Question

What is the mass in grams of a single atom of each of the following elements: (a) \(\mathrm{Ag},\) (b) \(\mathrm{K}\) ?

Short answer

The mass of one Ag atom is approximately \(1.79 \times 10^{-22}\) g, and one K atom is approximately \(6.49 \times 10^{-23}\) g.

Step-by-step solution

Determine atomic masses

First, look up the atomic mass (molar mass) of each element in the periodic table. Silver (\(\text{Ag}\)) has an atomic mass of approximately 107.87 g/mol, and potassium (\(\text{K}\)) has an atomic mass of approximately 39.10 g/mol.

Use Avogadro's Number

Avogadro's Number, \(6.022 \times 10^{23}\) atoms/mol, tells us the number of atoms in one mole of any substance. We'll use it to convert the molar masses from grams per mole to grams per atom.

Calculate mass of one atom of Ag

To find the mass of one atom of silver, divide its molar mass by Avogadro's Number: \[\text{Mass of one } \text{Ag atom} = \frac{107.87 \text{ g/mol}}{6.022 \times 10^{23} \text{ atoms/mol}}\approx 1.79 \times 10^{-22} \text{ g/atom}\]

Calculate mass of one atom of K

Similarly, determine the mass of one atom of potassium by dividing its molar mass by Avogadro's Number: \[\text{Mass of one } \text{K atom} = \frac{39.10 \text{ g/mol}}{6.022 \times 10^{23} \text{ atoms/mol}}\approx 6.49 \times 10^{-23} \text{ g/atom}\]

Key concepts

Atomic Mass

The atomic mass of an element is a crucial concept in chemistry. It represents the average mass of atoms of an element, typically expressed in atomic mass units (amu). You can usually find it on the periodic table, right below the chemical symbol for each element. The atomic mass accounts for the weighted average of all naturally occurring isotopes of that element.
For example, silver (\(\text{Ag}\)) has an atomic mass of approximately 107.87 amu, which includes its isotopes \(^{107}{\rm{Ag}}\) and \(^{109}{\rm{Ag}}\). Similarly, potassium (\(\text{K}\)) has an atomic mass of about 39.10 amu, accounting for its dominant isotope, \(^{39}{\rm{K}}\).
To relate to daily use, the atomic mass allows scientists to calculate the mass of a single atom when needed. It's fundamental in chemical reactions and stoichiometry to determine how substances will react and in what proportions.

Avogadro's Number

Avogadro's Number, denoted as \(6.022 \times 10^{23}\), is a constant that represents the number of atoms or molecules in one mole of a substance. This number helps bridge the gap between the macroscopic and microscopic worlds.
Think of Avogadro's Number as a kind of cosmic scale, allowing us to "weigh" individual atoms or molecules by providing a relationship between moles and the number of entities involved. For instance, if you want to calculate how much one atom of silver (\(\text{Ag}\)) weighs in grams, you'd use its molar mass and divide by Avogadro's Number, converting from grams per mole to grams per atom.
Without Avogadro's Number, converting between molar quantities and the number of atoms or molecules would be much more challenging.

Molar Mass

Molar mass is another foundational concept in chemistry, and it's particularly vital for converting between moles and grams. It is defined as the mass of one mole of a substance, typically expressed in units of grams per mole (g/mol).
For example, if you look at silver (\(\text{Ag}\)) on the periodic table, you'll see that its molar mass is about 107.87 g/mol. This means that one mole of silver atoms weighs 107.87 grams. Potassium (\(\text{K}\)) has a molar mass of 39.10 g/mol.
Understanding molar mass is essential for tasks such as calculating how many grams of a substance you need for a reaction, figuring out yields, and scaling reactions for laboratory or industrial settings. When performing these calculations, the concept of molar mass allows you to work with bulk quantities that are measurable and practical, as opposed to individual atoms.

Periodic Table

The periodic table is an organized tabular display of all known chemical elements. It arranges elements in order of increasing atomic number—the number of protons in an atom's nucleus—and groups them into columns based on similar chemical properties.
It's essentially the reference guide of chemistry, providing critical information such as atomic masses, electron configurations, and chemical properties. For example, when you want to find out the atomic mass of silver (\(\text{Ag}\)) or potassium (\(\text{K}\)), you can quickly locate these elements in the periodic table and gather this data, which is essential for various chemical calculations.
The periodic table helps scientists predict how elements will react with one another, understand trends in element properties, and explore the synthesis of new compounds. It's a road map for chemists when studying the behavior of matter at the atomic and molecular levels.