Question

Calculation of Molar Ratios of Conjugate Base to Weak Acid from pll For a weak acid with a pK of \(6.00\), calculate the ratio of conjugate base to acid at a pH of \(5.00\).

Short answer

The molar ratio of conjugate base to acid is 0.10.

Step-by-step solution

Understand Problem Context

We are given a weak acid where the pK (also known as pKa) is \(6.00\), and the pH of the solution is \(5.00\). We need to calculate the ratio of the conjugate base to the acid in this solution using the Henderson-Hasselbalch equation.

Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation relates the pH, pKa, and the ratio of the concentration of the conjugate base \([A^-]\) to the weak acid \([HA]\) as follows: \[\text{pH} = \text{pKa} + \log\left(\frac{[A^-]}{[HA]}\right)\]We can rearrange this equation to solve for the ratio \(\frac{[A^-]}{[HA]}\).

Rearrange for Ratio

Rearrange the Henderson-Hasselbalch equation to find the molar ratio:\[\log\left(\frac{[A^-]}{[HA]}\right) = \text{pH} - \text{pKa}\]Substitute the given values of pH and pKa into the equation:\[\log\left(\frac{[A^-]}{[HA]}\right) = 5.00 - 6.00 = -1.00\]

Calculate the Ratio

To find the ratio \(\frac{[A^-]}{[HA]}\), we need to convert the logarithmic expression into its exponential form:\[\frac{[A^-]}{[HA]} = 10^{-1.00} = 0.10\]

Conclusion

The molar ratio of the conjugate base \([A^-]\) to the weak acid \([HA]\) in the solution is \(0.10\). This means that for every part of the acid, there is 0.10 parts of its conjugate base.

Key concepts

Molar Ratios

Molar ratios in the context of chemistry refer to the proportional amounts of substances present in a solution. They are critical in understanding the balance between reactants and products in a chemical reaction. In the exercise above, the focus is on the molar ratio between a weak acid and its conjugate base. This ratio helps us understand how much of the acid has ionized to form its conjugate base. To determine this ratio, we use the Henderson-Hasselbalch equation. This equation allows us to calculate the concentration ratio of the base form to the acid form in the solution based on the pH and the pKa. Once you've calculated the difference between the pH and the pKa (in this case -1), you transform it into an exponent of 10. Therefore, a log difference of -1 corresponds to a molar ratio of 0.10. This means, in simple terms, that for each molecule of the weak acid, there are 0.10 molecules of the conjugate base present.

pH and pKa Relationship

The relationship between pH and pKa is foundational for understanding chemical equilibria involving weak acids and bases. measures the acidity or alkalinity of a solution. A lower pH indicates a more acidic environment, whereas a higher pH suggests a more basic one. The is a specific constant that tells you how readily an acid gives up its hydrogen ion. In the context of the Henderson-Hasselbalch equation:

• pH is the current state of the solution's acidity.
• pKa represents the inherent tendency of the weak acid to lose a proton.

When pH equals pKa, the concentrations of the weak acid and conjugate base are equal. If the pH is lower than the pKa, more of the weak acid is undissociated, leading to a higher concentration of acid to its conjugate base. Conversely, if pH is higher than pKa, the preference shifts towards the base form.

Weak Acid and Conjugate Base

A weak acid, unlike a strong acid, does not completely dissociate in solution. This means that it only partially releases its hydrogen ions into the solution. Each dissociation of a weak acid forms a conjugate base. This reaction is reversible and reaches an equilibrium between the acid and its conjugate base. The conjugate base is what is left after the weak acid loses a hydrogen ion. It can accept a hydrogen ion back, which is why it's called 'conjugate' – it links between the acid and base states. In practical terms:

• Take acetic acid as an example. It is a weak acid that dissociates in water to form acetate, its conjugate base.
• The extent of this dissociation is represented by the equilibrium constant, Ka, derived from pKa.

The ratio of this acid and its conjugate base in any solution determines how the solution behaves under different conditions, notably its buffer capacity or its ability to resist changes in pH when acids or bases are added.