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: 7

Answer

a. Californian: $[\mathrm{H}^{+}]\approx 6.3\times 10^{-4}$ M Italian: $[\mathrm{H}^{+}]\approx 1.26\times 10^{-3}$ M b. Californian red

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 $[\mathrm{H}^{+}]=10^{-pH}$ California red: $pH=3.2\Rightarrow[\mathrm{H}^{+}]=10^{-3.2}\approx 6.3\times 10^{-4}$ M Italian: $pH=2.9\Rightarrow[\mathrm{H}^{+}]=10^{-2.9}\approx 1.26\times 10^{-3}$ M
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