Multiple Choice
A sample of seawater has a strontium concentration of 57 ppm. What is the mass of strontium in grams in 1 liter of seawater, assuming the density of seawater is 1.025 g/mL?
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14. Solutions
Parts per Million (ppm)
Multiple Choice
If the pH of rainwater is 5.6, what is the approximate concentration of CO_2 in parts per million (ppm) in the rainwater?
A
1.7 ppm
B
0.17 ppm
C
17 ppm
D
0.017 ppm
Verified step by step guidance1
Recognize that the pH of rainwater is related to the concentration of hydrogen ions \([\mathrm{H}^+]\) by the formula \(\mathrm{pH} = -\log[\mathrm{H}^+]\). Use this to calculate \([\mathrm{H}^+]\) from the given pH of 5.6 by rearranging to \([\mathrm{H}^+] = 10^{-\mathrm{pH}}\).
Understand that the acidity of rainwater is primarily due to dissolved carbon dioxide forming carbonic acid, which partially dissociates to produce \(\mathrm{H}^+\) ions. The equilibrium between dissolved \(\mathrm{CO}_2\) and \(\mathrm{H}^+\) is governed by Henry's law and the acid dissociation constants.
Use the equilibrium expression for carbonic acid dissociation: \(\mathrm{CO}_2 (aq) + \mathrm{H}_2\mathrm{O} \leftrightarrow \mathrm{H}_2\mathrm{CO}_3 \leftrightarrow \mathrm{H}^+ + \mathrm{HCO}_3^-\). The concentration of \(\mathrm{H}^+\) is related to the dissolved \(\mathrm{CO}_2\) concentration by the combined constants for Henry's law and the first dissociation constant of carbonic acid.
Apply Henry's law to relate the concentration of dissolved \(\mathrm{CO}_2\) to its partial pressure in the atmosphere: \([\mathrm{CO}_2] = k_H \times P_{\mathrm{CO}_2}\), where \(k_H\) is Henry's law constant for \(\mathrm{CO}_2\) in water at the given temperature.
Rearrange the expressions to solve for \(P_{\mathrm{CO}_2}\) (partial pressure of \(\mathrm{CO}_2\)), then convert this partial pressure to ppm by volume using the relation \(\mathrm{ppm} = P_{\mathrm{CO}_2} \times 10^6\) (assuming atmospheric pressure is 1 atm). This will give the approximate concentration of \(\mathrm{CO}_2\) in ppm corresponding to the given pH.
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