Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 6: Problem 9

A sample of \(\mathrm{O}_{2}(\mathrm{g})\) has a volume of \(26.7 \mathrm{L}\) at 762 Torr. What is the new volume if, with the temperature and amount of gas held constant, the pressure is (a) lowered to 385 Torr; (b) increased to 3.68 atm?

Short Answer

Expert verified
The new volumes of \(O_{2}\) gas under different pressures are: (a) 53.1L at 385 Torr; (b) 7.26L at 3.68 atm.

Step by step solution

01

Conversion of pressure units

Since the units of pressure in the given exercise are not the same, we need to convert them to the same units for calculations. We have 1 atm = 760 Torr. Hence, 762 Torr = \( \frac{762}{760} = 1.003 \) atm. Now the pressure values are: initial pressure (P1) = 1.003 atm, pressure for part (a) (P2) = \( \frac{385}{760} = 0.506 \) atm, and pressure for part (b) (P3) = 3.68 atm.
02

Use Boyle's Law to find the new volume

Boyle's Law is given by \(P1(V1) = P2(V2)\), where P1 and V1 are initial pressure and volume respectively, P2 is the new pressure and V2 is the new volume to be found. For part (a), we have \(1.003(V1) = 0.506(V2)\). Substituting \(V1 = 26.7L\) gives \(V2 = \frac{1.003 * 26.7}{0.506} = 53.1L\). For part (b), we have \(1.003 * 26.7 = 3.68 * V3\). Solving for V3 gives \(V3 = \frac{1.003 * 26.7}{3.68} = 7.26L\)
03

Interpret the result

The results of the calculations indicate that when the pressure decreases, the volume of the gas sample increases, while when the pressure increases, the volume decreases. This is consistent with the principle of Boyle's Law.

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

A sounding balloon is a rubber bag filled with \(\mathrm{H}_{2}(\mathrm{g})\) and carrying a set of instruments (the payload). Because this combination of bag, gas, and payload has a smaller mass than a corresponding volume of air, the balloon rises. As the balloon rises, it expands. From the table below, estimate the maximum height to which a spherical balloon can rise given the mass of balloon, \(1200 \mathrm{g} ;\) payload, \(1700 \mathrm{g}\) : quantity of \(\mathrm{H}_{2}(\mathrm{g})\) in balloon, \(120 \mathrm{ft}^{3}\) at \(0.00^{\circ} \mathrm{C}\) and \(1.00 \mathrm{atm}\); diameter of balloon at maximum height, 25 ft. Air pressure and temperature as functions of altitude are: $$\begin{array}{ccl} \hline \text { Altitude, km } & \text { Pressure, mb } & \text { Temperature, } \mathrm{K} \\ \hline 0 & 1.0 \times 10^{3} & 288 \\ 5 & 5.4 \times 10^{2} & 256 \\ 10 & 2.7 \times 10^{2} & 223 \\ 20 & 5.5 \times 10^{1} & 217 \\ 30 & 1.2 \times 10^{1} & 230 \\ 40 & 2.9 \times 10^{0} & 250 \\ 50 & 8.1 \times 10^{-1} & 250 \\ 60 & 2.3 \times 10^{-1} & 256 \\ \hline \end{array}$$

When working with a mixture of gases, it is sometimes convenient to use an apparent molar mass (a weightedaverage molar mass). Think in terms of replacing the mixture with a hypothetical single gas. What is the apparent molar mass of air, given that air is \(78.08 \% \mathrm{N}_{2}\) \(20.95 \% \mathrm{O}_{2,0.93 \%} \mathrm{Ar}_{\left(\text {and } 0.036 \% \mathrm{CO}_{2},\text { by volume? } \right.}\)

What is the partial pressure of \(\mathrm{Cl}_{2}(\mathrm{g}),\) in millimeters of mercury, at \(0.00^{\circ} \mathrm{C}\) and 1.00 atm in a gaseous mixture that consists of \(46.5 \% \mathrm{N}_{2}, 12.7 \% \mathrm{Ne},\) and \(40.8 \%\) \(\mathrm{Cl}_{2},\) by mass?

A 3.57 g sample of a \(\mathrm{KCl}-\mathrm{KClO}_{3}\) mixture is decomposed by heating and produces \(119 \mathrm{mL} \mathrm{O}_{2}(\mathrm{g})\) measured at \(22.4^{\circ} \mathrm{C}\) and \(738 \mathrm{mm} \mathrm{Hg}\). What is the mass percent of \(\mathrm{KClO}_{3}\) in the mixture? $$2 \mathrm{KClO}_{3}(\mathrm{s}) \longrightarrow 2 \mathrm{KCl}(\mathrm{s})+3 \mathrm{O}_{2}(\mathrm{g})$$

A 35.8 L cylinder of \(\mathrm{Ar}(\mathrm{g})\) is connected to an evacuated 1875 L tank. If the temperature is held constant and the final pressure is \(721 \mathrm{mmHg}\), what must have been the original gas pressure in the cylinder, in atmospheres?
See all solutions

Recommended explanations on Chemistry Textbooks

Chemical Analysis

Read Explanation

The Earths Atmosphere

Read Explanation

Ionic and Molecular Compounds

Read Explanation

Kinetics

Read Explanation

Physical Chemistry

Read Explanation

Making Measurements

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