Final answer:
The rates of consumption and formation in a chemical reaction are determined based on the stoichiometry of the balanced chemical equation and the change in concentration over time. The rate of consumption of reactants and formation of the products can be expressed negatively and positively, respectively. For first-order reactions, the integrated rate law can be expressed using exponentials or logarithms.
Step-by-step explanation:
To relate the rates of consumption of the reactants and the rates of formation of the products in a chemical reaction, we need to consider the stoichiometry of the balanced chemical equation. Consider a general reaction where aA + bB → cC + dD. Here, A and B are reactants, while C and D are products, with their corresponding stoichiometric coefficients a, b, c, and d. The rate of the reaction can be expressed in terms of the change in concentration of reactants or products over time.
The rate expressions are given by:
- Rate = -1/a (d[A]/dt) = -1/b (d[B]/dt)
- Rate = 1/c (d[C]/dt) = 1/d (d[D]/dt)
Where d[X]/dt denotes the rate of change of concentration of substance X with time. The negative signs indicate consumption of reactants, while positive signs indicate formation of products.
The integrated rate law for a first-order reaction can be expressed using exponentials or logarithms. The exponential form relates the concentration of reactant at any time t to its initial concentration:
[A]t = [A]0 * e-kt
Where [A]0 is the initial concentration, [A]t is the concentration at time t, k is the rate constant, and e is the base of the natural logarithm.