One molecule of an unknown compound is found to have a mass of \(3.27 \times 10^{-22} \mathrm{~g}\). What is the molar mass of this compound?

Avogadro's number is a fundamental constant in chemistry and is essential for understanding the relationship between individual molecules and moles of a substance. It is denoted as \(N_A\) and its value is \6.022 \times 10^{23}\ particles/mol. This constant allows us to convert between the number of atoms or molecules in a single sample and the macroscopic quantities we handle in the lab. For example, since one mole of any substance contains Avogadro's number of molecules, if we know the mass of a single molecule, we can calculate the molar mass by multiplying the mass of one molecule by Avogadro's number. This provides a bridge between the microscopic world of individual atoms and molecules and the macroscopic quantities used in chemical calculations.

Mass conversion is a crucial step in chemistry when dealing with different units or scales. In this context, we are converting the mass of a single molecule to the mass of an entire mole of molecules. This is done by multiplying the mass of one molecule by Avogadro's number. For example, given the mass of one molecule \(3.27 \times 10^{-22} \mathrm{g}\) and Avogadro's number \6.022 \times 10^{23}\, we perform the multiplication:

\[ \text{Molar Mass (g/mol)} = 3.27 \times 10^{-22} \text{ g/molecule} \times 6.022 \times 10^{23} \text{ molecules/mol} \]. This step is critical as it translates molecular-scale measurement into a more practical macroscopic scale used in the laboratory.

When performing calculations, it's important to consider significant figures. Significant figures indicate the precision of a measurement. In our example, we initially have three significant figures (3.27). Upon calculating the molar mass, we maintain this precision: \( 3.27 \times 6.022 \times 10 = 19.7 \ g/mol\). By rounding to three significant figures, which matches the precision of our least precise measurement, we ensure our answer is as accurate as the initial data allows. Always round your final answer according to the number of significant figures in the initial data to maintain consistency and accuracy in scientific communication. This concept ensures reliability and standardization across scientific calculations and reporting.