Determine the [H 3 O + ] and pH of a 0.200 M solution of formic 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

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Tro 5th Edition

Ch.17 - Acids and Bases

Problem 64

Chapter 17, Problem 64

Determine the [H₃O⁺] and pH of a 0.200 M solution of formic acid.

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Identify the chemical formula for formic acid, which is HCOOH.

Write the dissociation equation for formic acid in water: \( \text{HCOOH} + \text{H}_2\text{O} \rightleftharpoons \text{H}_3\text{O}^+ + \text{HCOO}^- \).

Use the acid dissociation constant \( K_a \) for formic acid, which is typically given or can be found in a reference table.

Set up an ICE (Initial, Change, Equilibrium) table to determine the concentrations of the species at equilibrium.

Use the expression for \( K_a = \frac{[\text{H}_3\text{O}^+][\text{HCOO}^-]}{[\text{HCOOH}]} \) to solve for \([\text{H}_3\text{O}^+]\), and then calculate the pH using \( \text{pH} = -\log[\text{H}_3\text{O}^+] \).

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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 (H+) or accept protons. In this context, formic acid (HCOOH) is a weak acid that partially dissociates in water to produce H3O+ ions. Understanding the behavior of weak acids is crucial for calculating the concentration of hydronium ions in solution.

Dissociation Constant (Ka)

The dissociation constant (Ka) quantifies the strength of an acid in solution. For formic acid, Ka is used to determine the extent of its dissociation into H3O+ and its conjugate base (HCOO-). This constant is essential for calculating the equilibrium concentrations of the species in the solution.

pH Calculation

pH is a measure of the acidity of a solution, defined as the negative logarithm of the hydronium ion concentration: pH = -log[H3O+]. To find the pH of the formic acid solution, one must first determine the concentration of H3O+ using the dissociation constant and then apply the pH formula. This relationship is fundamental in acid-base chemistry.

Determine the [H3O+] and pH of a 0.200 M solution of formic acid.

Verified Solution

Key Concepts

Acid-Base Chemistry

Dissociation Constant (K<sub>a</sub>)

pH Calculation

Determine the [H₃O⁺] and pH of a 0.200 M solution of formic acid.