Question

Describe the steps used to convert the mass of an element to the number of atoms of the element

Short answer

To convert the mass of an element to the number of atoms, follow these steps: 1. Calculate the number of moles by dividing the given mass (in grams) by the molar mass of the element (in grams per mole): Number of moles = \(\frac{mass (g)}{molar\ mass (g/mol)}\). 2. Find the number of atoms by multiplying the number of moles by Avogadro's number, which is approximately \(6.022 \times 10^{23}\) particles per mole: Number of atoms = Number of moles × Avogadro's number. 3. Present the final answer with appropriate notation or significant figures, depending on the given values.

Step-by-step solution

Find the Number of Moles from the Mass and Molar Mass

: First, you will need to find the number of moles in the given mass of the element. To do this, you will need the mass of the element (in grams) and the molar mass of the element (in grams per mole). The molar mass can be found on a periodic table or any reference resource that provides this information. To find the number of moles, use the formula: Number of moles = \(\frac{mass (g)}{molar\ mass (g/mol)}\)

Calculate the Number of Atoms using Avogadro's Number

: Once you have the number of moles for the given mass, you can calculate the number of atoms using Avogadro's number. The formula to find the number of atoms is: Number of atoms = Number of moles × Avogadro's number Avogadro's number is approximately \(6.022 \times 10^{23}\) particles per mole.

Write the Final Answer

: After calculating the number of atoms, you will have your final result. Present the number of atoms with the appropriate notation or significant figures, depending on the values given in the exercise. By following these steps, you will be able to convert the mass of an element to the number of atoms of the element.

Key concepts

Mole Concept

The mole concept is a fundamental principle of chemistry that allows us to count particles at the atomic and molecular scale. A mole is defined as the amount of substance that contains as many elementary entities (like atoms, molecules, ions, or electrons) as there are atoms in exactly 12 grams of carbon-12. This is about \(6.022 \times 10^{23}\) entities and is known as Avogadro's number. Understanding the mole concept is crucial because it bridges the gap between the microscopic world of atoms and the macroscopic world we can measure and observe.

To put it simply, just as a 'dozen' refers to '12' of something, a 'mole' refers to approximately \(6.022 \times 10^{23}\) of something at the atomic scale. Using the mole concept allows chemists to calculate the number of atoms, molecules, or ions in a given mass of a substance by converting mass to moles and then to particles using Avogadro's number, making it an essential skill in chemical calculations.

Avogadro's Number

Avogadro's number is a constant that represents the number of particles found in one mole of a substance and is a key component in the mole concept. It is named after the Italian scientist Amedeo Avogadro, who proposed this concept in the early 19th century. The value of Avogadro's number is approximately \(6.022 \times 10^{23}\) particles per mole. It serves as a conversion factor between the number of moles and the number of particles.

For example, if we have 1 mole of hydrogen atoms, we actually have \(6.022 \times 10^{23}\) hydrogen atoms. This number is so large because atoms and molecules are incredibly small entities. Avogadro's number is essential for translating the microscopic world into quantities that are meaningful and workable for scientists and enables essential calculations in chemistry.

Molar Mass

Molar mass is the mass of one mole of a given substance and is expressed in grams per mole (g/mol). It is a vital link between the mass of a substance and the number of moles, and therefore, the number of particles (atoms, molecules, or ions) in a sample. The molar mass is typically found on the periodic table as the atomic weight for elements and can be calculated for compounds by adding up the atomic weights of each element within it.

To better understand molar mass, think of it as the weight of a mole of pennies compared to a mole of feathers; while both quantities would be enormous, the pennies would have a much higher molar mass than the feathers due to their weight. Knowing the molar mass of a substance is essential when converting between mass and moles in chemical calculations.

Chemical Calculations

Chemical calculations are the methods used to quantify substances and reactions in chemistry. These calculations often involve converting between mass, moles, and the number of particles using the concepts of molar mass and Avogadro's number. These calculations can determine the masses of reactants and products in a chemical reaction, the concentration of solutions, and yield of products, among other things.

To effectively perform chemical calculations, one must be comfortable with math concepts such as ratios, proportions, and algebraic manipulation. The ability to convert between units and scale up from microscopic to macroscopic quantities is what makes chemical calculations powerful tools in both industrial applications and scientific research.