Question

Using the average atomic masses for each of the following elements (see the table inside the front cover of this book), calculate the number of atoms present in each of the following samples. a. 40.08 amu of calcium b. 919.5 amu of tungsten c. 549.4 amu of manganese d. 6345 amu of iodine e. 2072 amu of lead

Short answer

The number of atoms in each of the given samples is: a. Calcium: \(6.022 \times 10^{23}\) atoms b. Tungsten: \(3.011 \times 10^{24}\) atoms c. Manganese: \(6.022 \times 10^{24}\) atoms d. Iodine: \(3.011 \times 10^{25}\) atoms e. Lead: \(6.022 \times 10^{24}\) atoms

Step-by-step solution

Find the molar mass of the elements

You can find the molar mass of each element by looking at the average atomic mass given in the periodic table (provided in the front cover of the book). The molar mass is expressed in grams per mole (g/mol) and is equal to the average atomic mass (amu). Calcium (Ca): Molar mass = 40.08 g/mol Tungsten (W): Molar mass = 183.84 g/mol Manganese (Mn): Molar mass = 54.94 g/mol Iodine (I): Molar mass = 126.90 g/mol Lead (Pb): Molar mass = 207.2 g/mol Step 2: Calculate the number of moles of each element

Calculate the number of moles

Divide the mass of the sample (given in amu) by the molar mass (g/mol) of the element. This will give you the number of moles of each element present in the sample. a. Calcium (40.08 amu): Moles of Ca = 40.08 amu / 40.08 g/mol = 1 mol b. Tungsten (919.5 amu): Moles of W = 919.5 amu / 183.84 g/mol = 5 mol c. Manganese (549.4 amu): Moles of Mn = 549.4 amu / 54.94 g/mol = 10 mol d. Iodine (6345 amu): Moles of I = 6345 amu / 126.90 g/mol = 50 mol e. Lead (2072 amu): Moles of Pb = 2072 amu / 207.2 g/mol = 10 mol Step 3: Calculate the number of atoms

Calculate the number of atoms

Use the Avogadro's constant (6.022 x 10^23 atoms/mol) to find the number of atoms in the given number of moles of each element. a. Calcium: Number of atoms = 1 mol × 6.022 x 10^23 atoms/mol = 6.022 x 10^23 atoms b. Tungsten: Number of atoms = 5 mol × 6.022 x 10^23 atoms/mol = 3.011 x 10^24 atoms c. Manganese: Number of atoms = 10 mol × 6.022 x 10^23 atoms/mol = 6.022 x 10^24 atoms d. Iodine: Number of atoms = 50 mol × 6.022 x 10^23 atoms/mol = 3.011 x 10^25 atoms e. Lead: Number of atoms = 10 mol × 6.022 x 10^23 atoms/mol = 6.022 x 10^24 atoms Therefore, the number of atoms in each of the given samples is: a. Calcium: 6.022 x 10^23 atoms b. Tungsten: 3.011 x 10^24 atoms c. Manganese: 6.022 x 10^24 atoms d. Iodine: 3.011 x 10^25 atoms e. Lead: 6.022 x 10^24 atoms

Key concepts

Molar Mass

Molar mass is a fundamental concept in chemistry, acting as a key conversion factor in chemical equations and reactions. It is the mass of one mole of any substance, whether it be an element or a compound. We express molar mass in grams per mole (g/mol). The periodic table provides the average atomic mass, and for elements, this value is numerically equal to the molar mass. For example, if the average atomic mass of calcium is 40.08 atomic mass units (amu), the molar mass is 40.08 g/mol. This shows us that 1 mole of calcium atoms weighs exactly 40.08 grams.
Understanding molar mass is crucial for converting between mass, number of moles, and even the number of atoms or molecules of a substance, making it a valuable tool in both theoretical and practical chemistry.

Avogadro's Constant

Avogadro's constant is a defining feature of a mole in chemistry. Its value is approximately \(6.022 \times 10^{23}\), representing the number of atoms, molecules, or particles in one mole of a substance. This constant allows chemists to convert between the number of particles and the amount in moles, facilitating calculations in chemical reactions and solutions.

• Example: If we have 1 mole of calcium, we have \(6.022 \times 10^{23}\) calcium atoms.
• For 5 moles of tungsten, we multiply 5 by Avogadro's constant, ending with \(3.011 \times 10^{24}\) atoms of tungsten.

Avogadro's constant bridges the microscopic world of atoms and the macroscopic world of grams and liters, making it a cornerstone of chemical calculations.

Number of Moles

The number of moles is a core concept in stoichiometry, providing a link between the mass of a substance and the number of particles it contains. You can calculate the number of moles by dividing the mass of the sample by the molar mass of the element or compound. This means

• \(\text{Moles} = \frac{\text{Mass (g)}}{\text{Molar Mass (g/mol)}}\)

In the given exercise, we're using atomic mass units (amu) directly related to the molar mass. For instance, 549.4 amu of manganese translates directly to 10 moles because 549.4 amu divided by a molar mass of 54.94 g/mol equals 10 moles.
Understanding the concept of moles is essential for accurately predicting how much reactant is needed or product is formed in a chemical reaction.

Periodic Table

The periodic table is an essential tool in chemistry, systematically organizing elements by their atomic number, electron configuration, and recurring chemical properties. It provides a wealth of information at a glance:

• Atomic number indicates the number of protons in an atom.
• Average atomic mass helps determine molar mass.
• Groups and periods reflect elements with similar chemical behaviors.

Using the periodic table, you can quickly find molar masses, like that of tungsten (183.84 g/mol). This thorough organization aids chemists in making predictions about element behavior during reactions and assists with calculations involving atomic mass and molar mass. The systematic arrangement ensures chemists worldwide utilize a consistent reference, making it an indispensable resource in all branches of chemistry.