The rate constant is numerically the same for three reactions of first ,second and third order resp. Which reaction should be the fastest and is this for all ranges of concentrations ??

Examples would be

first order:
rate1 = k(A)

second order:
rate2 = k(A)^2
third order:
rate3 = k(A)^3

So, do you think rate 1, 2, and 3 will be the same or will they be different.

To determine which reaction should be the fastest among the three reactions of first, second, and third order, we need to consider the rate constant (k) for each reaction.

For a reaction of first order, the rate equation is given by:
rate = k[A]

For a reaction of second order, the rate equation is given by:
rate = k[A]^2

For a reaction of third order, the rate equation is given by:
rate = k[A]^3

Now, let's compare the rate expressions for the three reactions.

First order: rate = k[A]
Second order: rate = k[A]^2
Third order: rate = k[A]^3

From these rate expressions, we can see that the rate constant (k) is numerically the same for all three reactions.

Now, to determine which reaction is the fastest, we need to consider the effect of the concentration ([A]) on the rate of each reaction.

For a first-order reaction: rate ∝ [A]
For a second-order reaction: rate ∝ [A]^2
For a third-order reaction: rate ∝ [A]^3

Based on these relations, we can conclude that the third-order reaction will be the fastest, as the rate increases significantly with increasing concentration ([A]) due to the exponent of three. The first-order and second-order reactions will be slower in comparison.

However, it is important to note that this conclusion is valid for a specific range of concentrations. At very high concentrations, the rate may be limited by other factors such as reactant collisions or other reaction mechanisms. Therefore, the result may not hold true for all ranges of concentrations.