Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 16: Problem 14

What is the pH of the buffer \(0.10 \mathrm{M} \mathrm{Na}_{2} \mathrm{HPO}_{4} /\) \(0.15 M \mathrm{KH}_{2} \mathrm{PO}_{4} ?\)

Short Answer

Expert verified
The pH of the given buffer is approximately 7.02.

Step by step solution

01

Identify the Buffer System

Firstly, identify the acid and its conjugate base in the buffer system. Here, the buffer solution is a mixture of \( \mathrm{Na_{2}HPO_{4}} \) and \( \mathrm{KH_{2}PO_{4}} \). These can be seen as salts that will release phosphate ions in solution to form a buffer. We can simplify this complex buffer system to the simple phosphate buffer system, depicted as \( \mathrm{H_{2}PO_{4}^{-}} \) (as acid) and \( \mathrm{HPO_{4}^{2-}} \) (as its conjugate base).
02

Use Henderson-Hasselbalch Equation

Now that we know the acid/base pair, we can use the Henderson-Hasselbalch equation which is: \[ \mathrm{pH} = \mathrm{pKa} + \log \left(\frac{[\mathrm{Base}]}{[\mathrm{Acid}]}\right) \] Here, the pKa for the conversion between \( \mathrm{H_{2}PO_{4}^{-}} \) and \( \mathrm{HPO_{4}^{2-}} \) is 7.2 (which can be found in a pKa table or given in the problem). The concentrations of base \(\mathrm{[HPO_{4}^{2-}]} = 0.10 M\) and acid \(\mathrm{[H_{2}PO_{4}^{-}]} = 0.15 M\) are given in the problem.
03

Substitute the Values and Solve

Now, substitute the values into the Henderson-Hasselbalch equation: \[ \mathrm{pH} = 7.2 + \log \left(\frac{0.10}{0.15}\right) \] Now, compute the logarithm and substitute it back into the equation. Using a calculator, the logarithm of \(\frac{0.10}{0.15}\) is approximately -0.18. Substituting this back into equation, we get \( \mathrm{pH} = 7.2 - 0.18 = 7.02 \). Hence, the pH of the buffer is approximately 7.02.

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

How many grams of \(\mathrm{CaCO}_{3}\) will dissolve in \(3.0 \times\) \(10^{2} \mathrm{~mL}\) of \(0.050 \mathrm{M} \mathrm{Ca}\left(\mathrm{NO}_{3}\right)_{2} ?\)

Calculate the \(\mathrm{pH}\) of the following two buffer solutions: (a) \(2.0 \mathrm{M} \mathrm{CH}_{3} \mathrm{COONa} / 2.0 \mathrm{M} \mathrm{CH}_{3} \mathrm{COOH}\), (b) \(0.20 \mathrm{M} \mathrm{CH}_{3} \mathrm{COONa} / 0.20 \mathrm{M} \mathrm{CH}_{3} \mathrm{COOH} .\) Which is the more effective buffer? Why?

For which of the following reactions is the equilibrium constant called a solubility product? $$ \begin{array}{l} \text { (a) } \mathrm{Zn}(\mathrm{OH})_{2}(s)+2 \mathrm{OH}^{-}(a q) \rightleftharpoons \\ \text { (b) } 3 \mathrm{Ca}^{2+}(a q)+2 \mathrm{PO}_{4}^{3-}(a q) \rightleftharpoons \mathrm{Ca}_{3}(\mathrm{OH})_{4}^{2-}(a q) \end{array} $$ (c) \(\mathrm{CaCO}_{3}(s)+2 \mathrm{H}^{+}(a q) \rightleftharpoons\) $$ \mathrm{Ca}^{2+}(a q)+\mathrm{H}_{2} \mathrm{O}(l)+\mathrm{CO}_{2}(g) $$ (d) \(\mathrm{PbI}_{2}(s) \rightleftharpoons \mathrm{Pb}^{2+}(a q)+2 \mathrm{I}^{-}(a q)\)

Calculate the \(\mathrm{pH}\) of the \(0.20 \mathrm{M} \mathrm{NH}_{3} / 0.20 \mathrm{M} \mathrm{NH}_{4} \mathrm{Cl}\) buffer. What is the pH of the buffer after the addition of \(10.0 \mathrm{~mL}\) of \(0.10 \mathrm{M} \mathrm{HCl}\) to \(65.0 \mathrm{~mL}\) of the buffer?

Calculate the \(\mathrm{pH}\) of \(1.00 \mathrm{~L}\) of the buffer \(1.00 \mathrm{M}\) \(\mathrm{CH}_{3} \mathrm{COONa} / 1.00 \mathrm{M} \mathrm{CH}_{3} \mathrm{COOH}\) before and after the addition of (a) \(0.080 \mathrm{~mol} \mathrm{NaOH},\) (b) \(0.12 \mathrm{~mol} \mathrm{HCl}\). (Assume that there is no change in volume.)
See all solutions

Recommended explanations on Chemistry Textbooks

Chemical Reactions

Read Explanation

Kinetics

Read Explanation

Organic Chemistry

Read Explanation

Chemistry Branches

Read Explanation

Making Measurements

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