Question

Calculate the number of moles of the indicated substance present in each of the following samples. a. \(1.28 \mathrm{g}\) of iron(II) sulfate b. \(5.14 \mathrm{mg}\) of mercury(II) iodide c. \(9.21 \mu g\) of tin(IV) oxide d. 1.26 lb of cobalt(II) chloride e. \(4.25 \mathrm{g}\) of copper(II) nitrate

Short answer

The number of moles for each substance are: a. 0.00842 moles of iron(II) sulfate b. \(1.13 \times 10^{-5}\) moles of mercury(II) iodide c. \(6.11 \times 10^{-8}\) moles of tin(IV) oxide d. 4.40 moles of cobalt(II) chloride e. 0.02265 moles of copper(II) nitrate

Step-by-step solution

Find the molar mass of iron(II) sulfate

The molecular formula for iron(II) sulfate is FeSO4. Using the periodic table, the molar mass is: Fe: 55.85 g/mol S: 32.07 g/mol O: (4 * 16.00) g/mol= 64.00 g/mol Total molar mass = 55.85 + 32.07 + 64.00 = 151.92 g/mol

Calculate the moles of iron(II) sulfate

Number of moles = mass / molar mass = 1.28 g / 151.92 g/mol = 0.00842 moles b. \(5.14 \mathrm{mg}\) of mercury(II) iodide

Find the molar mass of mercury(II) iodide

The molecular formula for mercury(II) iodide is HgI2. Using the periodic table, the molar mass is: Hg: 200.59 g/mol I: (2 * 126.90) g/mol = 253.80 g/mol Total molar mass = 200.59 + 253.80 = 454.39 g/mol

Calculate the moles of mercury(II) iodide

First, convert the mass from milligrams to grams: 5.14 mg = 0.00514 g Number of moles = mass / molar mass = 0.00514 g / 454.39 g/mol = 1.13 x 10^(-5) moles c. \(9.21 \mu g\) of tin(IV) oxide

Find the molar mass of tin(IV) oxide

The molecular formula for tin(IV) oxide is SnO2. Using the periodic table, the molar mass is: Sn: 118.71 g/mol O: (2 * 16.00) g/mol = 32.00 g/mol Total molar mass = 118.71 + 32.00 = 150.71 g/mol

Calculate the moles of tin(IV) oxide

First, convert the mass from micrograms to grams: 9.21 μg = 9.21 x 10^(-6) g Moles = mass / molar mass = 9.21 x 10^(-6) g / 150.71 g/mol = 6.11 x 10^(-8) moles d. 1.26 lb of cobalt(II) chloride

Find the molar mass of cobalt(II) chloride

The molecular formula for cobalt(II) chloride is CoCl2. Using the periodic table, the molar mass is: Co: 58.93 g/mol Cl: (2 * 35.45) g/mol = 70.90 g/mol Total molar mass = 58.93 + 70.90 = 129.83 g/mol

Calculate the moles of cobalt(II) chloride

First, convert the mass from pounds to grams: 1.26 lb * 453.592 g/lb = 571.52 g Moles = mass / molar mass = 571.52 g / 129.83 g/mol = 4.40 moles e. \(4.25 \mathrm{g}\) of copper(II) nitrate

Find the molar mass of copper(II) nitrate

The molecular formula for copper(II) nitrate is Cu(NO3)2. Using the periodic table, the molar mass is: Cu: 63.55 g/mol N: (2 * 14.01) g/mol = 28.02 g/mol O: (6 * 16.00) g/mol = 96.00 g/mol Total molar mass = 63.55 + 28.02 + 96.00 = 187.57 g/mol

Calculate the moles of copper(II) nitrate

Number of moles = mass / molar mass = 4.25 g / 187.57 g/mol = 0.02265 moles

Key concepts

Molar Mass Determination

Determining molar mass is a fundamental step in understanding chemical reactions and quantities. It is essentially the sum of the atomic masses of all atoms in a chemical formula. This figure is typically expressed in grams per mole (g/mol). To find the molar mass of a compound, such as iron(II) sulfate (FeSO₄), consult the periodic table to find the atomic mass of each element. For FeSO₄:

• Iron (Fe) has an atomic mass of 55.85 g/mol.
• Sulfur (S) has an atomic mass of 32.07 g/mol.
• Oxygen (O), occurring four times, has a total atomic mass of 4 x 16.00 = 64.00 g/mol.

Adding these values gives \[55.85 + 32.07 + 64.00 = 151.92 \text{ g/mol}.\]Molar mass helps convert between mass and moles, crucial for chemical quantification.

Conversion of Units

Unit conversion is vital for chemical calculations, ensuring all quantities are in compatible units. For example, converting mass from milligrams to grams, as demonstrated in the mercury(II) iodide problem. Use these simple conversion formulas:

• Milligrams to grams: \[m = \frac{\text{mg}}{1000}\]
• Pounds to grams: \[m = \text{lb} \times 453.592\]
• Micrograms to grams:\[m = \frac{\mu\text{g}}{10^6}\]

Ensuring the correct unit conversion enables straightforward calculation of moles, avoiding errors in stoichiometry.

Chemical Formulas

Chemical formulas provide the blueprint of a compound, showing the types and numbers of atoms present. For instance, in iron(II) sulfate (FeSO₄), there is one Fe, one S, and four O atoms. Understanding chemical formulas:

• Learn to interpret subscripts indicating the number of atoms of each type in a molecule.
• Recognize polyatomic ions like sulfate (SO₄) and nitrate (NO₃), common in many compounds.
• Helps in calculating molar mass and in balancing chemical equations.

Grasping chemical formulas adds clarity to chemical equations and assists in predicting properties and behaviors of substances.

Stoichiometry

Stoichiometry deals with measuring and calculating the quantities of reactants and products in chemical reactions. Everyday stoichiometry involves determining how much of a chemical is needed or produced, much like a recipe. The basic formula involves the concept of the mole, where given mass and molar mass helps find moles:\[\text{moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}}\]Applying stoichiometry to find out mole quantities in each example:

• Helps balance chemical equations.
• Ensures correct proportions of reactants and products.
• Maximizes efficiency and minimizes waste in reactions.

Mastering stoichiometry is essential for any chemical calculation and experiment feasibility analysis.

Periodic Table Use

The periodic table is a chemist's guidebook, organizing elements in a systematic manner. It provides essential details such as atomic mass, useful for molar mass calculations. To use the periodic table effectively:

• Locate elements quickly to find their atomic masses.
• Understand elemental groups for insight into chemical properties.
• Identify transition metals like iron and cobalt and their common oxidation states.

The periodic table is more than just a chart; it is a tool for predicting reactions, understanding trends, and calculating the stoichiometry of chemical compounds.