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Chapter 13: Problem 93

Most fish need at least 4 ppm dissolved \(\mathrm{O}_{2}\) for survival. (a) What is this concentration in \(\mathrm{mol} / \mathrm{L} ?\) (b) What partial pressure of \(\mathrm{O}_{2}\) above the water is needed to obtain this concentration at \(10^{\circ} \mathrm{C} ?\) (The Henry's law constant for \(\mathrm{O}_{2}\) at this temperature is \(\left.1.71 \times 10^{-3} \mathrm{~mol} / \mathrm{L}-\mathrm{atm} .\right)\)

Short Answer

Expert verified
To obtain 4 ppm dissolved O2 in water, the molar concentration is \(1.25 \times 10^{-4}\,mol/L\). To achieve this concentration at 10°C, the partial pressure of O2 above the water should be 0.0731 atm.

Step by step solution

01

(a) Conversion of concentration from ppm to mol/L

First, we need to convert the given concentration of dissolved oxygen from parts per million (ppm) to moles per liter (mol/L). 1 ppm = 1 mg/L Given that the concentration is 4 ppm: 4 ppm = 4 mg/L Now, we need to convert the mass concentration (mg/L) into molar concentration (mol/L) by dividing the mass concentration by the molar mass of O2. The molar mass of O2 is 32 g/mol. \(4\,mg/L = 0.004\,g/L\) Molar concentration = \(0.004\,g/L \div 32\,g/mol\)
02

Calculation of molar concentration

Dividing the mass concentration by the molar mass, we get: Molar concentration = \(1.25 \times 10^{-4}\,mol/L\)
03

(b) Application of Henry's law

Now, we need to determine the partial pressure of O2 needed to obtain this concentration using Henry's law. Henry's law states that: C = kH × P where, C is the concentration of the dissolved gas (mol/L) kH is the Henry's law constant (mol/L-atm) P is the partial pressure of the gas above the liquid (atm) We have the values of C and kH: C = \(1.25 \times 10^{-4}\,mol/L\) kH = \(1.71 \times 10^{-3}\,mol/L\,atm\) We need to find P.
04

Calculation of partial pressure

Rearranging the Henry's law formula, we get: P = C / kH Plugging in the values, we get: P = \((1.25 \times 10^{-4}\,mol/L)\ / (1.71 \times 10^{-3}\,mol/L\,atm)\) P = 0.0731 atm So, the partial pressure of O2 above the water needed to obtain the 4 ppm concentration at 10°C is 0.0731 atm.

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Most popular questions from this chapter

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