Final answer:
In chemistry, the differential dw in terms of the rates of consumption of reactants and rates of formation of products is expressed using rates of change in concentrations over time, scaled by the coefficients in the balanced chemical equation.
Step-by-step explanation:
The differential dw is related to the differentials of the independent variables in the context of a physical or chemical system undergoing a change. In the case of a chemical reaction, we can write equations that express the reaction rates as the rates of change in the concentrations of the reactants and products over time. Consider a general chemical reaction:
A + B → C + D
To write an expression for the reaction rate, we would use the formula:
Rate of reaction = -Change in concentration of A / Change in time = -(d[A] / dt)
The negative sign indicates consumption of reactants. Similarly, for the products, the expression would be:
Rate of formation of C = Change in concentration of C / Change in time = (d[C] / dt)
It's important to consider the stoichiometry of the reaction when writing these equations. For example, if the reaction were 2A + B → 3C + D, the rates of consumption and formation would be scaled by the coefficients:
Rate of consumption of A = -1/2 (d[A] / dt)
Rate of formation of C = 1/3 (d[C] / dt)
These equations are central to the study of reaction kinetics in chemistry.