Question

Refer to the periodic table and state the mass of \(6.02 \times 10^{23}\) atoms of each of the following metals: (a) lithium (b) titanium (c) gold (d) bismuth

Short answer

(a) 6.94 g; (b) 47.87 g; (c) 196.97 g; (d) 208.98 g.

Step-by-step solution

Understanding Avogadro's Number

Avogadro's number, given as \(6.02 \times 10^{23}\), represents the number of atoms in one mole of any substance. This means that if we have \(6.02 \times 10^{23}\) atoms of a metal, we essentially have one mole of that metal.

Using Molar Mass

Each element on the periodic table has a molar mass which represents the mass of one mole of atoms of that element, and it is usually given in grams per mole (g/mol). Therefore, to find the mass of \(6.02 \times 10^{23}\) atoms of each metal, we need to refer to the periodic table for their respective molar masses.

Mass of Lithium Atoms

The molar mass of lithium (Li) is approximately 6.94 g/mol. Since \(6.02 \times 10^{23}\) atoms correspond to one mole, the mass of \(6.02 \times 10^{23}\) lithium atoms is 6.94 grams.

Mass of Titanium Atoms

The molar mass of titanium (Ti) is approximately 47.87 g/mol. Therefore, the mass of \(6.02 \times 10^{23}\) titanium atoms is 47.87 grams.

Mass of Gold Atoms

The molar mass of gold (Au) is approximately 196.97 g/mol. Hence, the mass of \(6.02 \times 10^{23}\) gold atoms is 196.97 grams.

Mass of Bismuth Atoms

The molar mass of bismuth (Bi) is approximately 208.98 g/mol. Therefore, the mass of \(6.02 \times 10^{23}\) bismuth atoms is 208.98 grams.

Key concepts

Periodic Table

The periodic table is a crucial tool in chemistry, organizing all known elements according to their atomic number, electron configuration, and recurring chemical properties. Each element is placed in a specific position in the table, which allows scientists and students alike to predict and understand patterns in element behavior. For example, elements are arranged in rows called periods and columns known as groups or families.

• Atomic Number: This is the number of protons in the nucleus of an atom of the element. It is also the primary factor in determining the element's position on the table.
• Symbols: Each element is represented by its chemical symbol, usually derived from its English or Latin name.
• Molar Mass: This is indicated for each element, showing the mass in grams of one mole of atoms, a key concept when using Avogadro's number.

By referencing the periodic table, we can easily find the molar mass of any given element, which is essential for solving chemistry problems like the one involving the calculation of the mass of a specific number of atoms.

Molar Mass

Molar mass is an important concept in chemistry that represents the mass of one mole of a given substance. It is expressed in grams per mole (g/mol) and can be found listed on the periodic table for each element.

• Relationship with Avogadro's Number: Because a mole of any element contains Avogadro's number of atoms, the molar mass directly corresponds to the mass of Avogadro's number (or one mole) of atoms of that element.
• Units: Molar mass is always given in units of grams per mole, aligning with the amount of substance indicated by Avogadro's number.
• Utility in Calculations: Knowing the molar mass allows you to easily convert between the mass of a substance and the number of moles, which is particularly useful in chemical equations and reactions.

By using the molar mass, you are able to convert between grams and moles, seamlessly integrating Avogadro's concept into your calculations. This conversion forms the basis for many quantitative aspects of chemistry.

Chemistry Problem Solving

Effective problem solving in chemistry requires an understanding of the various concepts and how they interrelate. In the realm of chemistry exercises, such as determining the mass of a given number of atoms, several steps typically guide the process:

• Identify the Known Values: Begin by identifying and clearly stating the known quantities, such as the number of atoms or the element in question.
• Apply Avogadro's Number: Recognize that Avogadro's number allows you to convert between the number of atoms and moles.
• Utilize the Molar Mass: Use the periodic table to find the molar mass of the element, which helps convert moles to grams.
• Computing the Mass: Multiply the number of moles by the molar mass to determine the mass of the atoms in grams.

Understanding these steps and how they fit together is critical to solving any chemistry problem effectively. By mastering these fundamental principles, you can approach chemical equations and exercises with confidence, ensuring the correct interpretation and solution for each task.