Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 10: Problem 74

A sample of \(3.00 \mathrm{~g}\) of \(\mathrm{SO}_{2}(g)\) originally in a \(5.00-\mathrm{L}\) vessel at \(21{ }^{\circ} \mathrm{C}\) is transferred to a \(10.0-\mathrm{L}\) vessel at \(26^{\circ} \mathrm{C}\). A sample of $2.35 \mathrm{~g}\( of \)\mathrm{N}_{2}(g)\( originally in a \)2.50-\mathrm{L}$ vessel at \(20^{\circ} \mathrm{C}\) is transferred to this same \(10.0-\mathrm{L}\) vessel. \((\mathbf{a})\) What is the partial pressure of \(\mathrm{SO}_{2}(g)\) in the larger container? (b) What is the partial pressure of \(\mathrm{N}_{2}(g)\) in this vessel? (c) What is the total pressure in the vessel?

Short Answer

Expert verified
(a) The partial pressure of \(SO_2\) in the 10.0-L vessel is approximately 0.115 atm. (b) The partial pressure of \(N_2\) in the 10.0-L vessel is approximately 0.405 atm. (c) The total pressure in the vessel is approximately 0.520 atm.

Step by step solution

01

Convert masses to moles

To find the moles of each gas, we divide the given mass by the molar mass: For \(SO_2\): \(\dfrac{3.00\, g}{(32.1+2\cdot16.0) g/mol} \approx 0.0465\, mol\) For \(N_2\): \(\dfrac{2.35\, g}{(2\cdot14.0) g/mol} \approx 0.0841\, mol\)
02

Find initial pressure of each gas

Using the Ideal Gas Law, we can find the initial pressure for each gas: \(P = \dfrac{nRT}{V}\) For \(SO_2\): \(P_{SO_2} = \dfrac{(0.0465\, mol)(0.0821\, L\, atm/mol\, K)(294\, K)}{5.00\, L} \approx 0.229\, atm\) For \(N_2\): \(P_{N_2} = \dfrac{(0.0841\, mol)(0.0821\, L\, atm/mol\, K)(293\, K)}{2.50\, L} \approx 0.808\, atm\)
03

Use the combined gas law to find the partial pressures in the new vessel

We can use the combined gas law to find the new partial pressures in the 10.0-L vessel at 26°C (299 K): \(\dfrac{P_1V_1}{T_1} = \dfrac{P_2V_2}{T_2}\) For \(SO_2\): \(\dfrac{(0.229\, atm)(5.00\, L)}{294\, K} = \dfrac{P_{SO_2} \cdot 10.0\, L}{299\, K}\) Solve for \(P_{SO_2}\): \(P_{SO_2} \approx 0.115\, atm\) For \(N_2\): \(\dfrac{(0.808\, atm)(2.50\, L)}{293\, K} = \dfrac{P_{N_2} \cdot 10.0\, L}{299\, K}\) Solve for \(P_{N_2}\): \(P_{N_2} \approx 0.405\, atm\) (a) The partial pressure of \(SO_2\) in the 10.0-L vessel is approximately 0.115 atm. (b) The partial pressure of \(N_2\) in the 10.0-L vessel is approximately 0.405 atm.
04

Calculate the total pressure

To find the total pressure, add the partial pressures of the two gases: \(P_{total} = P_{SO_2} + P_{N_2} = 0.115\, atm + 0.405\, atm \approx 0.520\, atm\) (c) The total pressure in the vessel is approximately 0.520 atm.

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

Determine whether each of the following changes will increase, decrease, or not affect the rate with which gas molecules collide with the walls of their container: (a) increasing the volume of the container, \((\mathbf{b})\) increasing the temperature, (c) increasing the molar mass of the gas.

Which statement concerning the van der Waals constants \(a\) and \(b\) is true? (a) The magnitude of \(a\) relates to molecular volume, whereas \(b\) relates to attractions between molecules. (b) The magnitude of \(a\) relates to attractions between molecules, whereas \(b\) relates to molecular volume. (c) The magnitudes of \(a\) and \(b\) depend on pressure. (d) The magnitudes of \(a\) and \(b\) depend on temperature.

A set of bookshelves rests on a hard floor surface on four legs, each having a cross-sectional dimension of \(4.0 \times 5.0 \mathrm{~cm}\) in contact with the floor. The total mass of the shelves plus the books stacked on them is $200 \mathrm{~kg}$. Calculate the pressure in atmospheres exerted by the shelf footings on the surface.

The physical fitness of athletes is measured by \({ }^{4} V_{\mathrm{O}_{2}}\) max," which is the maximum volume of oxygen consumed by an individual during incremental exercise (for example, on a treadmill). An average male has a \(V_{\mathrm{O}_{2}}\) max of \(45 \mathrm{~mL} \mathrm{O}_{2} / \mathrm{kg}\) body mass \(/ \mathrm{min}\), but a world-class male athlete can have a \(V_{\mathrm{O}_{2}}\) max reading of $88.0 \mathrm{~mL} \mathrm{O}_{2} / \mathrm{kg}$ body mass/min. (a) Calculate the volume of oxygen, in mL, consumed in \(1 \mathrm{hr}\) by an average man who weighs \(85 \mathrm{~kg}\) and has a \(V_{\mathrm{O}_{2}}\) max reading of \(47.5 \mathrm{~mL}\) $\mathrm{O}_{2} / \mathrm{kg}\( body mass \)/ \mathrm{min} .(\mathbf{b})\( If this man lost \)10 \mathrm{~kg},\( exercised, and increased his \)V_{\mathrm{O}_{2}}\( max to \)65.0 \mathrm{~mL} \mathrm{O}_{2} / \mathrm{kg}\( body mass \)/ \mathrm{min}$, how many mL of oxygen would he consume in \(1 \mathrm{hr} ?\)

Radon (Rn) is the heaviest (and only radioactive) member of the noble gases. How much slower is the root-mean-square speed of Rn than He at $300 \mathrm{K?}$
See all solutions

Recommended explanations on Chemistry Textbooks

Nuclear Chemistry

Read Explanation

The Earths Atmosphere

Read Explanation

Kinetics

Read Explanation

Inorganic Chemistry

Read Explanation

Chemistry Branches

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