Question

Formula Mass and the Mole Concept for Compounds Calculate the mass of each sample. $$ \begin{array}{l}{\text { a. } 15.7 \mathrm{mol} \mathrm{HNO}_{3}} \\ {\text { b. } 1.04 \times 10^{-3} \mathrm{mol} \mathrm{H}_{2} \mathrm{O}_{2}} \\\ {\text { c. } 72.1 \mathrm{mmol} \mathrm{SO}_{2}} \\ {\text { d. } 1.23 \mathrm{mol} \text { xenon difluoride }}\end{array} $$

Short answer

a. 989.157 g HNO3, b. 0.03538 g H2O2, c. 4.61764 g SO2, d. 208.2267 g XeF2

Step-by-step solution

Determine the Molar Mass of Each Compound

Find the molar mass (also known as formula mass or molecular weight) of each compound by adding up the atomic weights of its constituent atoms. This information can be obtained from the periodic table. The molar masses for the substances are: -HNO_3: (1x1.01) + (1x14.01) + (3x16.00)= 63.01 g/mol -H2O2: (2x1.01) + (2x16.00)= 34.02 g/mol -SO2: (1x32.07) + (2x16.00)= 64.07 g/mol -XeF2: (1x131.29) + (2x19.00)= 169.29 g/mol

Calculate Mass of Each Sample

The mass of a sample can be calculated by multiplying the number of moles of substance by its molar mass. Use the formula: mass = moles x molar mass.-For HNO3: 15.7 mol x 63.01 g/mol = 989.157 g -For H2O2: 1.04x10^-3 mol x 34.02 g/mol = 0.03538 g -For SO2: 72.1 mmol x 64.07 g/mol x 1g/1000mmol = 4.61764 g -For XeF2: 1.23 mol x 169.29 g/mol = 208.2267 g

Key concepts

Molar Mass Calculation

Understanding the concept of molar mass is essential for various calculations in chemistry. It represents the mass of one mole of a given substance and is expressed in grams per mole (g/mol). To calculate the molar mass of a compound, you sum the atomic weights of all the atoms in the molecule, as given by the periodic table.

For example, water (H₂O) has a molar mass of approximately 18.02 g/mol. This is calculated by adding twice the atomic weight of hydrogen (2 x 1.01 g/mol) to the atomic weight of oxygen (16.00 g/mol). In another case, for sulfur dioxide (SO₂), we would add the atomic weight of sulfur (32.07 g/mol) to twice that of oxygen, yielding 64.07 g/mol.

Remembering to consider both the quantity and atomic weight of each element is key. For complex compounds, ensure all subscripts in the formula are accounted for when calculating the totals.

Mole to Mass Conversion

Converting moles to mass is a straightforward process once you have the molar mass of the substance. Using the formula:
\[ \text{mass} = \text{moles} \times \text{molar mass} \]
You can find the mass of a compound if you know the number of moles present. For instance, with HNO₃, multiplying the number of moles (15.7) by its molar mass (63.01 g/mol) gives you the mass in grams.

It's important to keep track of units, especially when dealing with millimoles (mmol), as these must be converted to moles (by dividing by 1000) before using the above formula. This ensures correct mass calculation, whether you're working with small lab samples or larger amounts of substances.

Stoichiometry

Stoichiometry is the section of chemistry that involves the quantitative relationships between reactants and products in a chemical reaction. Using the balanced chemical equation, stoichiometry allows chemists to predict how much product will form from given amounts of reactants or vice versa.

Key to stoichiometry is the mole ratio, derived from the coefficients of each substance in a balanced equation. For example, if the equation states 2H₂ + O₂ → 2H₂O, it implies that 2 moles of hydrogen gas react with 1 mole of oxygen gas to produce 2 moles of water.

By understanding these ratios and the concept of the mole, you can calculate the amount of products formed from specific reactant quantities, or determine the amount of reactants required to produce a desired amount of product.

Chemical Formula and Compounds

A chemical formula is a symbolic representation of a substance's composition. It provides the types of atoms involved and the exact number of each atom in a single molecule of the compound. For example, the formula of hydrogen peroxide is H₂O₂, which tells us there are two hydrogen atoms and two oxygen atoms in one molecule of hydrogen peroxide.

Compounds are substances formed when two or more elements are chemically bonded together. Understanding the formula of a compound is essential for studying its properties and behavior in reactions. For instance, xenon difluoride (XeF₂) involves one atom of xenon and two atoms of fluorine, and its composition directly influences characteristics such as its molar mass and reactivity.

Chemical formulas are the foundational building blocks for more advanced concepts in chemistry, such as naming compounds, determining their structures, and contemplating their interactions in chemical reactions.