Question

Convert to moles. (a) \(128.3 \mathrm{~g}\) of sucralose, \(\mathrm{C}_{12} \mathrm{H}_{19} \mathrm{O}_{8} \mathrm{Cl}_{3},\) the active ingredient of the artificial sweetener Splenda \(^{\mathrm{TM}}\) (b) \(0.3066 \mathrm{~g}\) of uric acid, \(\mathrm{C}_{5} \mathrm{H}_{4} \mathrm{~N}_{4} \mathrm{O}_{3},\) the compound that can cause gout and arthritis (c) \(2.664 \mathrm{~g}\) of cadmium(II) telluride used to coat solar panels

Short answer

Question: Convert the following given masses of compounds to moles: (a) 128.3 g of sucralose, (b) 0.3066 g of uric acid, and (c) 2.664 g of cadmium(II) telluride. Answer: (a) 0.3227 mol of sucralose, (b) 0.001823 mol of uric acid, and (c) 0.0111 mol of cadmium(II) telluride.

Step-by-step solution

Calculate the molar mass of each compound

To find the molar mass, first identify the atomic mass of each element present, then multiply it by the number of atoms in the molecule. Add up the total masses for each element to get the molar mass of the entire compound. (a) Sucralose (C12 H19 O8 Cl3): Molar mass = (12 × 12.01) + (19 × 1.01) + (8 × 16.00) + (3 × 35.45) = 397.64 g/mol (b) Uric acid (C5 H4 N4 O3): Molar mass = (5 × 12.01) + (4 × 1.01) + (4 × 14.01) + (3 × 16.00) = 168.11 g/mol (c) Cadmium(II) telluride (CdTe): Molar mass = (1 × 112.41) + (1 × 127.60) = 240.01 g/mol

Convert the given masses to moles

Now that we have the molar masses for each compound, we can convert the given masses to moles by dividing the mass of the compound by its molar mass. (a) Moles of sucralose: Moles = (128.3 g) / (397.64 g/mol) = 0.3227 mol (b) Moles of uric acid: Moles = (0.3066 g) / (168.11 g/mol) = 0.001823 mol (c) Moles of cadmium(II) telluride: Moles = (2.664 g) / (240.01 g/mol) = 0.0111 mol The given masses of the compounds have been successfully converted to moles.

Key concepts

Molar Mass Calculation

Molar mass is a fundamental concept in chemistry that relates the mass of a substance to its number of particles, specifically moles. The molar mass of a compound is calculated by summing the atomic masses of all the atoms in the formula. Each element's atomic mass can be found on the periodic table and is usually expressed in grams per mole (g/mol).

For example, take sucralose, which has the chemical formula \(\mathrm{C}_{12} \mathrm{H}_{19}\mathrm{O}_{8} \mathrm{Cl}_{3}\). To calculate its molar mass, we multiply the atomic masses of carbon (C), hydrogen (H), oxygen (O), and chlorine (Cl) by the number of atoms of each element present in the molecule and then add those amounts together:

• Carbon: 12 atoms \times 12.01 g/mol
• Hydrogen: 19 atoms \times 1.01 g/mol
• Oxygen: 8 atoms \times 16.00 g/mol
• Chlorine: 3 atoms \times 35.45 g/mol

The result is the molar mass of sucralose, 397.64 g/mol. This value is critical as it acts as a conversion factor between grams and moles, allowing us to perform stoichiometric calculations.

Stoichiometry

Stoichiometry is the branch of chemistry that deals with the quantitative relationships between reactants and products in a chemical reaction. It allows chemists to predict the amounts of substances consumed and produced in a reaction. This is crucial not only for understanding the composition of a reaction, but also for scaling up reactions for industrial applications where efficiency and cost-effectiveness are key.

Using the molar mass as a conversion factor, stoichiometry enables us to convert grams to moles (and vice versa), which is essential when we work with chemical equations and need to measure out precise amounts of each substance. In practical terms, knowing stoichiometry contributes to making precise predictions about yields and reactant consumption, which in turn aids in optimizing the use of resources in the lab or industry.

Conversion to Moles

Converting grams to moles is a fundamental skill in chemistry. This conversion allows scientists to use the mole, which is a standard unit of measurement in chemistry, to count particles at the atomic and molecular level. A mole is defined as the quantity of a substance that contains as many elementary entities (atoms, molecules, or other particles) as there are atoms in 12 grams of pure carbon-12, which is approximately \(6.022 \times 10^{23}\) entities.

To convert a given mass of a substance to moles, we divide the mass by the molar mass of the substance. The calculation for the conversion is straightforward: Moles = Mass (g) / Molar Mass (g/mol). For instance, to find out how many moles are in 128.3 grams of sucralose, we divide 128.3 grams by the molar mass of sucralose (397.64 g/mol), resulting in 0.3227 moles. Understanding this conversion process is key to analyzing chemical reactions quantitatively and is a stepping stone to mastering more complex concepts in chemical analysis and engineering.