Question

Which has more atoms, 10.0 g of C or 10.0 g of Ca? How many atoms does each have?

Short answer

10.0 g of C has more atoms than 10.0 g of Ca. There are \(5.01 \times 10^{23}\) atoms in 10.0 g of C, while there are \(1.50 \times 10^{23}\) atoms in 10.0 g of Ca.

Step-by-step solution

Find the molar masses of C and Ca

The molar masses for C and Ca can be found on the periodic table: Molar mass of C = 12.01 g/mol Molar mass of Ca = 40.08 g/mol

Calculate moles of C and Ca

Using the molar masses, we will now calculate the moles of each element. For C: No. of moles, n = mass / molar mass n(C) = \( \frac{10.0 \,g}{12.01 \,g/mol} \) = 0.8326 mol For Ca: No. of moles, n = mass / molar mass n(Ca) = \( \frac{10.0 \, g}{40.08 \,g/mol} \) = 0.2495 mol

Calculate the number of atoms using Avogadro's number

Avogadro's number (N) = \(6.022 \times 10^{23}\) atoms/mol For C: No. of atoms = No. of moles × Avogadro's number Atoms of C = \(0.8326 \, mol \times 6.022 \times 10^{23} \, atoms/mol\) = \(5.01 \times 10^{23}\) atoms For Ca: No. of atoms = No. of moles × Avogadro's number Atoms of Ca = \(0.2495 \, mol \times 6.022 \times 10^{23} \, atoms/mol\) = \(1.50 \times 10^{23}\) atoms

Compare the number of atoms and determine the element with more atoms.

Atoms of C = \(5.01 \times 10^{23}\) atoms Atoms of Ca = \(1.50 \times 10^{23}\) atoms Since \(5.01 \times 10^{23}\) atoms (C) is greater than \(1.50 \times 10^{23}\) atoms (Ca), there are more atoms in 10.0 g of C than in 10.0 g of Ca.

Key concepts

Molar Mass

Molar mass is a fundamental concept in chemistry that refers to the mass of one mole of a given substance. This is usually expressed in grams per mole (g/mol). Every element has a unique molar mass, which can be found on the periodic table. For example, the molar mass of carbon (C) is 12.01 g/mol, while calcium (Ca) has a molar mass of 40.08 g/mol.
Understanding molar mass is essential for converting between the mass of a substance and the amount of substance in moles. This conversion is crucial because many chemical calculations require you to use moles as the standard unit of measuring substance amount. To find the moles from a given mass, you can use the formula:
\[\text{moles} = \frac{\text{mass (in grams)}}{\text{molar mass (g/mol)}}\]This relationship is pivotal in solving chemical exercises, such as determining how many atoms are in a given mass as seen in our example with C and Ca.

Avogadro's Number

Avogadro's number is a fundamental constant in chemistry that allows scientists to connect the macroscopic world with the microscopic atomic world. Defined as approximately \(6.022 \times 10^{23}\) atoms or molecules per mole, Avogadro's number is the key to converting between moles and atoms or molecules.
This figure is named after the Italian scientist Amedeo Avogadro, who first proposed that the volume of a gas (at a given temperature and pressure) is directly proportional to the number of atoms or molecules, regardless of their type.
To calculate the number of atoms from moles, simply multiply the number of moles by Avogadro's number:

• \[\text{Number of atoms} = \text{moles} \times \left(6.022 \times 10^{23} \text{ atoms/mol} \right)\]

Through this conversion, you can quickly determine the vast number of atoms in even a small sample of material, bridging everyday quantities with the invisible atomic scale.

Moles to Atoms Conversion

The conversion from moles to atoms is a common and essential calculation in chemistry. It is the process of determining the total number of atoms in a given sample of a substance, which is often needed to solve practical problems in chemistry.
Consider a typical exercise: you have a certain mass of an element and wish to find out how many atoms it contains. The process involves two main steps:

• First, determine the number of moles from the given mass using the element's molar mass. This involves dividing the mass by the molar mass.
• Second, convert the moles to atoms using Avogadro's number.

By combining these steps, we can handle real-world chemical quantities and translate them into atomic-scale data. For example, in the problem with carbon and calcium, these steps allow us to find more atoms in the same mass of carbon compared to calcium, illustrating differences in molar mass and atomic compositions.