   Chapter 10, Problem 21PS

Chapter
Section
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: PV=nRT

R=0.0827L.atmK.molTshouldbeexpressedinKPshouldbeexpressedinatm

Given data:

P=737mmHg=0.97atmT=25°C=25+273=298Km=?V=1.2×107L

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

From ideal gas equation:

n=PVRT=0.97atm×1.2×107L0.0827L.atm/K.mol×298K=4

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