This is an incomplete question, here is a complete question and an image is attached below.
The following diagrams represent mixtures of NO(g) and O₂(g). These two substances react as follows:
![2NO(g)+O_2(g)\rightarrow 2NO_2(g)](https://tex.z-dn.net/?f=2NO%28g%29%2BO_2%28g%29%5Crightarrow%202NO_2%28g%29)
It has been determined experimentally that the rate is second order in NO and first order in O₂.
Based on this fact, which of the following mixtures will have the fastest initial rate?
The mixture (1). The mixture (2). The mixture (3).
Answer : The mixture 1 has the fastest initial rate.
Explanation :
The given chemical reaction is:
![2NO(g)+O_2(g)\rightarrow 2NO_2(g)](https://tex.z-dn.net/?f=2NO%28g%29%2BO_2%28g%29%5Crightarrow%202NO_2%28g%29)
The rate law expression is:
![Rate=k[NO]^2[O_2]](https://tex.z-dn.net/?f=Rate%3Dk%5BNO%5D%5E2%5BO_2%5D)
Now we have to determine the number of molecules of ![NO\text{ and }O_2](https://tex.z-dn.net/?f=NO%5Ctext%7B%20and%20%7DO_2)
In mixture 1 : There are 5
and 4
molecules.
In mixture 2 : There are 7
and 2
molecules.
In mixture 3 : There are 3
and 5
molecules.
Now we have to determine the rate law expression for mixture 1, 2 and 3.
The rate law expression for mixture 1 is:
![Rate=k[NO]^2[O_2]](https://tex.z-dn.net/?f=Rate%3Dk%5BNO%5D%5E2%5BO_2%5D)
![Rate=k(5)^2\times (4)](https://tex.z-dn.net/?f=Rate%3Dk%285%29%5E2%5Ctimes%20%284%29)
![Rate=k(100)](https://tex.z-dn.net/?f=Rate%3Dk%28100%29)
The rate law expression for mixture 2 is:
![Rate=k[NO]^2[O_2]](https://tex.z-dn.net/?f=Rate%3Dk%5BNO%5D%5E2%5BO_2%5D)
![Rate=k(7)^2\times (2)](https://tex.z-dn.net/?f=Rate%3Dk%287%29%5E2%5Ctimes%20%282%29)
![Rate=k(98)](https://tex.z-dn.net/?f=Rate%3Dk%2898%29)
The rate law expression for mixture 3 is:
![Rate=k[NO]^2[O_2]](https://tex.z-dn.net/?f=Rate%3Dk%5BNO%5D%5E2%5BO_2%5D)
![Rate=k(3)^2\times (5)](https://tex.z-dn.net/?f=Rate%3Dk%283%29%5E2%5Ctimes%20%285%29)
![Rate=k(45)](https://tex.z-dn.net/?f=Rate%3Dk%2845%29)
Hence, the mixture 1 has the fastest initial rate.