Question

Which element, \(\mathrm{Cu}, \mathrm{P}, \mathrm{Ag}\), or \(\mathrm{B}\), contains the least moles of atoms in a \(5.0-\mathrm{g}\) sample?

Short answer

In a \(5.0-\mathrm{g}\) sample, silver (Ag) contains the least moles of atoms.

Step-by-step solution

Determine Atomic Masses

Refer to the periodic table so as to determine the atomic masses of each of the elements. The atomic masses (in grams per mole) are approximately 63.5 for Cu (copper), 30.974 for P (phosphorus), 107.87 for Ag (silver), and 10.81 for B (boron).

Calculate Number of Moles

Apply the formula for calculating the number of moles (moles = mass / atomic mass) for each element. For Cu, \(moles = 5.0g / 63.5g/mol ≈ 0.079 moles\). For P, \(moles = 5.0g / 30.974g/mol ≈ 0.161 moles\). For Ag, \(moles = 5.0g / 107.87g/mol ≈ 0.046 moles\). And for B, \(moles = 5.0g / 10.81g/mol ≈ 0.462 moles\).

Compare Number of Moles

Compare the number of moles calculated for each element. The element with the lowest number of moles in a 5.0g sample is the one which has the highest atomic mass. In this case, it's Ag (silver) with approximately 0.046 moles.

Key concepts

Understanding Moles

The concept of moles is fundamental in chemistry for quantifying substances. A mole is a unit that measures the amount of substance. It is based on Avogadro's number, which is approximately 6.022 x 10²³ entities. When we say one mole of atoms, we are referring to 6.022 x 10²³ atoms. This concept helps chemists express amounts of a substance in a scientific and manageable way.

To find the number of moles in a given sample, you use the formula:

• Moles = Mass (in grams) / Atomic Mass (in grams per mole)

This equation allows you to determine how many moles of an element are present in a specific mass of that element. For example, if we have a 5.0 g sample of phosphorus with an atomic mass of approximately 30.974 g/mol, the number of moles is calculated as:

• Moles = 5.0 g / 30.974 g/mol ≈ 0.161 moles

This calculation shows the versatility of using moles to work with various amounts of substances in a chemical context.

The Power of the Periodic Table

The periodic table is an essential tool for anyone studying chemistry. It organizes all the known chemical elements based on their atomic number, electron configurations, and recurring chemical properties. The table is structured to show elements in increasing atomic number from left to right and top to bottom. This organization provides valuable insights into the properties of elements.

The atomic mass of an element, found on the periodic table, is crucial for calculating moles. The atomic mass is a weighted average of all the isotopes of an element, measured in grams per mole. For example, copper (Cu) has an atomic mass of approximately 63.5 g/mol, while boron (B) is much lighter at 10.81 g/mol.

Knowing the atomic mass allows you to convert a measured mass into moles by providing the bridge between the macroscopic scale (grams) and the molecular scale (atoms/molecules via moles). This connection is vital for interpreting chemical reactions and stoichiometry.

Atoms - Building Blocks of Matter

Atoms are the smallest units of matter that retain all the chemical properties of an element. Each atom consists of a nucleus made of protons and neutrons, surrounded by a cloud of electrons. Although atoms are incredibly small, they form the foundation for all the matter we see around us.

In any chemical element, the number of protons defines what the element is, while the number of electrons influences how it interacts with other atoms. Elements like copper (Cu) and silver (Ag) have different numbers of protons and electrons, giving them unique properties and uses.

When comparing how many atoms are in a sample, the concept of moles becomes invaluable. A larger atomic mass means fewer atoms per gram, as seen with silver having fewer moles in our example due to its higher atomic mass. This illustrates how understanding atoms and their relationships in compounds is essential for the study of chemistry and helps elucidate the behavior of substances on a molecular level.