Question

Lactic acid (CH \(\left._{3} \mathrm{CH}(\mathrm{OH}) \mathrm{COOH}\right)\) has one acidic hydrogen. A \(0.10 \mathrm{M}\) solution of lactic acid has a \(\mathrm{pH}\) of \(2.44\) Calculate \(K_{a}\)

Short answer

The acid dissociation constant, \(K_a\), for lactic acid is approximately \(1.85 \times 10^{-4}\).

Step-by-step solution

Determine the concentration of hydrogen ions (H+)

Based on the given pH value of the solution, we can calculate the concentration of hydrogen ions (H+) present. The formula for this is: \[ \mathrm{pH} = - \log[H^+] \] We need to solve this equation for [H+].

Calculate the concentration of hydroxide ions (OH-)

Given the concentration of hydrogen ions, we can now calculate the concentration of the conjugate base (lactate ions, CH3CH(OH)COO-) using the formula for Ka and the information we have about the concentration of lactic acid. The equation for Ka is: \[ K_a = \frac{[\mathrm{CH3CH(OH)COO^-}][\mathrm{H^+}]}{[\mathrm{CH3CH(OH)COOH}]}\]

Calculate the Ka value

Now that we have the concentration of hydrogen ions and lactate ions, we can finally calculate the Ka value. Plug in the values determined in the previous steps into the formula for Ka and solve for Ka.

Key concepts

pH Calculation

Understanding pH is crucial when studying acids and bases in chemistry. The pH scale measures how acidic or basic a solution is. It ranges from 0 to 14, with 7 being neutral, below 7 acidic, and above 7 basic. The pH value is a negative logarithm of the hydrogen ion concentration in a solution.

Mathematically, it is expressed as: \[ \text{pH} = - \log[H^+] \]. Say, for example, a solution has a pH of 2.44. To find the hydrogen ion concentration represented as [H⁺], we need to reverse the pH calculation: \[ [H^+] = 10^{-\text{pH}} = 10^{-2.44} \]. This calculation gives us insight into the actual concentration of hydrogen ions present in the solution.

Hydrogen Ion Concentration

The hydrogen ion concentration, or [H⁺], is a measure of the amount of hydrogen ions present in a solution. On the molecular level, these ions are responsible for the acidic nature of substances. When we talk about the strength of an acid, we're discussing its ability to donate these H⁺ ions to a solution.

In the context of our exercise, once the pH is known, the hydrogen ion concentration can be determined through the equation: \[ [H^+] = 10^{-\text{pH}} \]. This step is essential because the hydrogen ion concentration is pivotal for further calculations, such as determining the acid dissociation constant, Ka, which helps quantify an acid’s strength.

Lactic Acid

When we delve into the world of organic acids, lactic acid, with the chemical formula \( \text{C₃H₆O₃} \), is a prime example. It possesses one carboxyl group (\( -COOH \)), which is capable of donating a hydrogen ion, thus making it an acid. It can be found in various biological systems and foods, such as fermented dairy products.

In biochemical scenarios, lactic acid acts as an intermediate in the lactic acid fermentation process, which is essential for energy production in cells when oxygen is scarce. For our pH calculation, understanding that lactic acid can release a hydrogen ion into solution is crucial, as this is the event that defines its acidic properties and influences the solution's pH.

Chemical Equilibrium

The concept of chemical equilibrium is foundational in understanding various chemical reactions, including acid-base reactions. At equilibrium, the rate of the forward reaction is equal to the rate of the reverse reaction, resulting in a constant ratio of product and reactant concentration over time, though both reactions are still occurring.

For acids, the acid dissociation constant, Ka, represents the equilibrium constant for the dissociation of an acid into its conjugate base and hydrogen ions. The equilibrium expression for a weak acid like lactic acid dissociating in water \( \text{HA} \rightleftharpoons \text{H⁺} + \text{A^-} \) would be: \[ K_a = \frac{[\text{A^-}][\text{H⁺}]}{[\text{HA}]} \]. Understanding this helps in calculating the exact strength of the acid, as knowing Ka allows chemists to predict how much acid will dissociate in a solution.