PH Calculation Of Potassium Butanoate Solution A Step-by-Step Guide

Hey guys! Let's dive into a chemistry problem where we'll calculate the pH of a potassium butanoate solution. This is a fun one because it involves a weak acid and its conjugate base, so buckle up!

Understanding the Problem

We're tasked with finding the pH of a 0.94 M solution of potassium butanoate (KC₃H₇CO₂). We know that butanoic acid (HC₃H₇CO₂) is a weak acid with a pKa of 4.82. The key here is that potassium butanoate is the salt of a weak acid, meaning it will undergo hydrolysis in water, affecting the pH.

To accurately calculate the pH, we need to consider the equilibrium established when the butanoate ion (C₃H₇CO₂⁻) reacts with water. This reaction forms butanoic acid and hydroxide ions (OH⁻), making the solution basic. The concentration of these hydroxide ions will directly influence the pH value that we are looking for. To solve this problem effectively, it’s important to first identify that we’re dealing with a weak acid salt hydrolysis problem. Recognizing this sets the stage for applying the correct methodologies and formulas. Now, let's break down the steps to tackle this problem like chemistry pros!

Step 1: Identify the Base and its Kb

So, potassium butanoate (KC₃H₇CO₂) is the salt of a weak acid, butanoic acid (HC₃H₇CO₂), and a strong base (KOH). When this salt dissolves in water, the butanoate ion (C₃H₇CO₂⁻) acts as a base and reacts with water. This is a classic example of salt hydrolysis. We need to find the base dissociation constant (Kb) for the butanoate ion. We know the pKa of butanoic acid, and we can use the following relationship:

Kw = Ka * Kb pKw = pKa + pKb

Where Kw is the ion product of water (1.0 x 10⁻¹⁴ at 25°C), Ka is the acid dissociation constant, and Kb is the base dissociation constant. Since pKw = 14 at 25°C, we can calculate pKb:

pKb = pKw - pKa pKb = 14 - 4.82 pKb = 9.18

Now, let's find Kb:

Kb = 10^(⁻pKb) Kb = 10^(⁻9.18) Kb ≈ 6.61 x 10⁻¹⁰

Step 2: Set up the ICE Table

Now that we have the Kb value, we can set up an ICE (Initial, Change, Equilibrium) table to determine the hydroxide ion concentration ([OH⁻]) at equilibrium. The butanoate ion reacts with water as follows:

C₃H₇CO₂⁻(aq) + H₂O(l) ⇌ HC₃H₇CO₂(aq) + OH⁻(aq)

Here's our ICE table:

Step 3: Solve for [OH⁻]

We can now write the equilibrium expression for Kb:

Kb = [HC₃H₇CO₂][OH⁻] / [C₃H₇CO₂⁻] 6. 61 x 10⁻¹⁰ = (x * x) / (0.94 - x)

Since Kb is small, we can assume that x is much smaller than 0.94, so 0.94 - x ≈ 0.94. This simplifies the equation:

6. 61 x 10⁻¹⁰ = x² / 0.94 x² = 6.61 x 10⁻¹⁰ * 0.94 x² ≈ 6.21 x 10⁻¹⁰ x ≈ √(6.21 x 10⁻¹⁰) x ≈ 2.49 x 10⁻⁵ M

So, [OH⁻] ≈ 2.49 x 10⁻⁵ M

Step 4: Calculate pOH

Next, let's calculate the pOH using the hydroxide ion concentration:

pOH = -log[OH⁻] pOH = -log(2.49 x 10⁻⁵) pOH ≈ 4.60

Step 5: Calculate pH

Finally, we can calculate the pH using the relationship:

pH + pOH = 14 pH = 14 - pOH pH = 14 - 4.60 pH ≈ 9.4

Conclusion

Therefore, the pH of a 0.94 M solution of potassium butanoate at 25°C is approximately 9.4. Remember, the key to solving these problems is understanding the chemistry involved, setting up the equilibrium expressions correctly, and making appropriate approximations when necessary. Keep practicing, and you'll become a pH calculation master in no time! This step-by-step approach should help anyone tackling similar problems, providing a clear pathway to the solution.

Additional Tips for Mastering pH Calculations

To really nail these pH calculations, here are a few more tips and tricks to keep in your chemistry toolkit. First off, always double-check your work, especially the small details. Did you use the correct Ka or Kb value? Did you make the right approximations? These little things can make a big difference in your final answer. When you calculate the pH, ensure that your answer makes sense in the context of the problem. For example, if you're dealing with a basic solution, your pH should be above 7. If it’s not, that’s a red flag to revisit your calculations.

Another pro tip is to practice a variety of problems. The more you work through different scenarios, the better you’ll get at recognizing patterns and applying the right formulas. Try working through examples with different weak acids and bases, and challenge yourself with buffer solutions and titrations. Each type of problem will help solidify your understanding of pH calculations. Consider using online resources and textbooks for additional practice problems. Many websites offer step-by-step solutions that can help you understand the problem-solving process.

Also, make friends with your calculator! pH calculations often involve logarithms and exponents, so make sure you're comfortable using these functions on your calculator. Practice converting between pH, pOH, [H⁺], and [OH⁻] to build your fluency. Being quick and accurate with these calculations will save you time and reduce errors on exams. Don’t forget to pay attention to significant figures in your calculations and final answer. Your answer should reflect the precision of your given values. This is a small detail, but it shows your attention to detail and understanding of scientific notation.

Lastly, teaching someone else is a fantastic way to reinforce your own learning. If you have a study buddy, try explaining the steps involved in a pH calculation. This not only helps the other person understand the material, but it also solidifies your own understanding. Sometimes, explaining a concept out loud can reveal gaps in your knowledge that you didn’t realize were there.

So, there you have it! With these tips and the step-by-step guide, you’ll be well-equipped to tackle any pH calculation that comes your way. Remember, practice makes perfect, and a solid understanding of the fundamentals will take you far in chemistry. Keep up the great work, and you’ll be acing those chemistry problems in no time! And hey, if you ever get stuck, don’t hesitate to ask for help. Chemistry can be challenging, but it’s also incredibly rewarding when you finally crack a tough problem. Happy calculating!