Question

What is the mass in grams of each elemental sample? (a) 6.64 mol W (b) 0.581 mol Ba (c) 68.1 mol Xe (d) 1.57 mol S

Short answer

The mass in grams of each element is: (a) 1220.50 g W, (b) 79.80 g Ba, (c) 8939.89 g Xe, and (d) 50.35 g S.

Step-by-step solution

Determine the molar mass of each element

To convert moles to grams, first, we need the molar mass of each element. It can be found on the periodic table of elements. Using the periodic table, we find the molar masses: Tungsten (W) has a molar mass of approximately 183.84 g/mol, Barium (Ba) has a molar mass of approximately 137.33 g/mol, Xenon (Xe) has a molar mass of approximately 131.29 g/mol, and Sulfur (S) has a molar mass of approximately 32.07 g/mol.

Convert moles of Tungsten (W) to grams

Use the formula mass (g) = number of moles × molar mass (g/mol) to convert moles to grams. For Tungsten (W), this is calculated as: mass (g) = 6.64 mol × 183.84 g/mol.

Convert moles of Barium (Ba) to grams

Apply the same formula for Barium (Ba): mass (g) = 0.581 mol × 137.33 g/mol.

Convert moles of Xenon (Xe) to grams

Again, apply the formula for Xenon (Xe): mass (g) = 68.1 mol × 131.29 g/mol.

Convert moles of Sulfur (S) to grams

Finally, apply the formula for Sulfur (S): mass (g) = 1.57 mol × 32.07 g/mol.

Calculate the mass of each elemental sample

Use the multiplication results from steps 2, 3, 4, and 5 to obtain the mass in grams for each element. For W: 6.64 mol × 183.84 g/mol = 1220.50 grams. For Ba: 0.581 mol × 137.33 g/mol = 79.80 grams. For Xe: 68.1 mol × 131.29 g/mol = 8939.89 grams. For S: 1.57 mol × 32.07 g/mol = 50.35 grams.

Key concepts

Mole to Gram Conversion

Understanding the conversion of moles to grams is a foundational concept in chemistry that involves using the molar mass of a substance. The molar mass is the weight in grams of one mole of a substance. It acts as a bridge between the number of moles and the mass in grams.

To perform a mole to gram conversion, you can use the formula:
\[ \text{mass (g)} = \text{number of moles} \times \text{molar mass (g/mol)} \]
This formula is essential for translating the abstract concept of moles (a count of particles) into a tangible quantity (grams) that can be measured physically. Without this conversion, it would be difficult to scale reactions to a practical size for laboratory work or industrial applications.

Avogadro's Number

Avogadro's number plays a pivotal role in mole to gram conversions. It is defined as the number of particles, such as atoms or molecules, in one mole of a substance. Precisely, it's approximately \(6.022 \times 10^{23}\) particles per mole.

This constant provides a direct link between the microscale world, where we count individual atoms and molecules, and the macroscale world of grams and kilograms that we interact with in everyday life. When chemists refer to the mole, they're tacitly invoking Avogadro's number to equate amounts at the particle level with amounts we can handle and measure.

Atomic Mass

The atomic mass is intimately connected to molar mass and represents the mass of a single atom, measured in atomic mass units (amu). Each element's atomic mass is listed in the periodic table and reflects the average mass of its isotopes relative to the mass of carbon-12.

The atomic mass of an element, when expressed in grams, corresponds to the mass of one mole of that element. This allows us to establish a link between the microscopic mass of single atoms and the macroscopic quantities we measure in the lab. Thus, molar mass can be seen as the atomic mass scaled up to Avogadro's number of atoms.

Stoichiometry

Stoichiometry is the mathematical relationship between the quantities of reactants and products in a chemical reaction. It's based on the conservation of mass and the concept of moles. Using stoichiometry, chemists can predict how much product will form from certain amounts of reactants or determine the required quantity of one reactant to completely react with another.

Central to stoichiometry is the use of balanced chemical equations, which provide the mole ratios of reactants and products. Combining these ratios with the concept of molar mass allows chemists to scale these mole ratios up to measurable quantities, facilitating the practical execution of chemical reactions in the lab.