Question

Calculate the number of moles of each compound in the following samples. (a) \(4.29 \mathrm{~g} \mathrm{H}_{2} \mathrm{O}_{2}\) (c) \(9.36 \mathrm{~g}\) calcium hydroxide (b) \(4.65 \mathrm{mg} \mathrm{NaAuCl}_{4}\) (d) \(38.2 \mathrm{~kg}\) lead \((\mathrm{II})\) sulfate

Short answer

Number of moles are: (a) 0.126 moles H2O2, (c) 0.126 moles Ca(OH)2, (b) 1.18 x 10^-5 moles NaAuCl4, (d) 126 moles PbSO4.

Step-by-step solution

Calculate the molar mass of H2O2

To find the molar mass of hydrogen peroxide (H2O2), sum the atomic masses of all the atoms in the compound. Each hydrogen atom has an approximate atomic mass of 1.008 g/mol and each oxygen atom has an approximate atomic mass of 16.00 g/mol. Thus, the molar mass of H2O2 is: (2 × 1.008 g/mol) + (2 × 16.00 g/mol) = 34.016 g/mol.

Calculate moles of H2O2

Use the molar mass of H2O2 to convert the sample's mass to moles: Number of moles = Mass of the sample (in g) / Molar mass (in g/mol). So, Number of moles of H2O2 = 4.29 g / 34.016 g/mol.

Calculate the molar mass of calcium hydroxide (Ca(OH)2)

To find the molar mass of calcium hydroxide, sum the atomic masses of its constituent elements. The atomic mass of calcium (Ca) is approximately 40.08 g/mol, oxygen (O) is 16.00 g/mol, and hydrogen (H) is 1.008 g/mol. So, the molar mass is: (1 × 40.08 g/mol) + (2 × 16.00 g/mol) + (2 × 1.008 g/mol) = 74.096 g/mol.

Calculate moles of Ca(OH)2

Convert the mass of the sample to moles using its molar mass: Number of moles = Mass of the sample (in g) / Molar mass (in g/mol). So, Number of moles of Ca(OH)2 = 9.36 g / 74.096 g/mol.

Calculate the molar mass of NaAuCl4

To find the molar mass of sodium gold(III) chloride (NaAuCl4), sum the atomic masses: sodium (Na) is approximately 22.99 g/mol, gold (Au) is 196.97 g/mol, and chlorine (Cl) is 35.45 g/mol. The molar mass is: (1 × 22.99 g/mol) + (1 × 196.97 g/mol) + (4 × 35.45 g/mol) = 393.78 g/mol.

Convert milligrams to grams

Before calculating moles, convert the given mass from milligrams to grams: Mass in grams = Mass in milligrams / 1000. Therefore, 4.65 mg = 4.65 mg / 1000 = 0.00465 g.

Calculate moles of NaAuCl4

Now, convert the mass of NaAuCl4 to moles: Number of moles = Mass of the sample (in g) / Molar mass (in g/mol). So, Number of moles of NaAuCl4 = 0.00465 g / 393.78 g/mol.

Calculate the molar mass of lead (II) sulfate (PbSO4)

To calculate the molar mass of lead(II) sulfate, add up the atomic masses: lead (Pb) is approximately 207.2 g/mol, sulfur (S) is 32.07 g/mol, and oxygen (O) is 16.00 g/mol. The molar mass is: (1 × 207.2 g/mol) + (1 × 32.07 g/mol) + (4 × 16.00 g/mol) = 303.27 g/mol.

Convert kilograms to grams

Convert the given mass from kilograms to grams: Mass in grams = Mass in kilograms × 1000. Therefore, 38.2 kg = 38.2 kg × 1000 = 38200 g.

Calculate moles of PbSO4

Convert the mass of PbSO4 to moles: Number of moles = Mass of the sample (in g) / Molar mass (in g/mol). Thus, Number of moles of PbSO4 = 38200 g / 303.27 g/mol.

Key concepts

Understanding Molar Mass

Molar mass is a fundamental concept in chemistry that refers to the mass of one mole of a substance. It is expressed in grams per mole ((g/mol)). To calculate the molecular weight of any chemical compound, you add up the atomic masses of all the atoms in a molecule of the compound as found on the periodic table.
For instance, the molar mass of water (H₂O) is calculated by adding twice the atomic mass of hydrogen to the atomic mass of oxygen. Calculating molar mass accurately is critical because it serves as a conversion factor between the mass of a substance and the amount in moles, allowing us to relate the microscale (atoms and molecules) to the macroscale (grams).
When improving calculations of molar mass in exercises, it's essential to ensure that the atomic masses used are current and precise. Moreover, adding real-world applications or visualization techniques, such as comparing the mass of molecules to everyday objects, can substantially aid in understanding this abstract concept.

The Role of Stoichiometry

Stoichiometry is the quantitative relationship between reactants and products in a chemical reaction. It is based on the conservation of mass and the concept of moles. Stoichiometry allows chemists to predict the amounts of substances consumed and produced in a reaction, making it a cornerstone of chemical calculations.
For a balanced chemical equation, stoichiometry provides the ratio of moles of each substance involved. This means that if you know the quantity of one reactant or product, you can calculate the quantities of all the other substances.
In the context of textbook exercises, it is vital to confirm that chemical equations are balanced before performing stoichiometric calculations. Additionally, providing clear instructions on how to use stoichiometric ratios and encouraging the use of dimensional analysis as a method for checking their calculations can greatly assist students in mastering this concept.

Identifying Chemical Compounds

Chemical compounds are pure substances composed of two or more elements that are chemically bonded in a fixed ratio. Each compound has a unique composition and properties that distinguish it from other compounds. Identifying a compound involves understanding its molecular or empirical formula, which indicates the types and numbers of atoms contained in the compound.
The ability to correctly identify and write formulas for chemical compounds is essential when calculating molar masses and performing stoichiometric conversions. Moreover, in education, it's important to provide ample practice through varied examples of compounds and encourage memorization of common ions and their charges, as well as nomenclature rules for inorganic and organic compounds.
Using visual aids like molecular models and providing real-life contexts where these compounds are used can enhance the conceptual understanding and recognition of different chemical compounds.

Conversion of Units

Conversion of units is a fundamental skill in chemistry because different measurements are often used, and it's essential to convert these measurements to work effectively with the data. Common conversions in chemistry include changing milligrams to grams or kilograms to grams as necessary for stoichiometric calculations.
When performing mole calculations, it's imperative to convert the given substance's mass into the appropriate units to align with the molar mass units (typically grams per mole). The concept of dimensional analysis, or the factor-label method, is widely used in conversions; this method involves using conversion factors to cancel out units until the desired unit is obtained.
In crafting instructive content, reinforcing the importance of always checking units to ensure they are consistent throughout a calculation is crucial. Additionally, providing a clear explanation of the relationship between different units of measurement and offering ample practice with conversions of various difficulty levels can help students develop a strong foundation in this area.