Determine the [H 3 O + ] and pH of a 0.100 M solution of benzoic acid.

Hey everyone we're asked what is the ph of 45 mL of 0.187 moller economic asset tight traded with zero mL of 0.200 molar sodium hydroxide first. Let's go ahead and write out our reaction. We know that economic acid is a weak acid so we can simply write H. A. To represent ethanol like acid. And we react this with water and we end up with the an ion of economic acid plus our hydro ni um ions. We can then create our ice chart. And we know that initially we had 0.187 moller of our economic acid and we had zero of our products. Initially we can disregard our water since it is a liquid and our change is going to be minus X. For our economic acid and a plus X. On our product side. Since we're losing reactant and gaining products in our equilibrium, we have 0.187 minus eggs for our economic acid and an X. And an X. In our products. When we check our textbooks, we find that the K. A. Of economic acid is 1.8 times 10 to the negative five to sell for X. We know that our K. Is equivalent to our products over our reactant. So it would be X. Times X over 0.187 minus X. Now in order to check if we can disregard our X. We can go ahead And take our 0. And divide this by our K. A. of 1.8 times 10 to the -5. We find that our answer comes up to 10,388 which is greater than 500. And since it is greater than 500 we can go ahead and disregard our X. In our denominator. To simplify this a bit further, we have 1.8 times 10 to negative five is going to be equal to X squared over 0.187. We can go ahead and multiply both sides by 0.187. And we then get X squared equals 3.366 times 10 to the negative six. Taking the square root. We end up with X equals 1.8347 times 10 to the -3. And this is going to be the concentration of our hydro ni um ions. And since our question was asking us for the Ph We can then take the negative log of 1.8347 times 10 to the negative third. And this will get us to a ph of 2.74 which is going to be our final answer. So I hope that made sense. And let us know if you have any questions

Ch.17 - Acids and Bases

All textbooks

Tro 5th Edition

Ch.17 - Acids and Bases

Problem 63

Chapter 17, Problem 63

Determine the [H₃O⁺] and pH of a 0.100 M solution of benzoic acid.

Verified step by step guidance

Identify the chemical formula of benzoic acid, which is C_6H_5COOH, and recognize it as a weak acid.

Write the equilibrium expression for the dissociation of benzoic acid in water: C_6H_5COOH \rightleftharpoons C_6H_5COO^- + H_3O^+.

Use the acid dissociation constant (K_a) for benzoic acid, which is typically provided in a table, to set up the expression: K_a = \frac{[C_6H_5COO^-][H_3O^+]}{[C_6H_5COOH]}.

Assume that the initial concentration of benzoic acid is 0.100 M and that the change in concentration due to dissociation is x, leading to the equilibrium concentrations: [C_6H_5COOH] = 0.100 - x, [C_6H_5COO^-] = x, and [H_3O^+] = x.

Substitute these equilibrium concentrations into the K_a expression and solve for x, which represents [H_3O^+]. Then, calculate the pH using the formula pH = -\log[H_3O^+].

Verified Solution

Video duration:

This video solution was recommended by our tutors as helpful for the problem above.

Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Acid-Base Chemistry

Acid-base chemistry involves the study of substances that can donate protons (acids) or accept protons (bases). In this context, benzoic acid acts as a weak acid, partially dissociating in solution to produce hydronium ions (H3O+). Understanding the behavior of weak acids is crucial for calculating the concentration of H3O+ in solution.

Dissociation Constant (Ka)

The dissociation constant (Ka) quantifies the strength of an acid in solution, representing the equilibrium between the undissociated acid and its ions. For benzoic acid, the Ka value allows us to determine the extent of its dissociation in a 0.100 M solution, which is essential for calculating the concentration of H3O+ and subsequently the pH.

pH Scale

The pH scale measures the acidity or basicity of a solution, defined as the negative logarithm of the hydronium ion concentration: pH = -log[H3O+]. A lower pH indicates a more acidic solution. Understanding how to convert the concentration of H3O+ into pH is vital for interpreting the acidity of the benzoic acid solution.