Question

Calculate the mass in grams of each elemental sample. (a) 1.32 * 1020 uranium atoms (b) 2.55 * 1022 zinc atoms (c) 4.11 * 1023 lead atoms (d) 6.59 * 1024 silicon atoms

Short answer

The mass in grams of each elemental sample is: (a) 0.05212 g, (b) 2.762 g, (c) 141.23 g, (d) 3076.67 g.

Step-by-step solution

Understanding the Concept - Avogadro's Number

First, it's important to understand that Avogadro's Number (6.022 × 10^23) is the number of atoms in one mole of a substance. The mass of one mole of a substance, in grams, is equal to the substance's atomic mass.

Calculate the Number of Moles for Each Element

For each elemental sample, divide the number of atoms given in the problem by Avogadro's Number to find the number of moles of the substance.

Determine the Atomic Mass

Using the periodic table, find the atomic mass of each element: Uranium (U) has an atomic mass of 238 g/mol, Zinc (Zn) has an atomic mass of 65.38 g/mol, Lead (Pb) has an atomic mass of 207.2 g/mol, and Silicon (Si) has an atomic mass of 28.085 g/mol.

Calculate the Mass in Grams for Each Element

Multiply the number of moles of each element by its atomic mass to obtain the mass in grams for each elemental sample.

Perform the Calculations for Each Element

(a) For uranium atoms: (1.32 × 10^20 atoms) / (6.022 × 10^23 atoms/mol) × 238 g/mol = 0.05212 g. (b) For zinc atoms: (2.55 × 10^22 atoms) / (6.022 × 10^23 atoms/mol) × 65.38 g/mol = 2.762 g. (c) For lead atoms: (4.11 × 10^23 atoms) / (6.022 × 10^23 atoms/mol) × 207.2 g/mol = 141.23 g. (d) For silicon atoms: (6.59 × 10^24 atoms) / (6.022 × 10^23 atoms/mol) × 28.085 g/mol = 3076.67 g.

Key concepts

The Mole Concept

The mole concept is a fundamental principle in chemistry that provides a bridge between the microscopic world of atoms and the macroscopic world of grams and liters. It is defined as the amount of substance that contains as many entities as there are atoms in exactly 12 grams of pure carbon-12. This number, known as Avogadro's Number, is approximately equal to \(6.022 \times 10^{23}\) entities and is a key component in translating atomic-scale observations to a laboratory scale.

Using the mole concept allows us to count atoms, molecules, or ions by weighing them. Since it's not practical to count individual atoms because they are exceedingly small and numerous, we use the mole as a counting unit. For example, saying that we have 1 mole of hydrogen atoms means we have \(6.022 \times 10^{23}\) hydrogen atoms, and this also leads us to a predictable mass that corresponds to that many atoms of hydrogen based on its atomic mass.

Understanding Atomic Mass

Atomic mass is essentially the weight of a single atom of an element. It is usually expressed in atomic mass units (amu), where one amu is defined as one twelfth the mass of one carbon-12 atom. However, when dealing with moles, we use the atomic mass in grams per mole (g/mol), which can be found on the periodic table next to each element.

For practical applications, like calculations in a chemistry class, the atomic mass tells us the mass of a mole of that element. For instance, if the atomic mass of carbon is 12.01 g/mol, this means that one mole of carbon atoms has a mass of 12.01 grams. This concept is crucial in converting between moles and grams, enabling us to perform stoichiometric calculations effectively.

Stoichiometry and Calculations

Stoichiometry is the area of chemistry that pertains to the quantitative relationships between the amounts of reactants and products in a chemical reaction. It's based on the law of conservation of mass and the mole concept.

Calculations in stoichiometry often involve using the balanced chemical equation to find the mole ratio between reactants and products, then converting moles to grams or liters using atomic or molecular masses and molar volumes of gases. This method allows chemists to predict how much product can be formed from certain amounts of reactants or how much of each reactant is needed to make a desired quantity of product. Understanding the mole concept, atomic mass, and how they interact is essential for making accurate stoichiometric predictions.

Periodic Table Usage

The periodic table is a comprehensive grid that organizes chemical elements according to their atomic number, electron configuration, and recurring chemical properties. It is a vital tool in chemistry that helps predict the types of chemical reactions that a particular element is likely to participate in.

For our calculations discussed here, the periodic table provides the atomic masses of elements, which are essential for converting between moles and grams. By understanding how to read and interpret the periodic table, students and chemists can efficiently access a wealth of information about the elements, including their atomic mass and valence electron configurations, which ultimately aids in executing accurate chemical calculations and understanding the behavior of elements in various chemical reactions.