Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 5: Problem 5

A cylinder with a movable piston records a volume of \(12.6 \mathrm{~L}\) when \(3.0 \mathrm{~mol}\) of oxygen is added. The gas in the cylinder has a pressure of \(5.83\) atm. The cylinder develops a leak and the volume of the gas is now recorded to be \(12.1 \mathrm{~L}\) at the same pressure. How many moles of oxygen are lost?

Short Answer

Expert verified
Answer: About 0.13 mol of oxygen was lost.

Step by step solution

01

Write down the initial state of the cylinder

The initial state of the cylinder is described by a volume of \(12.6 \mathrm{~L}\), a pressure of \(5.83\,\mathrm{atm}\), and \(3.0\,\mathrm{mol}\) of oxygen.
02

Write down the final state of the cylinder

The final state of the cylinder is described by a volume of \(12.1\,\mathrm{L}\), a pressure of \(5.83\,\mathrm{atm}\), and an unknown number of moles of oxygen (which we will call \(n_2\)).
03

Set up the proportional relationship equation

Because the pressure and temperature remain constant, we can use the proportional relationships between volume and the number of moles to find the number of moles lost. The relationship can be written as: \(\frac{V_1}{n_1} = \frac{V_2}{n_2}\) Where \(V_1\) and \(V_2\) are the initial and final volumes, and \(n_1\) and \(n_2\) are the initial and final number of moles, respectively.
04

Solve the equation for \(n_2\)

Insert the given values of \(V_1\), \(V_2\), and \(n_1\) into the equation: \(\frac{12.6\,\mathrm{L}}{3.0\,\mathrm{mol}} = \frac{12.1\,\mathrm{L}}{n_2}\) Solve the equation for \(n_2\), which represents the final number of moles of oxygen: \(n_2 = \frac{12.1\,\mathrm{L} \times 3.0\,\mathrm{mol}}{12.6\,\mathrm{L}}\) \(n_2 \approx 2.87\,\mathrm{mol}\)
05

Calculate the number of moles lost

To find the number of moles of oxygen lost, simply subtract the final number of moles \(n_2\) from the initial number of moles \(n_1\): Moles lost = \(n_1 - n_2\) Moles lost = \(3.0\,\mathrm{mol} - 2.87\,\mathrm{mol}\) Moles lost = \(0.13\,\mathrm{mol}\)
06

Write down the final answer

Therefore, during the leak, about \(0.13\,\mathrm{mol}\) of oxygen was lost.

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

Sketch a cylinder with ten molecules of helium (He) gas. 'The cylinder has a movable piston. Label this aketch before. Make an after abetch to represent (a) decrease in temperature at constant pressure. (b) a decrease in pressure fram \(1000 \mathrm{~mm} \mathrm{Hg}\) to \(500 \mathrm{~mm} \mathrm{Hg}\) at constant temperature. (c) five molecules of \(\mathrm{H}_{2}\) gas added at constant temperature and pressure.

Dinitrogen oxide, commonly called nitrous oxide, is used as a propellant gas for whipped-cream dispensers. It is prepared by heating ammonium nitrate to \(250^{\circ} \mathrm{C}\). Water vapor is also formed. (a) Write a balanced equation for the decomposition of ammonium nitrate into nitrous oxide and steam. (b) What volume of dinitrogen oxide gas is formed at \(250^{\circ} \mathrm{C}\) and 1,0 atm when \(5.00 \mathrm{~g}\) of \(\mathrm{NH}_{4} \mathrm{NO}_{3}\) is heated? Assume \(100 \%\) yield.

The buoyant force on a balloon is equal to the mass of air it displaces. The gravitational force on the balloon is equal to the sum of the masses of the balloon, the gas it contains, and the balloonist. If the balloon and the balloonist together weigh \(168 \mathrm{~kg}\), what would the diameter of a spherical hydrogen-filled balloon have to be in meters if the rig is to get off the ground at \(22^{\circ} \mathrm{C}\) and \(758 \mathrm{~mm} \mathrm{Hg}\) ? (Take \(\mathrm{MM}_{\text {air }}=29.0 \mathrm{~g} /\) mol.)

A sample of \(\mathrm{CO}_{2}\) gas at \(22^{\circ} \mathrm{C}\) and \(1.00 \mathrm{~atm}\) has a volume of \(2.00 \mathrm{~L}\). Determine the ratio of the original volume to the final volume when (a) the pressure and amount of gas remain unchanged and the Celsius temperature is doubled. (b) the pressure and amount of gas remain unchanged and the Kelvin temperature is doubled.

A 38.0-L gas tank at \(35^{\circ} \mathrm{C}\) has nitrogen at a pressure of \(4.65 \mathrm{~atm}\). The contents of the tank are transferred without loss to an evacuated 55.0-L tank in a cold room where the temperature is \(4^{\circ} \mathrm{C}\). What is the pressure in the tank?
See all solutions

Recommended explanations on Chemistry Textbooks

Ionic and Molecular Compounds

Read Explanation

Organic Chemistry

Read Explanation

Nuclear Chemistry

Read Explanation

Physical Chemistry

Read Explanation

Making Measurements

Read Explanation

Chemistry Branches

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