Chemistry: The Molecular Nature of Matter and Change
Chemistry: The Molecular Nature of Matter and Change
8th Edition
ISBN: 9781259631757
Author: Martin Silberberg Dr., Patricia Amateis Professor
Publisher: McGraw-Hill Education
Question
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Chapter 12, Problem 12.29P
Interpretation Introduction

Interpretation:

The heat that is required to convert 2.500 kg of solid SO2 at the melting point to gas at 60°C is to be calculated.

Concept introduction:

Specific heat capacity (c) of a substance is the amount of heat needed to raise the temperature of 1g of a substance by 1K. The formula to calculate heat required is as follows:

q=(mass)(c)(T2T1) (1)

Here,

T2 is the final temperature.

T1 is the initial temperature.

q is the heat released or absorbed.

c is the specific heat capacity of the substance.

The formula to calculate heat at phase change is as follows:

q=(mol)(ΔH) (2)

Here,

ΔH is the enthalpy change.

Expert Solution & Answer
Check Mark

Answer to Problem 12.29P

The heat that is required to convert 2.500 kg of solid SO2 at the melting point to gas at 60°C is 1.606×106J.

Explanation of Solution

The formula to calculate the number of moles of SO2 is as follows:

Numberof moles=(givenmassmolecularmassofSO2) (3)

Substitute 2.500 kg for a given mass and 64.06.02g/mol for molecular mass of SO2 in the equation (3).

Numberof moles=(2.500 kg64.06g/mol)(1000g1kg)=39.0259132mol

Substitute 39.0259132mol for mol and 8.619kJ/mol for ΔHfus° in the equation (2) to change the phase of solid SO2 at 73°C to liquid SO2 at 73°C.

q1=(39.0259132mol)(8.619kJ/mol)=336.364346kJ(1000J1kJ)=336364.3J

Substitute 2.500 kg for mass, 0.995J/g°C for cliquid, 10°C for T2 and 73°C for T1 in the equation (1) to calculate the heat required to increase the temperature of liquid SO2 from 73°C to 10°C.

q2=(2.500 kg)(1000g1kg)(0.995J/g°C)(10°C(73°C))=156712.5J

Substitute 39.0259132mol for mol and 25.73kJ/mol for ΔHvap in the equation (2) to change the phase of liquid SO2 at 10°C to gas SO2 at 10°C.

q3=(39.0259132mol)(25.73kJ/mol)=1004.13675kJ(1000J1kJ)=1004136.75J

Substitute 2.500 kg for mass, 0.622J/g°C for cgas, 60°C for T2 and 10°C for T1 in the equation (1) to calculate the heat required to increase the temperature of water from 10°C to 60°C.

q4=(2.500 kg)(1000g1kg)(0.622J/g°C)(60°C(10°C))=108850J

The formula to calculate the total heat required is as follows:

qtotal=q1+q2+q3+q4 (4)

Substitute 336364.3J for q1, 156712.5J for q2, 004136.75J for q3 and 108850J for q4 in the equation (4).

qtotal=336364.3J+156712.5J+004136.75J+108850J=1,606,063.5J1.606×106J

Conclusion

The heat that is required to convert 2.500 kg of solid SO2 at the melting point to gas at 60°C is 1.606×106J.

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Chapter 12 Solutions

Chemistry: The Molecular Nature of Matter and Change

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