Answered: Radon (Rn) is the heaviest, and only…

Introduction to Chemical Engineering Thermodynamics

8th Edition

ISBN:9781259696527

Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart

Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart

Chapter1: Introduction

Section: Chapter Questions

Problem 1.1P

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Question

Radon (Rn) is the heaviest, and only radioactive, member ofGroup 8A(18) (noble gases). It is a product of the disintegrationof heavier radioactive nuclei found in minute concentrations inmany common rocks used for building and construction. In recent years, health concerns about the cancers caused from in-haled residential radon have grown. If 1.0x10^15atoms of ra-dium (Ra) produce an average of 1.373x10^4atoms of Rn persecond, how many liters of Rn, measured at STP, are producedper day by 1.0 g of Ra?

Expert Solution

Step 1

The volume of radon at the STP produced by the 1 g of Radium is to be determined.

Step 2

Mass of the radium given = 1 g

Molar mass of radium = 226 g/mol

Thus, the number of moles of radium is the ratio of the mass of the radium given to the molar mass of radium.

Thus,

$n_{R} = \frac{1 g}{226 g / mol} = 0.004425 mol$

n_R = Number of moles of radium

Step 3

Let Avogadro number = N_A = 6.22 x 10²³ atoms

The number of atoms of radium present is given as:-

$N_{R} = n_{R} \times N_{A} N_{R} = 0.004425 \times 6.22 \times 10^{23} atoms N_{R} = 2.75 \times 10^{21} atoms$

N_R = Number of atoms of radium

Step 4

Let the number of atoms of radon produced by radium = Z

It is given that 1 x 10¹⁵ atoms of radium produces 1.373 x 10⁴ atoms of radon per second.

Thus,

$Z = \frac{1.373 \times 10^{4}}{10^{15}} \times 2.75 \times 10^{21} atoms / \sec Z = 3.77575 \times 10^{10} atoms / \sec 1 day = 86400 \sec Z = 3.77575 \times 10^{10} \times 86400 atoms / day Z = 3.26 \times 10^{15} atoms / day$

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