Refer to a typical Escherichia coli bacterium. This is a cylindrical cell about \(2 \mu\) m long and \(1 \mu\)m in diameter, weighing about \(2 \times 10^{-12}\)g and containing about \(80 \%\) water by volume. Calculate the number of lipid molecules present, assuming their average molecular mass to be 700 u and the lipid content to be \(2 \%\) by mass.

Avogadro's number is a key building block in chemistry, named after Italian scientist Amedeo Avogadro. It specifies the number of constituent particles, usually atoms or molecules, that are contained in one mole of a substance. This constant is approximately equal to \(6.022 \times 10^{23}\) entities per mole.

For instance, if we're discussing the lipid molecules in a bacterial cell, Avogadro's number helps us translate the amount in moles to actual numbers of molecules. With this understanding, students can comprehend how we can quantify the incredibly numerous but tiny constituents that make up matter, such as lipids in biological structures.

Molecular mass, often referred to as molecular weight, is the sum of the mass of all the atoms in a molecule. It is typically expressed in unified atomic mass units (u), with one atomic mass unit roughly equivalent to the mass of a single proton or neutron. Essentially, the molecular mass tells us how ‘heavy’ a molecule is compared to a carbon-12 atom.

Understand that the larger the molecular mass, the heavier the molecule. In biological chemistry, knowing the molecular mass of lipids or other biomolecules is essential since it helps in the calculation of moles, which then facilitates the understanding of quantities involved in biochemical reactions and structures.

The concept of the mole is central to chemistry. It's a unit of measurement that provides a bridge between the atomic world and the macroscopic world we can observe. One mole of any substance contains the same number of entities (atoms, molecules, ions, etc.) as there are atoms in 12 grams of carbon-12, this number is Avogadro's number.

For students learning about mole calculations, the key formula to remember is: \[ \text{Number of moles} = \frac{\text{Mass of substance (g)}}{\text{Molar mass (g/mol)}} \] This formula allows us to convert mass into a count of particles when dealing with substances at the molecular level, quite crucial when calculating specific components like the number of lipid molecules in a bacterium.

Percent by mass (or weight percent) is a concentration measurement that expresses the mass of a compound as a percentage of the total mass of the mixture it's in. It is calculated by the formula: \[ \text{Percent by mass} = \left(\frac{\text{Mass of component}}{\text{Total mass of mixture}} \right) \times 100\% \] In biological chemistry, this helps quantify how much of a particular substance, such as lipids, is contained within a cell relative to the cell's total mass. It's an excellent tool for picturing the composition of biological structures, enabling us to analyze the distribution of various molecules in complex systems like the bacterial cell in our exercise.

Biological chemistry, also known as biochemistry, is the study of chemical processes within and relating to living organisms. It's a discipline that merges the knowledge of biology and chemistry to explore the molecular mechanisms that underlie various biological functions.

Understanding the mass and number of molecules, like lipids in bacteria cells, is fundamental in biochemistry. Lipids are a crucial component of the cell membrane, serving functions related to energy storage, cellular structure, and signaling. Accurate calculation and understanding of their presence in cellular structures enable biochemists to investigate how these molecules affect cell function and overall health. It's a beautiful example of how macroscopic and microscopic worlds intertwine within the sphere of life sciences.