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Chapter 3: Problem 148

Terephthalic acid is an important chemical used in the manufacture of polyesters and plasticizers. It contains only \(\mathrm{C}, \mathrm{H}\) , and O. Combustion of 19.81 \(\mathrm{mg}\) terephthalic acid produces 41.98 \(\mathrm{mg} \mathrm{CO}_{2}\) and 6.45 \(\mathrm{mg} \mathrm{H}_{2} \mathrm{O}\) . If 0.250 mole of terephthalic acid has a mass of \(41.5 \mathrm{g},\) determine the molecular formula for terephthalic acid.

Short Answer

Expert verified
The empirical formula of terephthalic acid is C_6H_4O_4, and its molecular formula is C_8H_6O_4.

Step by step solution

01

Determine the mass of carbon, hydrogen, and oxygen in the combustion products

From the combustion of terephthalic acid, we know that 19.81 mg of terephthalic acid produces 41.98 mg of carbon dioxide (CO2) and 6.45 mg of water (H2O). From these masses, we can now determine the mass of carbon, hydrogen, and oxygen in the 19.81 mg of terephthalic acid: For CO2: Mass of C = (mass of CO2) × (molar mass of C)/(molar mass of CO2) = \(41.98 \times \frac{12.01}{44.01}\) mg For H2O: Mass of H = (mass of H2O) × (molar mass of H)/(molar mass of H2O) = \(6.45 \times \frac{2.02}{18.02}\) mg Since terephthalic acid only contains C, H, and O, we can find the mass of oxygen by difference: Mass of O = Mass of terephthalic acid - Mass of C - Mass of H Calculate these masses.
02

Convert the masses to moles

Now, we will convert the masses of carbon, hydrogen, and oxygen to moles using their respective molar masses: Moles of C = Mass of C / Molar mass of C Moles of H = Mass of H / Molar mass of H Moles of O = Mass of O / Molar mass of O Calculate the number of moles of each element.
03

Determine the empirical formula

To find the empirical formula, divide the moles of each element by the smallest number of moles: Mole ratio of C = Moles of C / smallest number of moles Mole ratio of H = Moles of H / smallest number of moles Mole ratio of O = Moles of O / smallest number of moles These mole ratios give us the empirical formula of terephthalic acid.
04

Calculate the molar mass of the empirical formula

Now, we need to determine the molar mass of the empirical formula: Molar mass = (Mole ratio of C × molar mass of C) + (Mole ratio of H × molar mass of H) + (Mole ratio of O × molar mass of O) Calculate the molar mass of the empirical formula.
05

Determine the molecular formula

We are given that 0.250 mole of terephthalic acid has a mass of 41.5 grams. Therefore, we can find the molar mass of terephthalic acid by: Molar mass of terephthalic acid = Mass of terephthalic acid / Moles of terephthalic acid = \(41.5 \div 0.250\) g/mol Now, we can determine the molecular formula by dividing the molar mass of terephthalic acid by the molar mass of the empirical formula: Multiplier = Molar mass of terephthalic acid / Molar mass of empirical formula Round the multiplier to the nearest whole number. The molecular formula will be the empirical formula multiplied by the rounded multiplier. Write the molecular formula of terephthalic acid.

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Most popular questions from this chapter

The reusable booster rockets of the U.S. space shuttle employ a mixture of aluminum and ammonium perchlorate for fuel. A possible equation for this reaction is $$ 3 \mathrm{Al}(s)+3 \mathrm{NH}_{4} \mathrm{ClO}_{4}(s) \longrightarrow $$ $$ \mathrm{Al}_{2} \mathrm{O}_{3}(s)+\mathrm{AlCl}_{3}(s)+3 \mathrm{NO}(g)+6 \mathrm{H}_{2} \mathrm{O}(g) $$ What mass of \(\mathrm{NH}_{4} \mathrm{ClO}_{4}\) should be used in the fuel mixture for every kilogram of Al?

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