Chapter 10, Problem 21PS

### Chemistry & Chemical Reactivity

10th Edition
John C. Kotz + 3 others
ISBN: 9781337399074

Chapter
Section

### Chemistry & Chemical Reactivity

10th Edition
John C. Kotz + 3 others
ISBN: 9781337399074
Textbook Problem

# A balloon for long-distance flying contains 1.2 × 107 L of helium. If the helium pressure is 737 mm Hg at 25 °C, what mass of helium (in grams) does the balloon contain?

Interpretation Introduction

Interpretation:

The mass of helium should be calculated using the given temperature, volume and pressure.

Concept Introduction:

Different laws have been put forward to introduce properties of gases:

Boyle’s law:

At fixed temperature, the volume of a fixed amount of gas is inversely proportional to the pressure exerted by the gas.

P1V(n,Twillbeconstant)

Charles’s law: States that volume is directly proportional to temperature when the gas is held at constant pressure and number of molecules.

VT

General Gas Law: Combining Charles’s law and Boyle’s law we get the General gas law or combined gas law.

P1V1T1=P2V2T2

• To relate the amount of gas and the volume.
• VnatconstantTandP

Combining all these together ideal gas law is introduced:

PV=nRT

Explanation

Ideal gas law: PVâ€‰=â€‰nRT

â€‚Â Râ€‰=â€‰0.0827â€‰L.â€‰atmK.molTâ€‰â€‰â€‰shouldâ€‰beexpressedâ€‰inâ€‰KPâ€‰shouldâ€‰beâ€‰expressedâ€‰inâ€‰atm

Given data:

â€‚Â Pâ€‰=â€‰737â€‰mmâ€‰Hgâ€‰â€‰=â€‰â€‰0.97â€‰atmTâ€‰â€‰â€‰=â€‰25Â°Câ€‰â€‰=â€‰25+â€‰273â€‰=â€‰298â€‰Kmâ€‰=â€‰?Vâ€‰=â€‰1.2Ã—107â€‰L

In-order to calculate mass of the helium we need number of moles

From ideal gas equation:

â€‚Â nâ€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰=â€‰â€‰â€‰â€‰PVRTâ€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰=â€‰0.97â€‰atmâ€‰Ã—â€‰1.2Ã—107â€‰L0.0827â€‰L.atm/K.molâ€‰Ã—â€‰298â€‰Kâ€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰=â€‰â€‰4

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