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 ?
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To determine the relationship between k and k' as well as k and k" in the given chemical reaction, we need to apply the rate equation and the stoichiometry of the reaction.
The rate equation for a chemical reaction expresses how the rate of the reaction (in terms of the change in concentration over time) is related to the concentrations of the reactants. In this case, we have three rate equations:
1. d[N₂O5]/dt = k[N₂O5]
2. d[NO₂]/dt = k'[N₂O5]
3. d[O₂]/dt = k"[N₂O5]
Here, k, k', and k" represent the rate constants for the reaction.
To analyze the relationship between k and k', let's focus on equations 1 and 2. We can see that the rate of change of [N₂O5] with respect to time in equation 1 is equal to the rate of change of [NO₂] in equation 2. This suggests that the rate at which N₂O5 is consumed is equal to the rate at which NO₂ is formed.
Similarly, we can consider equations 1 and 3. The rate of change of [N₂O5] in equation 1 is equal to the rate of change of [O₂] in equation 3. This implies that the rate at which N₂O5 is consumed is equal to the rate at which O₂ is formed.
Based on these observations, we can conclude that k = k' and k = k" in the given reaction.
Therefore, the relationship between k and k' and between k and k" is that they are equal to each other, implying that k = k' = k".