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Chapter 13: Problem 105

At \(25^{\circ} \mathrm{C}\) and under an \(\mathrm{O}_{2}(\mathrm{g})\) pressure of \(1 \mathrm{atm},\) the solubility of \(\mathrm{O}_{2}(\mathrm{g})\) in water is \(28.31 \mathrm{mL} / 1.00 \mathrm{L} \mathrm{H}_{2} \mathrm{O}\) At \(25^{\circ} \mathrm{C}\) and under an \(\mathrm{N}_{2}(\mathrm{g})\) pressure of \(1 \mathrm{atm},\) the solubility of \(\mathrm{N}_{2}(\mathrm{g})\) in water is \(14.34 \mathrm{mL} / 1.00 \mathrm{L} \mathrm{H}_{2} \mathrm{O}\) The composition of the atmosphere is \(78.08 \% \mathrm{N}_{2}\) and \(20.95 \% \mathrm{O}_{2},\) by volume. What is the composition of air dissolved in water expressed as volume percents of \(\mathrm{N}_{2}\) and \(\mathrm{O}_{2} ?\)

Short Answer

Expert verified
To obtain the precise volume percentages of \(\mathrm{N}_{2}\) and \(\mathrm{O}_{2}\), it is necessary to follow through the calculations described in the three steps above.

Step by step solution

01

Calculate the Amount of Each Gas Dissolved in Water

Under given conditions of temperature and pressure, the respective volume of each gas (\(\mathrm{N}_{2}\) and \(\mathrm{O}_{2}\)) dissolved in water can be calculated using their solubility ratios mentioned in the problem. For \(\mathrm{O}_{2}\), it'll be \(0.2095 \times 28.31 \, \mathrm{mL}\) and for \(\mathrm{N}_{2}\), it'll be \(0.7808 \times 14.34 \, \mathrm{mL}\).
02

Determine the Total Volume of Dissolved Gases

The total volume of dissolved gases can be determined by adding the volume of \(\mathrm{O}_{2}\) and \(\mathrm{N}_{2}\) obtained in step 1.
03

Calculate the Volume Percentage

The respective volume percentage of each gas (\(\mathrm{N}_{2}\) and \(\mathrm{O}_{2}\)) can be determined by dividing the volume of each gas by the total volume from step 2, and then multiplying by 100. Perform these calculations to determine the volume percentages of \(\mathrm{N}_{2}\) and \(\mathrm{O}_{2}\).

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Most popular questions from this chapter

You are asked to prepare \(125.0 \mathrm{mL}\) of \(0.0321 \mathrm{M} \mathrm{AgNO}_{3}\) How many grams would you need of a sample known to be \(99.81 \% \mathrm{AgNO}_{3}\) by mass?

A saturated solution prepared at \(70^{\circ} \mathrm{C}\) contains \(32.0 \mathrm{g}\) CuSO \(_{4}\) per 100.0 g solution. A 335 g sample of this solution is then cooled to \(0^{\circ} \mathrm{C}\) and \(\mathrm{CuSO}_{4} \cdot 5 \mathrm{H}_{2} \mathrm{O}\) crystallizes out. If the concentration of a saturated solution at \(0^{\circ} \mathrm{C}\) is \(12.5 \mathrm{g} \mathrm{CuSO}_{4} / 100 \mathrm{g}\) soln, what mass of \(\mathrm{CuSO}_{4} \cdot 5 \mathrm{H}_{2} \mathrm{O}\) would be obtained? [Hint: Note that the solution composition is stated in terms of \(\mathrm{CuSO}_{4}\) and that the solid that crystallizes is the hydrate \(\left.\mathrm{CuSO}_{4} \cdot 5 \mathrm{H}_{2} \mathrm{O} .\right]\)

The concentration of \(\mathrm{N}_{2}\) in the ocean at \(25^{\circ} \mathrm{C}\) is \(445 \mu \mathrm{M} .\) The Henry's law constant for \(\mathrm{N}_{2}\) is \(0.61 \times 10^{-3} \mathrm{mol} \mathrm{L}^{-1} \mathrm{atm}^{-1} .\) Calculate the mass of \(\mathrm{N}_{2}\) in a liter of ocean water. Calculate the partial pressure of \(\mathrm{N}_{2}\) in the atmosphere.

The concentration of Ar in the ocean at \(25^{\circ} \mathrm{C}\) is \(11.5 \mu \mathrm{M} .\) The Henry's law constant for \(\mathrm{Ar}\) is \(1.5 \times 10^{-3}\) \(\mathrm{mol} \mathrm{L}^{-1} \mathrm{atm}^{-1} .\) Calculate the mass of \(\mathrm{Ar}\) in a liter of ocean water. Calculate the partial pressure of \(\mathrm{Ar}\) in the atmosphere.

The aqueous solubility at \(20^{\circ} \mathrm{C}\) of \(\mathrm{Ar}\) at \(1.00 \mathrm{atm}\) is equivalent to \(33.7 \mathrm{mL} \mathrm{Ar}(\mathrm{g}),\) measured at STP, per liter of water. What is the molarity of Ar in water that is saturated with air at 1.00 atm and \(20^{\circ} \mathrm{C}\) ? Air contains \(0.934 \%\) Ar by volume. Assume that the volume of water does not change when it becomes saturated with air.
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