Question

\(3.011 \times 10^{22}\) atoms of an element weight \(1.15 \mathrm{gm}\). The atomic mass of the element is: (a) 10 (b) \(2.3\) (c) \(35.5\) (d) 23

Short answer

The atomic mass of the element is (b) 23.

Step-by-step solution

Understand the Concept

The relationship between the number of atoms, the weight of these atoms, and the atomic mass can be derived from Avogadro's number. Avogadro's number, which is approximately equal to 6.022 x 10^23, tells us the number of atoms in one mole of an element. The atomic mass of an element, expressed in atomic mass units (amu), is numerically equal to the weight of one mole of the element in grams.

Calculate the Number of Moles

First, calculate the number of moles of the atoms using the given number of atoms and Avogadro's number. The number of moles (n) can be calculated using the formula n = (number of atoms)/(Avogadro's number).

Calculate the Atomic Mass

Then, calculate the atomic mass (M) using the formula M = (weight of the atoms in grams)/(number of moles). This will give you the atomic mass of the element in amu.

Compute the Solution

Using the given values: number of atoms = 3.011 x 10^22 and weight = 1.15 grams, calculate the number of moles and subsequently the atomic mass.

Key concepts

Avogadro's Number

Avogadro's number plays a fundamental role in physical chemistry and is one of the cornerstones of the mole concept. It is defined as the number of constituent particles, usually atoms or molecules, that are contained in one mole of a substance. The numerical value for Avogadro’s number is approximately \(6.022 \times 10^{23}\) particles per mole.

This constant enables chemists to count atoms by weighing, as one mole of any element will have a mass in grams equivalent to its atomic mass. Understanding Avogadro's number is crucial when dealing with substances at the atomic and molecular scale, as it establishes an understandable relation between microscopic particles and macroscopic amounts that can be measured in a laboratory setting.

Atomic Mass Calculation

Calculating atomic mass is essential for converting between the mass of a sample and the number of moles of the substance present. Atomic mass is usually expressed in atomic mass units (amu), which are also known as daltons. One amu is defined as one twelfth of the mass of an atom of carbon-12.

The atomic mass of an element can be calculated if the number of atoms and the mass of these atoms are known. By dividing the mass of the sample by Avogadro's number, you can determine the mass of one atom. This information can be scaled up to the atomic mass, which represents the mass of one mole of atoms (approximately \(6.022 \times 10^{23}\) atoms) of that element, and provides a link between the microscopic world of atoms and the macroscopic world that can be measured.

Mole Concept

The mole is a fundamental concept in chemistry, serving as a bridge between the atomic scale and the practical scale that we can observe and measure. It refers to the amount of substance that contains as many entities (atoms, molecules, ions, or other particles) as there are atoms in 12 grams of carbon-12. The mole allows chemists to count atoms, molecules, and ions in a given sample by weighing it.

To use the mole concept in practical calculations, chemists often relate the mass of a substance to its mole quantity through the substance's molar mass, which is the mass of one mole of the substance and has units of grams per mole (g/mol). Through the mole concept, very large quantities of tiny atoms or molecules are quantified in a manner that can be easily related to measurable quantities of material.