Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 4 - Section 4.7 - Logarithmic Scales - 4.7 Exercises - Page 385: 3

Answer

a. $[\mathrm{H}^{+}]=10^{-3}$ M b. $[\mathrm{H}^{+}]\approx 3.2\times 10^{-7}$ M

Work Step by Step

(see p.381) The $\mathrm{p}\mathrm{H}$ scale measures the acidity of a solution:$ \quad \mathrm{p}\mathrm{H}=-\log[\mathrm{H}^{+}]$ where $[\mathrm{H}^{+}]$ is the hydrogen ion concentration (in moles per liter, M). Solutions are neutral if $pH=7$ acidic if $pH < 7$ basic if $pH > 7$ ------------------ Solving for $[\mathrm{H}^{+}]$, $pH=-\log[\mathrm{H}^{+}]\qquad /\times(-1)$ $\log[\mathrm{H}^{+}]=-pH\qquad /$... apply $10^{(...)}$ to both sides $[\mathrm{H}^{+}]=10^{-pH}$ a. $pH=3.0\ \ \Rightarrow\ \ [\mathrm{H}^{+}]=10^{-3}$ M b. $pH=6.5\ \ \Rightarrow\ \ $ $[\mathrm{H}^{+}]=10^{-6.5}$ $\approx$3.1623$\times 10^{-7}\approx 3.2\times 10^{-7}$ M
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.