For the reaction A(g) + 12 B(g)->2 C(g), a. determine the expression for the rate of the reaction in terms of the change in concentration of each of the reactants and products. b. when C is increasing at a rate of 0.0025 M>s, how fast is B decreasing? How fast is A decreasing?

Understanding the rate of chemical reactions is vital for various fields such as chemistry, engineering, and environmental science. The rate of reaction expression quantifies how fast reactants convert into products over time. For any general reaction, it might appear complex, but it is a representation of the stoichiometry and the dynamics of a chemical process. To express the rate of a reaction, we use the change in concentration of the reactants or products per unit of time.

Taking the exercise's given reaction, where A(g) and B(g) are reactants and C(g) is the product: A(g) + 12 B(g) -> 2 C(g), we understand that for every one molecule of A that reacts, 12 molecules of B will react to produce 2 molecules of C based on stoichiometry. So, if the concentration of C increases, the concentrations of A and B must decrease. The rate expression connects these changes through the stoichiometric coefficients. Generally, it's expressed in moles per liter per second (M/s), reflecting how these concentrations change over time.

Stoichiometry is the study of the quantitative relationships or ratios between reactants and products in chemical reactions. These ratios are derived from the balanced chemical equations, providing insight into the proportions of substances needed or produced. The stoichiometry of a reaction is what allows us to set up the rate expressions that describe the reaction's progress.

For instance, in the provided exercise, the balanced reaction has a stoichiometric ratio of 1:12:2 for A:B:C. These numbers indicate that one molecule of A reacts with 12 molecules of B to form 2 molecules of C. When we look at the rate of the reaction, these ratios become crucial because they dictate the relative rates at which the reactants are consumed and the products are formed. Any change in the amount of one substance directly affects the amounts of the others, as they are all connected through these fixed stoichiometric ratios.

The concentration change rate is crucial to understanding how fast the reactants are being consumed and the products formed during a reaction. It's calculated by measuring the change in concentration of a species over a given time period. Generally, it gives us the speed at which a reactant disappears or a product appears in a solution.

In the context of our reaction, the rate of increase in the concentration of C automatically determines the rates of decrease for A and B. The rate at which B's concentration changes, for example, is 12 times faster than the rate at which C's concentration increases because of the 1:12 stoichiometric ratio. Recognizing this relationship helps scientists and engineers design and control reactions for desired outcomes, such as optimizing product yield or minimizing waste.

The calculation of the reaction rate involves using the concentrations of reactants or products measured over time. By understanding the stoichiometry of a chemical equation, we can relate the rate of disappearance of reactants to the rate of appearance of products. The calculation is not just about plugging numbers into a formula; it requires an understanding of the reaction's stoichiometry to appropriately relate the changes in concentration across all reactants and products.

In our example, once we know that C is increasing at a rate of 0.0025 M/s, the calculation involves using the stoichiometric coefficients to determine the rates of A and B. As shown in the solution, A and B are decreasing at a rate of 0.03 M/s, which comes from multiplying the rate at which C is formed by the respective stoichiometric ratios. Such calculations are essential for predicting how long a reaction will take to reach completion or how much of a product will be formed under specific conditions.