   # A spherical glass container of unknown volume contains helium gas at 25°C and 1.960 atm. When a portion of the helium is withdrawn and adjusted to 1.00 atm at 25°C, it is found to have a volume of 1.75 cm 3 . The gas remaining in the first container shows a pressure of 1.710 atm. Calculate the volume of the spherical container. ### 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 132AE
Textbook Problem
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## A spherical glass container of unknown volume contains helium gas at 25°C and 1.960 atm. When a portion of the helium is withdrawn and adjusted to 1.00 atm at 25°C, it is found to have a volume of 1.75 cm3. The gas remaining in the first container shows a pressure of 1.710 atm. Calculate the volume of the spherical container.

Interpretation Introduction

Interpretation: For the given data, volume of the spherical container 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.

Number of moles of gas can be calculated from the ideal gas equation is as follows,

n=PVRT

Volume of the gas can be determined from the ideal gas equation as follows,

V=nRTP

### Explanation of Solution

Explanation

To determine: the number of moles of He removed

Number of moles of He removed      7.16×10-5mol

According to ideal gas equation,

PV=nRT

Number of moles of gas can be calculated from the ideal gas equation is as follows,

n=PVRT

Fromthegivendata,tocalculatethemolofHeremoved,P=1atmV=1.75cm3=1.75×10-3LSince,1L=1000cm3R=0.08206L×atmK×molT=25°C=298KSince,K=(°C+273)K=(25°C+273)K=298Kn=1.00atm×1.75×10-3L0.08206L×atmK×mol×298K=7

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