( K_a \) from \( \mathrm{pK}_a \), we rearrange the formula: \[ K_a = 10^{-\mathrm{pK}_a} \] This formula allows us to compute \( K_a \) directly from the given \( \mathrm{pK}_a \).

Calculate \( K_a \) for Citric Acid

For citric acid, \( \mathrm{pK}_a = 3.14 \). Using the formula from Step 2: \[ K_a = 10^{-3.14} \] Calculate: \[ K_a \approx 7.24 \times 10^{-4} \]

Calculate \( K_a \) for Tartaric Acid

For tartaric acid, \( \mathrm{pK}_a = 2.98 \). Using the formula from Step 2: \[ K_a = 10^{-2.98} \] Calculate: \[ K_a \approx 1.05 \times 10^{-3} \]

Final Verification

Verify the calculations by checking a calculator's output for \( 10^{-3.14} \) and \( 10^{-2.98} \). Ensure the decimals align with provided results.

Key concepts

Understanding Citric Acid

Citric acid is a weak organic acid naturally found in citrus fruits like lemons and limes. It is known for its sour taste and its role in the food and beverage industry as a natural preservative and flavor enhancer. In the context of chemistry, citric acid is significant due to its multifaceted role. It is often used to adjust pH levels and as a buffer helping to maintain the stability of solutions.
The structure of citric acid makes it a triprotic acid. This means it can donate three protons (H⁺ ions) during a reaction, but for simplicity in most calculations, we usually focus on the first dissociation. Each dissociation level has its own value of the acid dissociation constant, or Ka, which reflects the strength of the acid in solution. A lower pKa value, like 3.14 for citric acid, indicates a stronger acid compared to ones with higher pKa values.
Understanding citric acid's dissociation properties helps in many applications, whether in designing industrial processes or understanding biological pathways like the citric acid cycle, a key energy-producing process in cellular metabolism.

Exploring Tartaric Acid

Tartaric acid is another important organic acid that is predominantly found in grapes and is a key component in winemaking. Besides its application in wine production, tartaric acid is used in baking powders, cream of tartar, and as an antioxidant. It is a diprotic acid, meaning it can donate two protons (H⁺ ions) in solution.
The pKa value of tartaric acid at 2.98 suggests it is slightly stronger than citric acid, given the smaller numerical pKa. This lower pKa indicates a higher concentration of hydrogen ions when the acid is dissolved in water, which can have implications in balancing the acidity of wine and controlling the tartness or sourness of various food products.
Tartaric acid's relevance extends into chemistry and biology, particularly for its role in stereochemistry as it possesses multiple stereoisomers, which have different physical properties and reactivities. This adds a layer of complexity and interest to its study beyond its primary dissociation capabilities.

Introduction to Chemical Equilibrium

Chemical equilibrium is a fundamental concept in chemistry where the rate of the forward reaction equals the rate of the reverse reaction. This state of balance results in the concentrations of reactants and products remaining constant over time. In the context of acid-base reactions, understanding equilibrium helps in computing and predicting how an acid like citric or tartaric reaches equilibrium in solution.
Equilibrium in these reactions is described by the equilibrium constant, K, which for acids is represented as the acid dissociation constant, Ka. This constant provides insight into the extent of dissociation of the acid in solution. The higher the Ka, the more the acid dissociates, producing more hydrogen ions, which contributes to the overall acidity of the solution.
In practical terms, knowing the Ka and pKa values enables chemists to predict reactions' behaviors, manipulate conditions to favor certain outcomes, and design buffers to stabilize pH in various applications, from industrial processes to biological systems. grasping this concept is crucial for a myriad of scientific developments and everyday applications like food preservation and pharmaceuticals.