Problem 114 - General Chemistry

Question

Sodium benzoate is a salt of benzoic acid, \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COOH} .\) A \(0.15 \mathrm{M}\) solution of this salt has a \(\mathrm{pOH}\) of 5.31 at room temperature.

Step-by-Step Solution

Answer

pH of the solution is 8.69.

Step 1: Understand the Relationship Between pH and pOH

The sum of the pH and pOH of a solution at room temperature (25°C) is always 14. This is based on the ion product constant of water, which states that \( \text{pH} + \text{pOH} = 14 \).

Step 2: Calculate the pH

We have the pOH given as 5.31. Using the relationship from Step 1, calculate the pH: \( \text{pH} = 14 - \text{pOH} = 14 - 5.31 = 8.69 \).

Step 3: Describe the Solution

Since the pH of the solution is greater than 7, this solution is basic. This is consistent with the behavior of sodium benzoate, which is a salt of a weak acid and a strong base.

Key Concepts

Ion Product Constant of Water

Water undergoes a self-ionization process where it dissociates into two ions: hydrogen ions \( ext{H}^{+} \) and hydroxide ions \( ext{OH}^{-} \). Despite being a weak reaction, this balance is crucial in defining the acidity or basicity of water-based solutions. This equilibrium is defined by the ion product constant of water, denoted as \( K_w \), which at room temperature (25°C) has a value of \( 1.0 \times 10^{-14} \).

• The equation for this constant is: \([H^{+}][OH^{-}] = 1.0 \times 10^{-14}\)
• At this temperature, the pH and pOH sum to \(14\)

This simple relationship is essential for calculating the pH or pOH of solutions, allowing us to switch between these two measures seamlessly. Since pH indicates how acidic a solution is and pOH how basic it is, knowing one allows us to find the other easily.

Sodium Benzoate

Sodium benzoate is a common food preservative and a derivative of benzoic acid, known for its antimicrobial properties. Sodium benzoate itself is a salt formed from the reaction of the weak acid, benzoic acid, and a strong base like sodium hydroxide. Because of its composition, in an aqueous solution, sodium benzoate acts differently than its acid counterpart.

• In water, sodium benzoate dissociates into sodium ions \( ext{Na}^{+} \) and benzoate ions \( ext{C}_6 ext{H}_5 ext{COO}^{-} \).
• The benzoate ion is the conjugate base of the weak acid benzoic acid.

This makes a solution of sodium benzoate slightly basic because it tends to shift the equilibrium in water to generate more hydroxide ions \( ext{OH}^{-} \). Thus, predicting its acid-base behavior involves understanding these dissociation dynamics.

Acid-Base Properties

Acid-base properties of compounds involve their ability to donate or accept protons. Acids are proton donors, while bases are proton acceptors. Sodium benzoate is the salt of a weak acid (benzoic acid) and a strong base (sodium hydroxide), giving it unique properties in solution.

• It does not donate protons easily, which is a characteristic of weak acids.
• Instead, it releases benzoate ions that combine with protons in the solution, reducing the overall free hydrogen ion concentration.

This reaction makes the solution basic, as indicated by its pH value above 7. Sodium benzoate is an example of a basic salt due to its reaction products in water.

pH Calculation

With any aqueous solution at 25°C, the pH can be determined if the pOH is known, thanks to the relationship \( ext{pH} + ext{pOH} = 14 \). This relation is derived from the ion product constant of water.In the case of sodium benzoate solution, we are given the pOH as \( 5.31 \). To find the pH, we use:\[ ext{pH} = 14 - ext{pOH} = 14 - 5.31 = 8.69\]

• Since the calculated pH is greater than 7, it indicates a basic solution.
• This calculation aligns with the chemistry of sodium benzoate, confirming its basic properties.

Remember, understanding the pH helps us anticipate the chemical behavior and potential reactions of compounds in the solution.