Dr. J’s MCAT Chemistry Notes
pH calculations made easy by Vernon W. Jeffrey, MD
Dr. J’s MCAT® Chemistry Notes: pH Calculations Made Easy Copyright © 2015 by DRJ Media, LLC All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopied, recorded, or otherwise, without the prior written permission of the publisher. MCAT® is as registered service mark of the Association of American Medical Colleges which is not affiliated with this book.
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Table of Contents Foreword……………………………………………………..……,,,....1
Strong Acids and Bases…………………………………..…...….........2
Table II: Hydronium Ion Concentration as pH………………………………………………………..…………...…3
Quick Review of Logarithms………………………………..……..…4
Calculating pH…………………………….......................................…6 -Calculating pH for Strong Acids and Bases…………………………..6 -Calculating pH for Weak Acids and Bases……………………….......9 -Determining Concentration from pH for Strong Acids and Bases…..12
Practice Questions……………………………………………….…..15
Answers………………………………………………….…………....17
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1 Foreword
With practice, anything can be mastered over time – including chemistry. One of the topics that takes a while to comprehend is the conversion of pH to concentration and vice versa. The use of logarithms, scientific notation, and chemistry concepts can seem confusing at times. With practice, it can be overcome. As I studied for the new MCAT, which does not require the use of calculators, I found that I often took some time to do pH calculations on paper, or in my head. I needed a faster way to do them, and as I learned about the method, I decided to take that small section of chemistry and put it in a small book to share with other students who are studying chemistry. The concepts and problems within this book should help you to become more comfortable with pH calculations without using a calculator. I begin by reviewing the basic concepts of logarithms and its relation to pH. Then, methodically, I walk you through converting pH to concentration with both strong and weak acids and bases. The best way to use this book is to read through and practice the sample problems in the book, along with the problems at the end. Through this effort, you will become comfortable with going back and forth between pH and concentration without having to pick up your calculator – a skill that is extremely handy for those taking the MCAT. Whether you are taking the MCAT, or any other standardized entrance exam, or just a student who is taking general chemistry, this book will be extremely helpful This book is no substitution for an actual chemistry textbook and should be used as a supplement. I hope that you will benefit from my notes.
Dr. J
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2 TABLE I
STRONG ACIDS
Acid
Name
HCl
Hydrochloric Acid
HBr
Hydrobromic Acid
HI
Hyrdoiodic Acid
H2SO4
Sulfuric Acid
HNO3
Nitric Acid
HClO4
Perchloric Acid
STRONG BASES The most common soluble strong bases are the ionic hydroxides of the alkali metals (group 1A) and the heavier alkaline earth metals (group 2A), such as NaOH, KOH, and Ca(OH)2. Strong bases are also created by certain substances that react with water to form OH-(aq). The most common of these contain the oxide ion (O2-): O2-(aq) + H2O(l) 2OH-(aq) Ionic hydrides and nitrides also react with H2O to form OH-: N3-(aq) + 3H2O(l) NH3(aq) + 3OH-(aq) H-(aq) + H2O(l) H2(g) + OH-(aq)
3 TABLE II EXPRESSING HYDRONIUM CONCENTRATION AS pH
[H3O+]
Scientific Notation
pH
10
1.0 x 101
-1
1.0
1.0 x 100
0
0.1
1.0 x 10-1
1
0.01
1.0 x 10-2
2
0.001
1.0 x 10-3
3
0.0001
1.0 x 10-4
4
0.00001
1.0 x 10-5
5
0.000001
1.0 x 10-6
6
0.0000001
1.0 x 10-7
7
0.00000001
1.0 x 10-8
8
0.000000001
1.0 x 10-9
9
0.0000000001
1.0 x 10-10
10
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4 QUICK REVIEW OF LOGARITHMS In mathematics, the logarithm of a number is the exponent to which another fixed value, the base, must be raised to produce that number. For chemistry and the MCAT, you will use the common logarithms which use 10 as a base. Example 1: The logarithm of 1000 to base 10 is 3. log101000 = 3 log10103 = 3 Each example represents the same expression. logarithm.
In each case, 10 is the base and 3 is the
Example 2: The logarithm of .001 to base 10 is -3. log10.001 = -3 log1010-3 = -3 Each example represents the same expression. In each case, 10 is the base and -3 is the logarithm. Log Properties: For the purposes of working with acids and bases, it is important to remember that when you multiply numbers, you add their logs. When you divide numbers, you subtract their logs. Example 3: Log (4 x 5) = log 4 + log 5 Log (8 á 2) = log 8 – log 2 Log (1 x 103) = log 1 + log 103 = 0 + 3 = 3
5 Table III LOGARITHM CONVERSIONS
Number
Mathematical Calculations
Log Value
1
Given Value
0
2
Given Value
.301
3
Given Value
.477
4
Log 4 = Log (2 x 2) = log 2 + log 2 = .301 + .301 = .602
.602
5
Log 5 = Log (10 ÷ 2) = log 10 - log 2 = 1.00 - .301 = .699
.699
6
Log 6 = Log (3 x 2) = log 3 + log 2 = .477 + .301 = .699
.778
7
Given Value
.845
8
Log 8 = Log (2 x 2 x 2) = 3 (log 2) = 3(.301) = .903
.903
9
Log 9 = Log (3 x 3) = log 3 + log 3 = .477 + .477 = .954
.954
10
Given Value
1
These log values should be memorized. You should also understand how their logs are derived as well. These log values are estimates, but will help you to solve any pH problem. Now, let’s begin to calculate pH values.
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6 CALCULATING pH As you already know, a solution’s acidy is measured in terms of its hydronium ion concentration ([H3O+]) using the pH scale. The pH value of a solution is determined using Equation 1: pH = -log [H3O+] A solution’s basicity is measured in terms of its hydroxide ion concentration ([OH-]) using the pOH scale. The pOH value of a solution is determined using the following Equation 2: pOH = -log [OH-] pH and pOH are related through Equation 3: pH + pOH = 14 Finding the pH values of numbers which are multiples of 10 (ex., .1, 10, 100) is relatively straightforward since the logs are all whole numbers. However, when finding pH values of other numbers, it can become somewhat cumbersome. However, there are tricks to calculating pH without using your calculator.
Calculating pH for Strong Acids and Bases: First, make sure that you review Table I at the beginning of this book so that you know what are the strong acids and bases. This is important for both your chemistry classes and the MCAT. Commit them to memory because, at some point, you will see a question on them. Calculating the pH for strong acids and bases is based on the principle that these solutions have full dissociation of the acids and bases: HCl (aq) H+ (aq) + Cl- (aq)
(~100% dissociation)
NaOH (aq) Na+ (aq) + OH- (aq)
(~100% dissociation)
Therefore, the concentration of the strong acid can be substituted for the concentration of [H3O+] in Equation 1, whereas the concentration of the strong base can be substituted for the concentration of hydroxide ion [OH-] in Equation 2. ______________________________________________________________________________ Question 1: What is the pH of 0.0020 M HCl (aq) ?
7 A. B. C. D.
2.00 2.70 3.00 3.70
Solution First, convert the concentration into an exponent to make the calculations easier to work with: 0.0020 M HCl = 2 x 10-3 M HCl Next, plug the value into Equation 1: pH = -log [2 x 10-3] Remember that when multiplying numbers, you add their logs: pH = - (log 2 + log 10-3) = - log 2 - log 10-3 pH = - log 2 - ( - 3) = 3 - log 2 From Table II, the log 2 = .301 pH = 3 – 0.3 = 2.7 The correct answer is choice B. You could have eliminated choices A and B because whole numbers only work if the concentration is a power of ten. From this example, you can use a shortcut for future problems. You might have noticed that the - log of 2 x 10-3 is equal to 3 - log 2. Therefore, you can use this relationship: Equation 4: -log (z x 10-y) = y – log z. ______________________________________________________________________________ Question 2: What is the pOH of 0.050 M KOH(aq)? A. B. C. D.
1.30 1.70 12.30 12.70
Solution The steps to solving for pOH are the same as for solving for pH. First, convert the concentration into an exponent to make the calculations easier to work with: Copyright © 2015 by DRJ Media, LLC