The Rate of Disappearance in the Reaction: A + 2B = 3C + 2D
The equation A + 2B = 3C + 2D represents a chemical reaction where one mole of reactant A reacts with two moles of reactant B to produce three moles of product C and two moles of product D. Understanding the rate of disappearance of reactants and the rate of appearance of products is crucial in studying chemical kinetics.
Rate of Disappearance of Reactants
The rate of disappearance of a reactant is the change in its concentration over time. For this reaction, the rate of disappearance of A is given by:
-d[A]/dt
Where:
- [A] represents the concentration of A
- t represents time
- d[A]/dt represents the change in concentration of A with respect to time
Similarly, the rate of disappearance of B is given by:
-d[B]/dt
Since B is consumed twice as fast as A (based on the stoichiometric coefficients), the rate of disappearance of B is twice the rate of disappearance of A:
-d[B]/dt = 2 * (-d[A]/dt)
Rate of Appearance of Products
The rate of appearance of a product is the change in its concentration over time. For this reaction, the rate of appearance of C is given by:
d[C]/dt
And the rate of appearance of D is given by:
d[D]/dt
The rates of appearance of products are related to the rate of disappearance of reactants through the stoichiometry of the reaction. In this case:
- d[C]/dt = 3 * (-d[A]/dt)
- d[D]/dt = 2 * (-d[A]/dt)
Important Points to Remember
- The rates of disappearance and appearance are always positive values. The negative sign in front of the rate of disappearance indicates a decrease in concentration over time.
- The rate of disappearance of reactants and the rate of appearance of products are proportional to each other and are determined by the stoichiometric coefficients in the balanced chemical equation.
- The rate of reaction can be expressed in terms of any reactant or product. However, it is important to use the correct stoichiometric coefficient when comparing rates.
Conclusion
The rate of disappearance of reactants and the rate of appearance of products in a chemical reaction are crucial concepts in chemical kinetics. Understanding these rates helps us study the reaction mechanism, determine the rate law, and calculate the activation energy of the reaction.
