Chemistry: An Atoms-Focused Approach (Second Edition)
Chemistry: An Atoms-Focused Approach (Second Edition)
2nd Edition
ISBN: 9780393614053
Author: Thomas R. Gilbert, Rein V. Kirss, Stacey Lowery Bretz, Natalie Foster
Publisher: W. W. Norton & Company
Question
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Chapter 9, Problem 9.126QA
Interpretation Introduction

To find: a)How specific heat and  molar heat capacity data for the metals support the law of Dulong and Petit.

b) Use these data to predict the specific heat values of nickel and platinum. 

Expert Solution & Answer
Check Mark

Answer to Problem 9.126QA

Solution:a)The product of the atomic mass of a metal times its specific heat equals to its molar heat capacity, therefore it is constant..

b) specific heat of Nickel=0.420 J/(g.0C)

specific heat of Platinum=0.127 J/(g.0C)

Explanation of Solution

Explanation: 1)    Concept:

Law of Dulong and Petit states that “the product of the atomic mass of a metal times its specific heat is approximately constant”.

Specific heat capacity is given by using formula,cp,n=qn×T

2) Given:

Metal in solid phase cp in J/(g.0C) cp,n in J/(mol.0C)
Aluminum 0.897 24.2
Carbon (graphite) 0.71 8.5
Carbon(diamond) 0.127 1.5
Chromium 0.449 23.3
Copper 0.385 24.5
Gold 0.129 25.4
Iron 0.45 25.1
Lead 0.129 26.7
Silicon 0.71 19.9
silver 0.233 25.1
Tin 0.227 26.9
Titanium 0.523 25.0
zinc 0.387 25.3

3) Calculation:

a)To calculate molar heat capacity of the metals, we use the specific heat of metal and atomic mass

For Aluminium:

specific heat×atomic mass=0.897J/(g.0C)×26.98gmol=24.2 J/(mol.0C)

For Chromium:

specific heat×atomic mass=0.449J/(g.0C)×51.99gmol=23.3 J/(mol.0C)

For Copper:

specific heat×atomic mass=0.385J/(g.0C)×63.55gmol=24.5 J/(mol.0C)

For gold:

specific heat×atomic mass=0.129J/(g.0C)×196.97gmol=25.4 J/(mol.0C)

For Iron:

specific heat×atomic mass=0.45J/(g.0C)×55.85gmol=25.1 J/(mol.0C)

For lead:

specific heat×atomic mass=0.129J/(g.0C)×207.2gmol=26.7 J/(mol.0C)

For Silicon:

specific heat×atomic mass=0.71J/(g.0C)×28.09gmol=19.9 J/(mol.0C)

For Silver:

specific heat×atomic mass=0.233J/(g.0C)×107.87gmol=25.1 J/(mol.0C)

For Tin:

specific heat×atomic mass=0.227J/(g.0C)×118.71gmol=26.9 J/(mol.0C)

For Titanium:

specific heat×atomic mass=0.523J/(g.0C)×47.87gmol=25.0 J/(mol.0C)

For Zinc:

specific heat×atomic mass=0.387J/(g.0C)×65.38gmol=25.3 J/(mol.0C)

The values of product of atomic mass of a metal and its specific heat are equal to its molar heat capacity. Molar heat capacity value for a metal is constant. Therefore, the Dulong and Petit law is true.

b) Take the average of all the above product values =24.7J/(mol.0C)

From the above law, we can write that, specific heat×atomic mass=constant

Therefore,specific heat=constantatomic mass 

Therefore,specific heat of Nickel=24.7J/(mol.0C)atomic mass of Nickel=24.7J/(mol.0C)58.69gmol=0.420 J/(g.0C)

specific heat of Platinum=24.7J/(mol.0C)atomic mass of Platinum=24.7J/(mol.0C)195.1gmol=0.127 J/(g.0C)

Conclusion:The product of the atomic mass of a metal times its specific heat is constant and equal to its molar heat capacity. From the given data and Dulong and Petit law, values of specific heat of nickel is 0.420 J/(g.0C) and platinum is 0.127 J/(g.0C).

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Chapter 9 Solutions

Chemistry: An Atoms-Focused Approach (Second Edition)

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