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: 5

Answer

approximately 4.8 to 6.4

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 $pH > 7$ ------------------ $[\mathrm{H}^{+}]=4.0\times 10^{-7}\Rightarrow$ $pH=-\log(4.0\times 10^{-7})\approx 6.4$ $[\mathrm{H}^{+}]=1.6\times 10^{-5}\Rightarrow$ $pH=-\log(1.6\times 10^{-5})\approx 4.8$ The range of pH readings: approximately 4.8 to 6.4
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