   # A sealed balloon is filled with 1.00 L helium at 23°C and 1.00 atm. The balloon rises to a point in the atmosphere where the pressure is 220. torr and the temperature is −31°C. What is the change in volume of the balloon as it ascends from 1.00 atm to a pressure of 220. torr? ### 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 63E
Textbook Problem
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## A sealed balloon is filled with 1.00 L helium at 23°C and 1.00 atm. The balloon rises to a point in the atmosphere where the pressure is 220. torr and the temperature is −31°C. What is the change in volume of the balloon as it ascends from 1.00 atm to a pressure of 220. torr?

Interpretation Introduction

Interpretation: For the given data, the change in the volume of the balloon should be determined.

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

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. For a gas at two conditions, the unknown variable can be determined by knowing the variables that change and remain constant and can be generated an equation for unknown variable from ideal gas equation.

### Explanation of Solution

Explanation

From the ideal gas equation the equation for number of moles of gas for a gas at two conditions can be derived by knowing initial pressure ( P1 ), temperature ( T1 ) and volume ( V1 )and final pressure( P2 ), temperature( T2 ). It is the ratio of product of initial pressure, volume and final temperature to the product of initial temperature and final pressure,.

According to ideal gas equation,

PV=nRT

By rearranging the above equation,

PVnT=R

R is a gas constant and here n is also constant. For a gas at two conditions the equation can be written as:

P1V1T1=nR=P2V2T2orP1V1T1=P2V2T2 (1)

From equation (1) the final volume of gas ( V2 ) can be determined as follows,

V2=V1P1T2P2T1 (2)

To find out the final volume, it is needed to take and write the given data and substitute their values in the equation (2). For two conditions problem, units for P and V just needed to be the same units and it is not needed to convert the standard units. But in the case of temperature, it must be converted to the Kelvin.

P1= 1 atm=760torrP2=220torrT1=23°C=296Ksince,1K=°C+273&#

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