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Chapter 16: Problem 42

Carbon dioxide in the atmosphere dissolves in raindrops to produce carbonic acid \(\left(\mathrm{H}_{2} \mathrm{CO}_{3}\right)\), causing the \(\mathrm{pH}\) of clean, unpolluted rain to range from about \(5.2\) to \(5.6\). What are the ranges of \(\left[\mathrm{H}^{+}\right]\) and \(\left[\mathrm{OH}^{-}\right]\) in the raindrops?

Short Answer

Expert verified
In clean, unpolluted rain with a pH range of 5.2 to 5.6, the concentration of hydrogen ions [H鈦篯 ranges from 2.51 脳 10^(-6) M to 6.31 脳 10^(-6) M, and the concentration of hydroxide ions [OH鈦籡 ranges from 1.58 脳 10^(-9) M to 3.98 脳 10^(-9) M.

Step by step solution

01

Find the concentrations of H鈦� ions from pH values.

Recall that the relationship between pH and the concentration of hydrogen ions [H鈦篯 is given by the equation: pH = -log[H鈦篯 We can rewrite this equation to find the concentration of H鈦�: [H鈦篯 = 10^(-pH) Now, we can use the given pH range of clean, unpolluted rain (5.2 to 5.6) to calculate the corresponding [H鈦篯 range.
02

Calculate the concentration of H鈦� ions at pH 5.2 and 5.6.

To find the concentrations of H鈦� ions at the given pH values, we will use the equation: [H鈦篯 = 10^(-pH) For pH = 5.2: [H鈦篯 = 10^(-5.2) For pH = 5.6: [H鈦篯 = 10^(-5.6) Then, we will find the numerical values for both concentrations.
03

Find the numerical values for the concentration of H鈦� ions.

Using a calculator, find the concentration of H鈦� ions for both pH values: For pH = 5.2: [H鈦篯 鈮� 6.31 脳 10^(-6) M For pH = 5.6: [H鈦篯 鈮� 2.51 脳 10^(-6) M So, the range of [H鈦篯 in the raindrops is between 2.51 脳 10^(-6) M and 6.31 脳 10^(-6) M.
04

Calculate the range of [OH鈦籡 in the raindrops using the ion product constant of water.

The ion product constant of water (Kw) is given by: Kw = [H鈦篯[OH鈦籡 At 25掳C, Kw = 1.0 脳 10^(-14) Now, we can rearrange this equation to find the concentration of [OH鈦籡: [OH鈦籡 = Kw / [H鈦篯 We will use the range of [H鈦篯 we calculated in Step 3 to find the range of [OH鈦籡 in the raindrops.
05

Calculate the concentration of OH鈦� ions for the given range of H鈦� ions.

To find the concentrations of OH鈦� ions for the given range of H鈦� ions, we will use the equation: [OH鈦籡 = Kw / [H鈦篯 For [H鈦篯 = 6.31 脳 10^(-6) M: [OH鈦籡 = (1.0 脳 10^(-14)) / (6.31 脳 10^(-6) M) For [H鈦篯 = 2.51 脳 10^(-6) M: [OH鈦籡 = (1.0 脳 10^(-14)) / (2.51 脳 10^(-6) M) Then, we will find the numerical values for both concentrations.
06

Find the numerical values for the concentration of OH鈦� ions.

Using a calculator, find the concentration of OH鈦� ions for both [H鈦篯 values: For [H鈦篯 = 6.31 脳 10^(-6) M: [OH鈦籡 鈮� 1.58 脳 10^(-9) M For [H鈦篯 = 2.51 脳 10^(-6) M: [OH鈦籡 鈮� 3.98 脳 10^(-9) M So, the range of [OH鈦籡 in the raindrops is between 1.58 脳 10^(-9) M and 3.98 脳 10^(-9) M. In conclusion, the range of the concentration of hydrogen ions [H鈦篯 in the raindrops is between 2.51 脳 10^(-6) M and 6.31 脳 10^(-6) M, while the range of the concentration of hydroxide ions [OH鈦籡 is between 1.58 脳 10^(-9) M and 3.98 脳 10^(-9) M.

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Most popular questions from this chapter

Predict which member of each pair produces the more acidic aqueous solution: (a) \(\mathrm{K}^{4}\) or \(\mathrm{Cu}^{2+}\), (b) \(\mathrm{Fe}^{2+}\) or \(\mathrm{Fe}^{3+}\), (c) \(\mathrm{Al}^{3+}\) or \(\mathrm{Ga}^{3+}\). Explain.

What are two kinds of molecules or ions that commonly function as weak bases?

Ephedrine, a central nervous system stimulant, is used in nasal sprays as a decongestant. This compound is a weak organic base: \(\mathrm{C}_{10} \mathrm{H}_{15} \mathrm{ON}(a q)+\mathrm{H}_{2} \mathrm{O}(l) \rightleftharpoons \mathrm{C}_{10} \mathrm{H}_{15} \mathrm{ONH}^{+}(a q)+\mathrm{OH}^{-}(a q)\) A \(0.035 \mathrm{M}\) solution of ephedrine has a pH of \(11.33 .\) (a) What are the equilibrium concentrations of \(\mathrm{C}_{10} \mathrm{H}_{15} \mathrm{ON}, \mathrm{C}_{10} \mathrm{H}_{15} \mathrm{ONH}^{+}\), and \(\mathrm{OH}^{-} ?\) (b) Calculate \(K_{b}\) for ephedrine.

How many milliliters of concentrated hydrochloric acid solution \((36.0 \%) \mathrm{HCl}\) by mass, density \(=1.18 \mathrm{~g} / \mathrm{mL}\) ) are required to produce \(10.0 \mathrm{~L}\) of a solution that has a pH of \(2.05 ?\)

(a) Give the conjugate base of the following BronstedLowry acids: (i) \(\mathrm{HIO}_{3}\), (ii) \(\mathrm{NH}_{4}{ }^{+}\) (b) Give the conjugate acid of the following Bronsted-Lowry bases: (i) \(\mathrm{O}^{2-}\), (ii) \(\mathrm{H}_{2} \mathrm{PO}_{4}^{-}\).
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