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Chapter 3: Problem 87

Sour Candy Tartaric acid, \(\mathrm{C}_{4} \mathrm{H}_{6} \mathrm{O}_{6},\) and citric acid, \(\mathrm{C}_{6} \mathrm{H}_{8} \mathrm{O}_{7},\) are both used commercially to give sour candies (Figure \(\mathrm{P} 3.87\) ) their characteristic sour taste. Which compound has the larger percent C by mass? (IMAGE CAN'T COPY)

Short Answer

Expert verified
Answer: Citric Acid has a larger percent of Carbon by mass.

Step by step solution

01

Find the molar mass of Tartaric Acid (C4H6O6) and Citric Acid (C6H8O7)

To find the molar mass of each compound, we need to multiply the number of each atom in the compound by its atomic mass, and sum them up. For Tartaric Acid (C4H6O6): Molar mass = (4 * 12.01 [C]) + (6 * 1.01 [H]) + (6 * 16.00 [O]) = 48.04 + 6.06 + 96.00 = 150.10 g/mol For Citric Acid (C6H8O7): Molar mass = (6 * 12.01 [C]) + (8 * 1.01 [H]) + (7 * 16.00 [O]) = 72.06 + 8.08 + 112.00 = 192.14 g/mol
02

Calculate the mass percent of Carbon in Tartaric Acid and Citric Acid

To calculate the mass percent of Carbon, divide the mass of Carbon by the total molar mass of the compound and multiply by 100. For Tartaric Acid: Mass percent of C = (Mass of Carbon / Molar mass of Tartaric Acid) * 100 Mass percent of C = (48.04 / 150.10) * 100 = 32.01% For Citric Acid: Mass percent of C = (Mass of Carbon / Molar mass of Citric Acid) * 100 Mass percent of C = (72.06 / 192.14) * 100 = 37.48%
03

Compare the mass percentages of Carbon in both compounds and determine which compound has the larger value

We compare the mass percent of Carbon in Tartaric Acid (32.01%) and Citric Acid (37.48%). As 37.48% > 32.01%, Citric Acid has the larger percent of Carbon by mass.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Molar Mass
Understanding molar mass is essential for many chemistry calculations, including determining the percent composition of elements in a compound. Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). It is calculated by summing the atomic masses of all atoms present in a chemical formula.
For instance, to find the molar mass of tartaric acid (\( ext{C}_4 ext{H}_6 ext{O}_6 \)), you would multiply the number of each type of atom by its respective atomic mass and then sum these values:
  • Carbon: 4 atoms x 12.01 g/mol = 48.04 g/mol
  • Hydrogen: 6 atoms x 1.01 g/mol = 6.06 g/mol
  • Oxygen: 6 atoms x 16.00 g/mol = 96.00 g/mol
  • Total Molar Mass = 150.10 g/mol
Similarly, the molar mass of citric acid (\( ext{C}_6 ext{H}_8 ext{O}_7 \)) is calculated by:
  • Carbon: 6 atoms x 12.01 g/mol = 72.06 g/mol
  • Hydrogen: 8 atoms x 1.01 g/mol = 8.08 g/mol
  • Oxygen: 7 atoms x 16.00 g/mol = 112.00 g/mol
  • Total Molar Mass = 192.14 g/mol
Knowing the molar mass of a compound is crucial for calculating other properties like the percent composition of individual elements within the compound.
Tartaric Acid
Tartaric acid is an organic compound that is often found in plants, especially in grapes. It鈥檚 well-known for its role in the winemaking process and is also used to give candies a sour taste. Its chemical formula is \( ext{C}_4 ext{H}_6 ext{O}_6 \).
This formula tells us several key things about tartaric acid:
  • It contains 4 carbon (C) atoms, 6 hydrogen (H) atoms, and 6 oxygen (O) atoms.
  • The molar mass is 150.10 g/mol, calculated from the atomic weights of its elements.
The percent composition of carbon in tartaric acid is determined by comparing the mass of carbon in the compound with its total molar mass. The calculation is as follows:
  • Mass of carbon = 48.04 g/mol
  • Total molar mass = 150.10 g/mol
  • Percent carbon by mass = (48.04 / 150.10) * 100 = 32.01%
Tartaric acid is not just limited to giving a zesty taste in candies. It has applications in baking, where it stabilizes egg whites, and in pharmaceuticals.
Citric Acid
Citric acid, another compound contributing to the sour taste in candies, is a weak organic acid that occurs naturally in citrus fruits. The chemical formula for citric acid is \( ext{C}_6 ext{H}_8 ext{O}_7 \).
This formula presents the structure of citric acid:
  • It consists of 6 carbon (C) atoms, 8 hydrogen (H) atoms, and 7 oxygen (O) atoms.
  • The molar mass of citric acid is 192.14 g/mol.
To calculate the percent composition of carbon in citric acid, follow this method:
  • Mass of carbon = 72.06 g/mol
  • Total molar mass = 192.14 g/mol
  • Percent carbon by mass = (72.06 / 192.14) * 100 = 37.48%
Citric acid plays a significant role beyond flavoring. It's also commonly used as a natural preservative and helps balance the pH levels in foods. Furthermore, it's a key ingredient in a variety of cleaning products due to its effective, natural cleaning properties.

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Most popular questions from this chapter

Using different-colored spheres to represent \(\mathrm{C}\) and \(\mathrm{O}\) sketch the reaction between five C atoms and the necessary number of \(\mathrm{O}_{2}\) molecules to produce a \(50 \%\) mixture of \(\mathrm{CO}\) and \(\mathrm{CO}_{2}\).

The burner in a gas grill mixes 24 volumes of air for every one volume of propane \(\left(\mathrm{C}_{3} \mathrm{H}_{8}\right)\) fuel. Like all gases, the volume that propane occupies is directly proportional to the number of moles of it at a given temperature and pressure. Air is \(21 \%\) (by volume) \(\mathrm{O}_{2} .\) Is the flame produced by the burner fuel-rich (excess propane in the reaction mixture), fuel-lean (not enough propane), or stoichiometric (just right)?

Of the nitrogen oxides \(-\mathrm{N}_{2} \mathrm{O}, \mathrm{NO}, \mathrm{N}_{2} \mathrm{O}_{3}, \mathrm{N}_{2} \mathrm{O}_{2}, \mathrm{NO}_{2},\) and \(\mathrm{N}_{2} \mathrm{O}_{4}-\) which are more than \(50 \%\) oxygen by mass? Which, if any, have the same empirical formula?

As a solution of copper sulfate slowly evaporates, beautiful blue crystals made of copper(II) and sulfate ions form such that water molecules are trapped inside the crystals. The overall formula of the compound is \(\mathrm{CuSO}_{4} \cdot 5 \mathrm{H}_{2} \mathrm{O}\) a. What is the percent water in this compound? b. At high temperatures, the water in the compound is driven off as steam. What mass percentage of the original sample of the blue solid is lost as a result?

Egyptian Cosmetics \(\mathrm{Pb}\) (OH) Cl, one of the lead compounds used in ancient Egyptian cosmetics, was prepared from PbO according to the following recipe:$$\mathrm{PbO}(s)+\mathrm{NaCl}(a q)+\mathrm{H}_{2} \mathrm{O}(\ell) \rightarrow \mathrm{Pb}(\mathrm{OH}) \mathrm{Cl}(s)+\mathrm{NaOH}(a q)$$.How many grams of \(\mathrm{PbO}\) and how many grams of \(\mathrm{NaCl}\) would be required to produce \(10.0 \mathrm{g}\) of \(\mathrm{Pb}(\mathrm{OH}) \mathrm{Cl} ?\)
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