Calculate the mass, in kg, of each sample. a. 7.55×10²⁶ cadmium atoms b. 8.15×10²⁷ nickel atoms c. 1.22×10²⁷ manganese atoms d. 5.48×10²⁹ lithium atoms

Verified step by step guidance

1. 1. To calculate the mass of a sample, we first need to know the number of moles. We can find this by using Avogadro's number, which is approximately $6.022 * 10^{23}$ atoms per mole. So, divide the given number of atoms by Avogadro's number to find the number of moles.
2. 2. For example, for cadmium atoms, the calculation would be $7.55 * 10^{26}$ atoms divided by $6.022 * 10^{23}$ atoms/mole.
3. 3. Once we have the number of moles, we can find the mass by multiplying the number of moles by the molar mass of the element. The molar mass of an element can be found on the periodic table. For cadmium, the molar mass is approximately 112.41 g/mole.
4. 4. So, for cadmium, multiply the number of moles calculated in step 2 by 112.41 g/mole. This will give you the mass in grams.
5. 5. To convert the mass from grams to kilograms, divide by 1000 since there are 1000 grams in a kilogram. Repeat these steps for each of the other elements, using the appropriate molar mass for each.

Key Concepts

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). It is calculated by summing the atomic masses of all the atoms in a molecule. For example, the molar mass of cadmium (Cd) is approximately 112.41 g/mol, which is essential for converting between the number of atoms and mass.

Avogadro's Number

Avogadro's number, approximately 6.022 x 10²³, is the number of atoms, ions, or molecules in one mole of a substance. This constant allows chemists to relate the macroscopic scale of substances to the microscopic scale of individual particles, enabling calculations involving the number of atoms in a sample.

Unit Conversion

Unit conversion is the process of converting a quantity expressed in one set of units to another. In this context, it involves converting the number of atoms to moles using Avogadro's number and then to mass using the molar mass. Understanding how to perform these conversions is crucial for accurately calculating the mass of the samples in kilograms.