The chemiacl reaction given:
[tex]2A\rightarrow A_2[/tex]We are given that the reaction:
Is second order reaction
Have a rate constant = 0.0265M-1min-1
Initial concentration of A = 2.50 M
time = 180.0 mins
We want the concentration of A after 180.0 minutes.
For the second order reaction, we use the following equation to calculate conentrattion (integrated rate law).
[tex]\frac{1}{\lbrack A\rbrack_t}=\frac{1}{\lbrack A\rbrack_o}+kt[/tex][A]t is the concentration of A at time t
[A]o is the initial concentration (at time = 0)
k is the rate constant for the reaction
Now lets plug in the values.
[tex]\begin{gathered} \frac{1}{\lbrack A\rbrack_t}=\frac{1}{2.50\text{ M}}+0.0265M^{-1}\min ^{-1}\text{ x 180.0 min} \\ \frac{1}{\lbrack A\rbrack_t}=5.17 \\ \lbrack A\rbrack_t=\text{ 0.193 M} \end{gathered}[/tex]