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Chapter 13: Problem 38

The partial pressure of \(\mathrm{O}_{2}\) in air at sea level is 0.21 atm. Using the data in Table \(13.1,\) together with Henry's law, calculate the molar concentration of \(\mathrm{O}_{2}\) in the surface water of a mountain lake saturated with air at \(20^{\circ} \mathrm{C}\) and an atmospheric pressure of 650 torr.

Short Answer

Expert verified
The molar concentration of \(\mathrm{O}_{2}\) in the surface water of the mountain lake is approximately \(2.34 \times 10^{-4}\, \frac{\text{mol}}{\text{L}}\).

Step by step solution

01

Convert the pressure to atm

We need to convert the atmospheric pressure given in torr to atmospheres (atm), as we are going to use atm in our calculations. The conversion factor is 1 atm = 760 torr. So, we have \[650\,\text{torr} \times \frac{1\,\text{atm}}{760\,\text{torr}} \approx 0.855\,\text{atm}\]
02

Calculate the partial pressure of O₂ in mountain lake air

We know that the partial pressure of \(\mathrm{O}_{2}\) in air at sea level is 21% (0.21 atm). Now, we must calculate the partial pressure of \(\mathrm{O}_{2}\) at the mountain lake air using the atmospheric pressure value we found in Step 1: \[0.21\,\text{atm}\times 0.855\,\text{atm}\approx 0.1796\,\text{atm}\]
03

Obtain the Henry's law constant for O₂

From Table 13.1, the Henry's law constant for \(\mathrm{O}_{2}\) in water at \(20^{\circ} \mathrm{C}\) is: \[k_{\mathrm{O}_{2}} = 1.3 \times 10^{-3}\, \frac{\text{mol}}{\text{L}\cdot\text{atm}}\]
04

Use Henry's law to calculate the molar concentration of O₂

Now, we can use Henry's law to find the molar concentration of \(\mathrm{O}_{2}\) in the surface water of the mountain lake: \[C_{\mathrm{O}_{2}} = k_{\mathrm{O}_{2}} \times P_{\mathrm{O}_{2}}\] \[C_{\mathrm{O}_{2}} = (1.3 \times 10^{-3}\, \frac{\text{mol}}{\text{L}\cdot\text{atm}}) \times 0.1796\, \text{atm}\] \[C_{\mathrm{O}_{2}} \approx 2.34 \times 10^{-4}\, \frac{\text{mol}}{\text{L}}\] The molar concentration of \(\mathrm{O}_{2}\) in the surface water of the mountain lake is approximately \(2.34 \times 10^{-4} \frac{\text{mol}}{\text{L}}\).

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Most popular questions from this chapter

(a) What is the molality of a solution formed by dissolving 1.12 mol of \(\mathrm{KCl}\) in 16.0 \(\mathrm{mol}\) of water? (b) How many grams of sulfur \(\left(S_{8}\right)\) must be dissolved in 100.0 g of naphthalene \(\left(\mathrm{C}_{10} \mathrm{H}_{8}\right)\) to make a 0.12 \(\mathrm{m}\) solution?

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