PH & Ionization: Propanoic Acid Calculation Explained

Hey guys! Let's dive into a common chemistry problem: calculating the pH and percent ionization of a weak acid solution. In this article, we will specifically tackle a 0.35 M solution of propanoic acid (CH₃CH₂COOH) at 25°C, given its acid dissociation constant (Ka) is 1.35 × 10⁻⁵. Understanding these calculations is crucial for grasping acid-base chemistry, so let's break it down step by step.

Understanding the Basics of Weak Acids

Before we jump into the calculations, let's quickly review some key concepts about weak acids. Unlike strong acids that completely dissociate in water, weak acids only partially dissociate, meaning they don't release all their hydrogen ions (H⁺). This partial dissociation is described by the acid dissociation constant, Ka. A smaller Ka value indicates a weaker acid, meaning it dissociates less. Propanoic acid (CH₃CH₂COOH) is a classic example of a weak acid. When dissolved in water, it establishes an equilibrium between the undissociated acid, the hydronium ion (H₃O⁺), and the propanoate ion (CH₃CH₂COO⁻).

The equilibrium reaction looks like this:

CH₃CH₂COOH(aq) + H₂O(l) ⇌ H₃O⁺(aq) + CH₃CH₂COO⁻(aq)

The acid dissociation constant (Ka) for this reaction is defined as:

Ka = [H₃O⁺][CH₃CH₂COO⁻] / [CH₃CH₂COOH]

This equation tells us the ratio of products (H₃O⁺ and CH₃CH₂COO⁻) to reactants (CH₃CH₂COOH) at equilibrium. A larger Ka means more dissociation, hence a stronger acid, while a smaller Ka, like the one for propanoic acid (1.35 × 10⁻⁵), indicates a weaker acid. Now that we've got the basics down, let's move on to calculating the pH.

Step 1: Setting up the ICE Table

To calculate the pH, we need to determine the concentration of H₃O⁺ ions at equilibrium. A handy tool for this is the ICE table, which stands for Initial, Change, and Equilibrium. It helps us organize the concentrations of the reactants and products throughout the reaction. Let's set up the ICE table for the dissociation of propanoic acid.

• Initial (I): We start with a 0.35 M solution of propanoic acid, and initially, there are no H₃O⁺ or propanoate ions in the solution.
• Change (C): As the propanoic acid dissociates, its concentration decreases by 'x', while the concentrations of H₃O⁺ and propanoate ions increase by 'x'.
• Equilibrium (E): At equilibrium, the concentrations are the initial concentrations plus the changes. So, the concentration of propanoic acid is 0.35 - x, and the concentrations of H₃O⁺ and propanoate ions are both 'x'.

Step 2: Using the Ka Expression

Now that we have the equilibrium concentrations in terms of 'x', we can plug them into the Ka expression:

Ka = [H₃O⁺][CH₃CH₂COO⁻] / [CH₃CH₂COOH]

1. 35 × 10⁻⁵ = (x)(x) / (0.35 - x)

Since Ka is small (1.35 × 10⁻⁵), we can make an approximation to simplify the calculation. We assume that 'x' is much smaller than 0.35, so we can ignore it in the denominator: 0.35 - x ≈ 0.35. This approximation makes the math much easier. However, it's always a good practice to check if this approximation is valid later on.

So, our simplified equation becomes:

1. 35 × 10⁻⁵ = x² / 0.35

Step 3: Solving for 'x'

Now, let's solve for 'x', which represents the equilibrium concentration of H₃O⁺:

x² = (1.35 × 10⁻⁵) * 0.35

x² = 4.725 × 10⁻⁶

x = √(4.725 × 10⁻⁶)

x ≈ 2.17 × 10⁻³ M

So, the equilibrium concentration of H₃O⁺ is approximately 2.17 × 10⁻³ M. Now we can calculate the pH.

Step 4: Calculating the pH

The pH is defined as the negative logarithm (base 10) of the hydronium ion concentration:

pH = -log[H₃O⁺]

pH = -log(2.17 × 10⁻³)

pH ≈ 2.66

Therefore, the pH of the 0.35 M propanoic acid solution is approximately 2.66. This acidic pH value is expected for a weak acid solution.

Step 5: Calculating Percent Ionization

Percent ionization tells us the percentage of the acid that has dissociated into ions at equilibrium. It's calculated using the following formula:

Percent Ionization = ([H₃O⁺] at equilibrium / [CH₃CH₂COOH] initial) * 100%

Plugging in our values:

Percent Ionization = (2.17 × 10⁻³ M / 0.35 M) * 100%

Percent Ionization ≈ 0.62%

So, the percent ionization of propanoic acid in this solution is approximately 0.62%. This small percentage confirms that propanoic acid is indeed a weak acid, as only a small fraction of it dissociates into ions in solution.

Step 6: Checking the Approximation

Remember that we made an approximation earlier by assuming that 'x' is much smaller than 0.35. Let's check if this approximation was valid. A common rule of thumb is that if 'x' is less than 5% of the initial concentration, the approximation is valid.

(2. 17 × 10⁻³ / 0.35) * 100% ≈ 0.62%

Since 0.62% is less than 5%, our approximation is valid, and we can be confident in our results.

Conclusion

Alright, guys! We've successfully calculated the pH and percent ionization of a 0.35 M propanoic acid solution. We found that the pH is approximately 2.66, indicating an acidic solution, and the percent ionization is about 0.62%, confirming propanoic acid's status as a weak acid. By using the ICE table and the Ka expression, we were able to systematically solve this problem. Understanding these steps will help you tackle similar problems in acid-base chemistry. Keep practicing, and you'll master these calculations in no time!

Key takeaways from this calculation:

• Weak acids only partially dissociate in water.
• The Ka value quantifies the extent of dissociation.
• ICE tables are useful for organizing equilibrium concentrations.
• The pH is a measure of the acidity of a solution.
• Percent ionization indicates the fraction of acid that has dissociated.

If you have any questions or want to explore other chemistry problems, feel free to ask! Keep exploring and learning! Happy chemistry, everyone!