How many molecules are in each sample? b. 12.1 kg K2CO3

Verified step by step guidance

1. Convert the mass of the sample from kilograms to grams. Since 1 kg = 1000 g, multiply 12.1 kg by 1000 to get the mass in grams.
2. Calculate the molar mass of \( K_2CO_3 \) by adding the atomic masses of all the atoms in the formula: 2 potassium (K), 1 carbon (C), and 3 oxygen (O) atoms.
3. Use the molar mass to convert the mass of \( K_2CO_3 \) from grams to moles by dividing the mass in grams by the molar mass.
4. Use Avogadro's number, \( 6.022 \times 10^{23} \) molecules/mol, to convert the number of moles to the number of molecules by multiplying the number of moles by Avogadro's number.
5. The result from the previous step gives the number of molecules in the 12.1 kg sample of \( K_2CO_3 \).

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 chemical formula. For potassium carbonate (K2CO3), the molar mass can be determined by adding the masses of 2 potassium (K), 1 carbon (C), and 3 oxygen (O) atoms, which is essential for converting grams to moles.

Avogadro's Number

Avogadro's number, approximately 6.022 x 10^23, is the number of particles (atoms, molecules, or ions) in one mole of a substance. This constant allows chemists to relate the mass of a substance to the number of molecules it contains. Understanding Avogadro's number is crucial for converting moles of a substance into the actual number of molecules present in a sample.

Conversion from Mass to Molecules

To find the number of molecules in a given mass of a substance, one must first convert the mass to moles using the molar mass. Once the number of moles is determined, it can be multiplied by Avogadro's number to find the total number of molecules. This conversion process is fundamental in stoichiometry and quantitative chemistry, allowing for the calculation of particle quantities from mass measurements.