The average concentration of bromine (as bromide) in seawater is \(65 \mathrm{ppm} .\) Calculate (a) the volume of seawater \(\left(d=64.0 \mathrm{lb} / \mathrm{ft}^{3}\right)\) in cubic feet required to produce one kilogram of liquid bromine. (b) the volume of chlorine gas in liters, measured at \(20^{\circ} \mathrm{C}\) and \(762 \mathrm{~mm}\) \(\mathrm{Hg}\), required to react with this volume of sea water.

In chemistry, understanding concentrations is crucial, and parts per million (ppm) is a measure used to express very dilute concentrations of substances. One ppm indicates one part of a solute per one million parts of the solution. Thinking in terms of scale, it's analogous to one minute in two years or one penny in $10,000.

To give context using the bromine extraction from seawater example, if seawater has 65 ppm of bromine, this means there are 65 parts of bromine in every million parts of seawater. For practical reasons, this can also be viewed as 65 grams of bromine in 1 million grams of seawater. When dealing with such small concentrations, ppm makes the math more approachable and comprehensible, especially when converting between units or scaling up for industrial applications.

Stoichiometry is a section of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. It is essentially the arithmetic of chemistry. The term originates from the Greek words for 'element' and 'measure'. Stoichiometry allows chemists to make predictions about the outcomes of reactions, determine the amounts of substances consumed and formed, and ensure the most efficient use of reactants.

Using stoichiometry, chemists can calculate how much seawater is needed to produce a certain amount of bromine. As illustrated in the reaction between bromide ions and chlorine gas, we use molar ratios from the balanced equation to relate the amount of chlorine gas needed to the amount of bromide. This is fundamental in calculating how much chlorine gas is required to react with a given volume of seawater, which was vital in the seawater bromine extraction problem.

The ideal gas law is a crucial equation in physical chemistry and expresses the relationship between pressure (P), volume (V), number of moles (n), temperature (T), and the ideal gas constant (R). Represented as PV = nRT, it describes the behavior of an ideal gas under various conditions but also works well for real gases at low pressure and high temperature.

In the context of extracting bromine from seawater, the ideal gas law is utilized to calculate the volume of chlorine gas required at a specific temperature and pressure. The situation in the problem provided gives us the needed values to plug into the equation, after which we find out that approximately 9.87 liters of chlorine gas at a given temperature and pressure are needed to react with the bromide ions in seawater. This step is pivotal to ensure a precise and efficient reaction, minimizing waste and optimizing production.