Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 15: Problem 34

A buffered solution is made by adding \(50.0 \mathrm{~g} \mathrm{NH}_{4} \mathrm{Cl}\) to \(1.00 \mathrm{~L}\) of a \(0.75 M\) solution of \(\mathrm{NH}_{3}\). Calculate the \(\mathrm{pH}\) of the final solution. (Assume no volume change.)

Short Answer

Expert verified
The pH of the final solution is 9.14.

Step by step solution

01

Calculate the moles of NH4Cl and NH3 in the solution

First, we'll find the moles of NH4Cl that are added: Moles of NH4Cl = mass / molar mass = \( \frac{50.0\,\text{g}}{53.49\,\text{g/mol}} \) = 0.935 moles Now we find the moles of NH3 in the solution: Moles of NH3 = concentration × volume = (0.75 mol/L) × (1.00 L) = 0.75 moles
02

Calculate the concentrations of NH4+ and NH3 after mixing

Assuming no volume change, the volume remains 1.00 L. Then, \[ [\mathrm{NH_4}^+] = \frac{0.935\,\text{moles}}{1.00\,\text{L}} = 0.935\,\text{M} \] \[ [\mathrm{NH_3}] = \frac{0.75\,\text{moles}}{1.00\,\text{L}} = 0.75\,\text{M} \]
03

Calculate the pKa for NH4+ using the pKb of NH3

First, we need to find the pKa of NH4+ using the formula: \[ pK_a + pK_b = 14 \] The pKb of NH3 is given as 4.75, so we can find pKa: \[ pK_a = 14 - pK_b = 14 - 4.75 = 9.25 \]
04

Calculate the final pH using the Henderson-Hasselbalch equation

Now we will use the Henderson-Hasselbalch equation to find the pH of the solution: \[ pH = pK_a + \log \frac{[\mathrm{conjugate\,base}]}{[\mathrm{weak\,acid}]} \] In our case, the conjugate base is NH3 and the weak acid is NH4+: \[ pH = 9.25 + \log \frac{0.75\,\text{M}}{0.935\,\text{M}} = 9.25 - 0.108 = 9.14 \] Therefore, the pH of the final solution is 9.14.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

A certain acetic acid solution has \(\mathrm{pH}=2.68\). Calculate the volume of \(0.0975 M \mathrm{KOH}\) required to reach the equivalence point in the titration of \(25.0 \mathrm{~mL}\) of the acetic acid solution.

A student dissolves \(0.0100 \mathrm{~mol}\) of an unknown weak base in \(100.0 \mathrm{~mL}\) water and titrates the solution with \(0.100 \mathrm{M} \mathrm{HNO}_{3}\). After \(40.0 \mathrm{~mL}\) of \(0.100 \mathrm{M} \mathrm{HNO}_{3}\) was added, the \(\mathrm{pH}\) of the resulting solution was \(8.00 .\) Calculate the \(K_{\mathrm{b}}\) value for the weak base.

The active ingredient in aspirin is acetylsalicylic acid. A \(2.51-g\) sample of acetylsalicylic acid required \(27.36 \mathrm{~mL}\) of \(0.5106 M\) \(\mathrm{NaOH}\) for complete reaction. Addition of \(13.68 \mathrm{~mL}\) of \(0.5106 \mathrm{M}\) \(\mathrm{HCl}\) to the flask containing the aspirin and the sodium hydroxide produced a mixture with \(\mathrm{pH}=3.48\). Determine the molar mass of acetylsalicylic acid and its \(K_{\mathrm{a}}\) value. State any assumptions you must make to reach your answer.

Amino acids are the building blocks for all proteins in our bodies. A structure for the amino acid alanine is All amino acids have at least two functional groups with acidic or basic properties. In alanine, the carboxylic acid group has \(K_{\mathrm{a}}=4.5 \times 10^{-3}\) and the amino group has \(K_{\mathrm{b}}=7.4 \times 10^{-5} .\) Because of the two groups with acidic or basic properties, three different charged ions of alanine are possible when alanine is dissolved in water. Which of these ions would predominate in a solution with \(\left[\mathrm{H}^{+}\right]=1.0 M ?\) In a solution with \(\left[\mathrm{OH}^{-}\right]=\) \(1.0 M ?\)

What volumes of \(0.50 \mathrm{M} \mathrm{HNO}_{2}\) and \(0.50 \mathrm{M} \mathrm{NaNO}_{2}\) must be mixed to prepare \(1.00 \mathrm{~L}\) of a solution buffered at \(\mathrm{pH}=3.55\) ?
See all solutions

Recommended explanations on Chemistry Textbooks

Making Measurements

Read Explanation

Physical Chemistry

Read Explanation

Organic Chemistry

Read Explanation

Inorganic Chemistry

Read Explanation

Kinetics

Read Explanation

Chemical Analysis

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free