Calculate these masses. (a) What is the mass of \(4.00 \mathrm{cm}^{3}\) of sodium, density \(=0.97 \mathrm{g} / \mathrm{cm}^{3} ?\) (b) What is the mass of 125 mL gaseous chlorine, density \(=3.16\) g/L?

Understanding the relationship between mass and density is foundational in chemistry. Density is defined as the mass per unit volume of a substance, which is typically expressed in grams per cubic centimeter (\text{g/cm}^3) for solids and liquids, and grams per liter (\text{g/L}) for gases.

To calculate the mass when you know the density, you use the formula: \( \text{Mass} = \text{Density} \times \text{Volume} \). It's crucial to ensure that the units for volume and density match when applying this formula.

For instance, if an exercise asks you to calculate the mass of a block of sodium with a known volume and density, you can directly apply the formula. Suppose the density is given as \(0.97 \text{g/cm}^3\) and the volume is given as \(4.00 \text{cm}^3\), then simply multiply the two to obtain the mass in grams.

In chemistry, having consistent units across all measurements is essential. Volume conversion is a common task when dealing with exercises that involve substances in different states or measurements in various unit systems. For example, liquid volumes might be measured in milliliters (mL) but gas volumes in liters (L).

To convert from milliliters to liters, remember that \(1 \text{L} = 1000 \text{mL}\). If a problem provides a volume in milliliters and the density in grams per liter, you need to convert the volume to liters before using the mass and density formula.

For example, if you're given the volume of gaseous chlorine as \(125 \text{mL}\), to find its mass using the density \(3.16 \text{g/L}\), you must first convert \(125 \text{mL}\) to liters by dividing by 1000, resulting in \(0.125 \text{L}\).

Stoichiometry is a section of chemistry that involves calculating the quantities of reactants and products in chemical reactions. It's based on the conservation of mass and the concept of moles. In stoichiometry, the molar mass - the mass of one mole of a substance - serves as a bridge between the mass of a substance and the amount of particles or moles present.

Molar mass is expressed in grams per mole (\text{g/mol}), and it allows chemists to convert between mass and moles of a substance using Avogadro's number \(6.022 \times 10^{23}\), which is the number of particles in one mole. Although stoichiometry doesn't directly come into play in simple mass calculations like those for sodium and chlorine presented in the exercise, it becomes critical when dealing with more complex problems involving chemical reactions and formula units.