CHEMICAL KINETICS
The rate of reaction
2N₂O5->4NO₂+O₂
can be written in three ways
-d[N₂O5]/dt= k[N₂O5]
d[NO₂]/dt= k'[N₂O5]
d[O₂]/dt =k"[N₂O5]
The relationship between k and k' and between k and k" are ?
To understand the relationships between k and k' and between k and k", we need to dive into the concepts of reaction rates and rate laws in chemical kinetics.
In chemical kinetics, the rate of a reaction is expressed as the change in concentration of reactants or products with respect to time. The rate law is an equation that describes how the rate of a reaction depends on the concentrations of the reactants.
In the given reaction, the rate of reaction is expressed in terms of the change in concentration of N₂O₅, NO₂, and O₂ over time, which can be written as:
-d[N₂O₅]/dt = k[N₂O₅]
d[NO₂]/dt = k'[N₂O₅]
d[O₂]/dt = k"[N₂O₅]
Here, k, k', and k" are the rate constants for the respective reactions.
Now, let's analyze the relationships between these rate constants:
1. Relationship between k and k':
By comparing the two rate equations, we can see that the rate of formation of NO₂ is directly proportional to the concentration of N₂O₅ (k' [N₂O₅]), indicating that k' = k.
Therefore, the relationship between k and k' is that they are equal, i.e., k = k'.
2. Relationship between k and k":
By comparing the two rate equations, we can see that the rate of formation of O₂ is directly proportional to the concentration of N₂O₅ (k" [N₂O₅]), indicating that k" = 2k.
Therefore, the relationship between k and k" is that k" is twice the value of k, i.e., k" = 2k.
In summary:
- The relationship between k and k' is that they are equal, k = k'.
- The relationship between k and k" is that k" is twice the value of k, k" = 2k.
The given reaction can be written as:
2N₂O5 -> 4NO₂ + O₂
The rate of reaction can be expressed in three different ways:
1. From the balanced equation, we can see that for every 2 moles of N₂O₅ that react, 4 moles of NO₂ and 1 mole of O₂ are produced. Therefore, the rate of disappearance of N₂O₅ can be written as:
-d[N₂O₅]/dt = k[N₂O₅]
2. Similarly, we can observe that for every 2 moles of N₂O₅ that react, 4 moles of NO₂ are produced. Hence, the rate of formation of NO₂ can be expressed as:
d[NO₂]/dt = k'[N₂O₅]
3. Finally, in the given reaction, for every 2 moles of N₂O₅ that react, only 1 mole of O₂ is produced. Thus, the rate of formation of O₂ can be written as:
d[O₂]/dt = k"[N₂O₅]
Therefore, the relationships between the rate constants are as follows:
k = k'
k = k"