Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 12: Problem 38

The solubility of \(\mathrm{N}_{2}\) in blood at \(37^{\circ} \mathrm{C}\) and at a partial pressure of \(0.80 \mathrm{~atm}\) is \(5.6 \times 10^{-4} \mathrm{~mol} / \mathrm{L} .\) A deep-sea diver breathes compressed air with the partial pressure of \(\mathrm{N}_{2}\) equal to 4.0 atm. Assume that the total volume of blood in the body is \(5.0 \mathrm{~L}\). Calculate the amount of \(\mathrm{N}_{2}\) gas released (in liters at \(37^{\circ} \mathrm{C}\) and \(1 \mathrm{~atm}\) ) when the diver returns to the surface of the water, where the partial pressure of \(\mathrm{N}_{2}\) is \(0.80 \mathrm{~atm}\)

Short Answer

Expert verified
The amount of nitrogen gas released when the diver returns to the surface is approximately 275 mL.

Step by step solution

01

Compute the initial amount of nitrogen

Begin by calculating the initial amount of \(N_{2}\) in the blood when the partial pressure is 4.0 atm. The given solubility is for a partial pressure of 0.80 atm, and this solubility directly proportional to pressure (Henri's law). Therefore, multiply the given solubility by the ratio of the pressures thus \(N_{2_{initial}} = solubility \times \frac{P_{initial}}{P_{given}} = 5.6 \times 10^{-4} \, mol/L \times \frac{4.0 \, atm}{0.80 \, atm} = 2.8 \times 10^{-3} \, mol/L \). Then calculate the total moles of \(N_{2}\) in the body by multiplying this value by the total volume of blood (5.0 L) to get \(N_{2_{initial}} = 2.8 \times 10^{-3} \, mol/L \times 5.0 \, L= 0.014 \, mol\)
02

Compute the final amount of nitrogen

When the diver returns to the surface the partial pressure of \(N_{2}\) drops to 0.80 atm. Now, find the final amount using the given solubility at this pressure \(N_{2_{final}} = solubility \times V_{blood} = 5.6 \times 10^{-4} \, mol/L \times 5.0 \, L = 0.0028 \, mol\)
03

Calculate the amount of nitrogen released

Subtract the final amount of nitrogen in the blood from the initial amount to find the amount of nitrogen released \[N_{2_{released}} = N_{2_{initial}} - N_{2_{final}} = 0.014 \,mol - 0.0028 \,mol = 0.0112 \,mol\] Using the ideal gas law at the given conditions (37 C and 1 atm), each mole of a gas occupies 24.5 liters. Therefore, find the volume of nitrogen released by multiplying the moles by 24.5 L/mol \[V_{N_{2_{released}}} = N_{2_{released}} \times V_{per \, mol} = 0.0112 \,mol \times 24.5 \,L/mol = 0.2748 \,L or 275 \,mL (to 3 significant figures)\]

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

The concentration of commercially available concentrated nitric acid is 70.0 percent by mass, or \(15.9 M\) Calculate the density and the molality of the solution.

Describe how hydrophilic and hydrophobic colloids are stabilized in water.

Write the equations relating boiling-point elevation and freezing-point depression to the concentration of the solution. Define all the terms, and give their units.

How does each of the following affect the solubility of an ionic compound? (a) lattice energy, (b) solvent (polar versus nonpolar), (c) enthalpies of hydration of cation and anion

The elemental analysis of an organic solid extracted from gum arabic (a gummy substance used in adhesives, inks, and pharmaceuticals) showed that it contained 40.0 percent \(\mathrm{C}, 6.7\) percent \(\mathrm{H},\) and 53.3 percent O. A solution of \(0.650 \mathrm{~g}\) of the solid in \(27.8 \mathrm{~g}\) of the solvent diphenyl gave a freezing-point depression of \(1.56^{\circ} \mathrm{C}\). Calculate the molar mass and molecular formula of the solid. \(\left(K_{\mathrm{f}}\right.\) for diphenyl is \(8.00^{\circ} \mathrm{C} / \mathrm{m} .\)
See all solutions

Recommended explanations on Chemistry Textbooks

Making Measurements

Read Explanation

Ionic and Molecular Compounds

Read Explanation

The Earths Atmosphere

Read Explanation

Inorganic Chemistry

Read Explanation

Organic Chemistry

Read Explanation

Chemical Analysis

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free