   # A particular balloon is designed by its manufacturer to be inflated to a volume of no more than 2.5 L. If the balloon is filled with 2.0 L helium at sea level, is released, and rises to an altitude at which the atmospheric pressure is only 500. mm Hg, will the balloon burst? (Assume temperature is constant.) ### Chemistry: An Atoms First Approach

2nd Edition
Steven S. Zumdahl + 1 other
Publisher: Cengage Learning
ISBN: 9781305079243

#### Solutions

Chapter
Section ### Chemistry: An Atoms First Approach

2nd Edition
Steven S. Zumdahl + 1 other
Publisher: Cengage Learning
ISBN: 9781305079243
Chapter 8, Problem 43E
Textbook Problem
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## A particular balloon is designed by its manufacturer to be inflated to a volume of no more than 2.5 L. If the balloon is filled with 2.0 L helium at sea level, is released, and rises to an altitude at which the atmospheric pressure is only 500. mm Hg, will the balloon burst? (Assume temperature is constant.)

Interpretation Introduction

Interpretation:

For the given condition of balloon, it should be checked will the balloon burst or not.

Concept introduction:

By combining the three gaseous laws namely Boyle’s law, Charles’s law and Avogadro’s law a combined gaseous equation is obtained. This combined gaseous equation is called Ideal gas law.

According to ideal gas law,

PV=nRT = constant

Where,

P = pressure in atmospheres

V= volumes in liters

n = number of moles

R =universal gas constant ( 0.08206L×atm/K×mol )

T = temperature in kelvins

By knowing any three of these properties, the state of a gas can be simply identified with applying the ideal gas equation.

At constant temperature, gas constant and number of moles the above equation becomes;

P1V1=P2V2

From the above equation final volume ( V2 ) can be calculated as follows;

V2=P1V1P2

### Explanation of Solution

Explanation

The given balloon is designed by its manufacturer to be inflated to a volume of no more than 2.5 litters.  The balloon is filled with 2.0L helium at sea level, is released, and rises to an altitude at which the atmospheric pressure is 500.mm. Hg. Now it is needed to check whether the balloon burst or not at the given condition. It can be checked as follows;

According to ideal gas equation,

PV=nRT

At constant temperature, gas constant and number of moles the above equation becomes;

P1V1=P2V2

From the above equation final volume ( V2 ) can be calculated as follows;

V2=P1V1P2

From the given data, calculate the final volume of balloon

Atsealevel,Pressure=1.00atm=760mmHgThatis,P1=760

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