   # Terephthalic acid is an important chemical used in the manufacture of polyesters and plasticizers. It contains only C, H, and O. Combustion of 19.81 mg terephthalic acid produces 41.98 mg CO 2 and 6.45 mg H 2 O. If 0.250 mole of terephthalic 41.98 mg CO 2 and 6.45 mg H 2 O. If 0.250 mole of terephthalic acid has a mass of 41.5 g, determine the molecular formula for terephthalic acid. ### Chemistry: An Atoms First Approach

2nd Edition
Steven S. Zumdahl + 1 other
Publisher: Cengage Learning
ISBN: 9781305079243

#### Solutions

Chapter
Section ### Chemistry: An Atoms First Approach

2nd Edition
Steven S. Zumdahl + 1 other
Publisher: Cengage Learning
ISBN: 9781305079243
Chapter 5, Problem 138AE
Textbook Problem
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## Terephthalic acid is an important chemical used in the manufacture of polyesters and plasticizers. It contains only C, H, and O. Combustion of 19.81 mg terephthalic acid produces 41.98 mg CO2 and 6.45 mg H2O. If 0.250 mole of terephthalic 41.98 mg CO2 and 6.45 mg H2O. If 0.250 mole of terephthalic acid has a mass of 41.5 g, determine the molecular formula for terephthalic acid.

Interpretation Introduction

Interpretation: The combustion of a given amount of terephthalic acid to produce carbon dioxide and water is given. The molecular formula of terephthalic acid is to be calculated.

Concept introduction: The total number of molecules existing in a compound is depicted by the molecular formula of a compound, whereas the empirical formula of a compound gives the simplest ratio of elements present in a compound.

To determine: The molecular formula of terephthalic acid.

### Explanation of Solution

To determine: The empirical formula of terephthalic acid.

Given

The mass of CO2 produced is 41.98mg .

The mass of H2O produced is 6.45mg .

The mass of 0.250mol of terephthalic acid is 41.5g .

The mass of terephthalic acid taken is 19.81mg .

The atomic mass of carbon is 12g/mol .

The atomic mass of oxygen is 16g/mol .

The atomic mass of hydrogen is 1g/mol .

The molar mass of CO2 =C+2O=(12+(2×16))g/mol=44g/mol

The molar mass of H2O =2H+O=((2×1)+16)g/mol=18g/mol

Formula

The mass of an element in a compound is calculated by the formula,

Massoftheelement=(Givenmassofthecompound×Atomicmassofelement)Molarmassofthecompound

The mass of carbon in CO2 is calculated by the formula,

Massofcarbon=(GivenmassofCO2×Atomicmassofcarbon)MolarmassofCO2

Substitute the value of the given mass of CO2 , atomic mass of C and the molar mass of CO2 in the above expression.

Massofcarbon=((41.98×12)44)mg=11.45mg=11.45×103g

The mass of hydrogen in H2O is calculated by the formula,

Massofhydrogen=(GivenmassofH2O×Atomicmassofhydrogen)MolarmassofH2O

Substitute the value of the given mass of H2O , atomic mass of H and the molar mass of H2O in the above expression.

Massofhydrogen=((6.45×(2×1))18)mg=0.72mg=0.72×103g

The mass of terephthalic acid taken for combustion is 19.81mg .

The mass of oxygen produced is calculated by the formula,

Massofoxygen=19.81(Massofcarbonproduced+Massofhydrogenproduced)

Substitute the value of the mass of carbon and hydrogen produced, in the above expression.

Massofoxygen=(19.81(11.45+0.72))mg=7

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