Problem 36 - Chemistry The Science in Context

Question

Calculate the molar masses of the following common sweeteners:. a. sucrose, \(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\). b. saccharin, \(\mathrm{C}_{7} \mathrm{H}_{5} \mathrm{NO}_{3} \mathrm{S}\). c. aspartame, \(\mathrm{C}_{14} \mathrm{H}_{18} \mathrm{N}_{2} \mathrm{O}_{5}\). d. fructose, \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\).

Step-by-Step Solution

Answer

Answer: a. Sucrose: 342 g/mol b. Saccharin: 183 g/mol c. Aspartame: 294 g/mol d. Fructose: 180 g/mol

Step 1: Find the atomic molar masses for all elements present

Refer to a periodic table to find the atomic molar masses for the elements: Carbon (C), Hydrogen (H), Oxygen (O), Nitrogen (N) and Sulfur (S). The values are approximately: Carbon (C) = 12 g/mol Hydrogen (H) = 1 g/mol Oxygen (O) = 16 g/mol Nitrogen (N) = 14 g/mol Sulfur (S) = 32 g/mol

Step 2: Calculate the molar mass of Sucrose (C12H22O11)

Multiply the atomic molar masses by the number of atoms and add the products together: (12 * 12) + (22 * 1) + (11 * 16) = 144 + 22 + 176 = 342 g/mol Sucrose has a molar mass of 342 g/mol.

Step 3: Calculate the molar mass of Saccharin (C7H5NO3S)

Multiply the atomic molar masses by the number of atoms and add the products together: (7 * 12) + (5 * 1) + (1 * 14) + (3 * 16) + (1 * 32) = 84 + 5 + 14 + 48 + 32 = 183 g/mol Saccharin has a molar mass of 183 g/mol.

Step 4: Calculate the molar mass of Aspartame (C14H18N2O5)

Multiply the atomic molar masses by the number of atoms and add the products together: (14 * 12) + (18 * 1) + (2 * 14) + (5 * 16) = 168 + 18 + 28 + 80 = 294 g/mol Aspartame has a molar mass of 294 g/mol.

Step 5: Calculate the molar mass of Fructose (C6H12O6)

Multiply the atomic molar masses by the number of atoms and add the products together: (6 * 12) + (12 * 1) + (6 * 16) = 72 + 12 + 96 = 180 g/mol Fructose has a molar mass of 180 g/mol. Now we have calculated the molar masses of each sweetener: a. Sucrose = 342 g/mol b. Saccharin = 183 g/mol c. Aspartame = 294 g/mol d. Fructose = 180 g/mol

Key Concepts

Stoichiometry

Stoichiometry is the branch of chemistry that deals with the quantitative relationships between reactants and products in a chemical reaction. Think of it as the recipe for a chemical reaction, where the ingredients are mixed in the right ratios to produce a desired product.

When calculating molar masses, stoichiometry plays a crucial role because it involves understanding the proportions of each element within a compound. Each molecule is made up of a definite number of atoms of each element, and stoichiometry helps us understand how these combine to give the overall mass of the molecule. The principles of stoichiometry are applied when we calculate the molar mass of compounds, such as the sweeteners in the exercise, by adding together the atomic molar masses according to the number of each type of atom present in a molecule.

Periodic Table

The periodic table is a tabular arrangement of the chemical elements, organized on the basis of their atomic numbers, electron configurations, and recurring chemical properties. Elements are presented in order of increasing atomic number.

The periodic table is an indispensable tool for chemists as it provides essential information about the elements, including their atomic molar masses, which are required for calculating the molar mass of compounds. As in the exercise provided, the first step in calculating the molar mass of a compound is to reference the atomic molar masses for all elements present from the periodic table.

Atomic Molar Mass

Atomic molar mass, also known as atomic weight, refers to the mass of a mole of atoms of a particular element. It is expressed in units of grams per mole (g/mol) and can be found on the periodic table for each element.

For example, the atomic molar mass of carbon (C) is approximately 12 g/mol. This means that one mole of carbon atoms weighs about 12 grams. When calculating the molar mass of a compound, you multiply the atomic molar mass of each element by the number of atoms of that element in the molecule. This process is clearly demonstrated in Steps 2 to 5 of the provided sweetener molar mass calculation exercise.

Molecular Formula

A molecular formula shows the exact number of atoms of each element in a single molecule of a compound. It provides the blueprint for building a molecule from its constituent atoms.

In reference to our exercise, sucrose has a molecular formula of \(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\), which tells us there are 12 carbon atoms, 22 hydrogen atoms, and 11 oxygen atoms in each molecule of sucrose. By following the molecular formula, we calculate the molar mass by multiplying the number of each type of atom by its atomic molar mass and then summing these values, as was done for the sweeteners sucrose, saccharin, aspartame, and fructose.