Chapter 10, Problem 18PS

### 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 holds 30.0 kg of helium. What is the volume of the balloon if its pressure is 1.20 atm and the temperature is 22 °C?

Interpretation Introduction

Interpretation:

The volume of the balloon should be calculated using the given temperature, amount of gas 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€‰1â€‰atmTâ€‰â€‰â€‰=â€‰22Â°Câ€‰â€‰=â€‰22+â€‰273â€‰=â€‰295â€‰Kmâ€‰=â€‰30â€‰â€‰kgâ€‰â€‰â€‰=â€‰30Ã—103â€‰gVâ€‰=â€‰?

In-order to calculate the number of moles we can use the equation:

â€‚Â No.â€‰ofâ€‰molesâ€‰â€‰â€‰=â€‰â€‰massmolarâ€‰massâ€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰=â€‰30Ã—10

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