Final answer:
The rates of consumption of reactants and the rates of formation of products in a chemical reaction are related through differential equations, considering the stoichiometry of the balanced chemical equation.
Step-by-step explanation:
The rates at which the reactants are consumed and the products are formed in a chemical reaction can be described by a set of differential equations. These rates can be related to each other through the stoichiometry of the balanced chemical equation. For a general reaction where aA + bB → cC + dD, where A and B are reactants and C and D are products, and a, b, c, and d represent the respective stoichiometric coefficients, the rates can be expressed as:
- Rate of consumption of A = - (1/a) d[A]/dt
- Rate of consumption of B = - (1/b) d[B]/dt
- Rate of formation of C = + (1/c) d[C]/dt
- Rate of formation of D = + (1/d) d[D]/dt
The negative signs indicate that the concentration of the reactants A and B decreases over time, while the positive signs indicate that the concentration of the products C and D increases. It is important to note that the rates of consumption and formation must take into account the stoichiometry to accurately reflect the balanced chemical equation. By using these equations, one can determine the rate at which a reactant is used up or a product is created during a reaction.