Answer:
13. t = 1183 min and 0.50 M.
14.
![t_(1/2)=2.67x10^(-8)hr](https://img.qammunity.org/2022/formulas/chemistry/college/lg0yk25jj77dd7s8dv5mosi8vpc33eatx3.png)
Step-by-step explanation:
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13. In this case, according to the units, we infer this is a second-order reaction which has the following integrated rate law:
![(1)/([A]) =(1)/([A]_0) +kt](https://img.qammunity.org/2022/formulas/chemistry/college/3hy5v6y559513rfsaybpbyvcsskxoixdbb.png)
Which can be solved for the time as shown below:
![t=( (1)/([A])-(1)/([A]_0))/(k)](https://img.qammunity.org/2022/formulas/chemistry/college/87855pzt3ec7jh40wv1g23jx8ypxoaf0h1.png)
Thus, we plug in the given concentrations and rate constant to obtain:
![t=( (1)/(0.250M)-(1)/(0.850M))/(0.002387M^(-1)min^(-1))\\\\t= 1183min](https://img.qammunity.org/2022/formulas/chemistry/college/zlpl1ridif09vzbdubaqjfvia9s20tzgd4.png)
For the second part, we proceed by using the same rate constant and the new initial concentration as follows:
![(1)/([A]) =(1)/([A]_0) +kt\\\\(1)/([A]) =(1)/(0.750M) +0.680M^(-1)min^(-1)*0.996min\\\\(1)/([A]) =1.99,M](https://img.qammunity.org/2022/formulas/chemistry/college/97bxie3anmf7pa6igvii04ze03x30ddmeq.png)
![[A]=0.50M](https://img.qammunity.org/2022/formulas/chemistry/college/s0sk3j8irifpbgcu4fosvej4yuzl9gm88w.png)
14. In this case, according to the units of the rate constant, we infer this is a zeroth-order reaction, therefore we compute the half-life has shown below:
![t_(1/2)=([A]_0)/(2k)](https://img.qammunity.org/2022/formulas/chemistry/college/qf7rvybb2ruwosnn65ozl45h327bec54k2.png)
Thus, we plug in to obtain:
![t_(1/2)=(2.696x10^(-6)M)/(2*50.5M*hr^(-1))](https://img.qammunity.org/2022/formulas/chemistry/college/mg2cslal017jfpf7nxqbk4mlmc7ny94192.png)
![t_(1/2)=2.67x10^(-8)hr](https://img.qammunity.org/2022/formulas/chemistry/college/lg0yk25jj77dd7s8dv5mosi8vpc33eatx3.png)
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