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Chapter 3: Problem 16

Explain which of the following statement(s) is (are) correct for sorbic acid, \(\mathrm{C}_{6} \mathrm{H}_{8} \mathrm{O}_{2},\) an inhibitor of mold and yeast. (a) It has a \(\mathrm{C}: \mathrm{H}:\) O mass ratio of 3: 4: 1 (b) It has the same mass percent composition as the aquatic herbicide, acrolein, \(\mathrm{C}_{3} \mathrm{H}_{4} \mathrm{O}\) (c) It has the same empirical formula as aspidinol, \(\mathrm{C}_{12} \mathrm{H}_{16} \mathrm{O}_{4},\) a drug used to kill parasitic worms. (d) It has four times as many \(\mathrm{H}\) atoms as \(\mathrm{O}\) atoms, but four times as much O as H by mass.

Short Answer

Expert verified
Among the provided statements about sorbic acid, statement (d) is the only correct one.

Step by step solution

01

Calculate the mole ratios

To determine if statement (a) is correct, calculate the mole ratio of \(\mathrm{C}:\mathrm{H}:\mathrm{O}\) for sorbic acid. Use the atomic masses of carbon (12.01 g/mol), hydrogen (1.01 g/mol), and oxygen (16.00 g/mol) to calculate the moles of each element in one mole of sorbic acid.For Carbon, \( \frac{6 \times 12.01}{112.12} \) gives 0.643 moles. For Hydrogen, \( \frac{8 \times 1.01}{112.12} \) gives 0.072 moles. For Oxygen, \( \frac{2 \times 16.00}{112.12} \) gives 0.285 moles.
02

Compare with given ratio

The calculated mole ratio is approximately \(\mathrm{C}: \mathrm{H}: \mathrm{O}=0.643: 0.072: 0.285\), which is not the same as the given \(\mathrm{C}: \mathrm{H}: \mathrm{O}=3: 4: 1\). Therefore, statement (a) is incorrect.
03

Compare mass percent compositions

To determine if statement (b) is correct, compare the mass percent composition of sorbic acid and acrolein. The mass percent composition is the mass of each element in a compound divided by the overall mass. The mass percent of carbon in sorbic acid is \(\frac{6 \times 12.01}{112.12}\), and for hydrogen it is \(\frac{8 \times 1.01}{112.12}\), and for oxygen it is \(\frac{2 \times 16.00}{112.12}\).Perform similar calculations for acrolein to find its mass percent composition, and compare. Since the two molecules have different numbers of atoms of each element, they will not have the same mass percent composition. Statement (b) is incorrect.
04

Compare empirical formulas

To determine if statement (c) is correct, one can compare the empirical formulas of sorbic acid and aspidinol. The empirical formula is the lowest whole number ratio of the elements in a compound. For sorbic acid, the empirical formula is \(\mathrm{C}_{6} \mathrm{H}_{8} \mathrm{O}_{2}\), and for aspidinol it is \(\mathrm{C}_{12} \mathrm{H}_{16} \mathrm{O}_{4}\). Taking the ratio \(\frac{6}{8}\) and reducing, one get \(\frac{3}{4}\) as the ratio of C to H, different from the ratio in aspidinol. Therefore, statement (c) is incorrect.
05

Compare Hydrogen and Oxygen numbers and masses

To determine if statement (d) is correct, compare the number of hydrogen atoms to oxygen atoms, and the mass of hydrogen to the mass of oxygen. In this case, the ratio of hydrogen in sorbic acid to oxygen is indeed 4 to 1. The mass ratio is \( \mathrm{H}: \mathrm{O} = 8 \times 1.01 : 2 \times 16.00 \), which simplifies to 4:1, exactly as written in statement (d). Therefore, statement (d) is correct.

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