Answer:
![[SO_2Cl_2]=0.0175M](https://img.qammunity.org/2022/formulas/chemistry/college/zmtjyrxncc2a2cr5ecklxaa96ry3rszzll.png)
Step-by-step explanation:
Hello!
In this case, considering that the decomposition reaction of SO2Cl2 is first-order, we can write the rate law shown below:
![r=-k[SO_2Cl_2]](https://img.qammunity.org/2022/formulas/chemistry/college/9nbtviurezf78wqdwjqpy4ykdggxlbwece.png)
We also consider that the integrated rate law has been already reported as:
![[SO_2Cl_2]=[SO_2Cl_2]_0exp(-kt)](https://img.qammunity.org/2022/formulas/chemistry/college/2wpqw5x47evf5vqrfkhmykn8jlqd65xw8w.png)
Thus, by plugging in the initial concentration, rate constant and elapsed time we obtain:
![[SO_2Cl_2]=0.0225Mexp(-2.90x10^(-4)s^(-1)*865s)](https://img.qammunity.org/2022/formulas/chemistry/college/gf942q9pchncyrsnvmii2khzodv8hgqwkl.png)
![[SO_2Cl_2]=0.0175M](https://img.qammunity.org/2022/formulas/chemistry/college/zmtjyrxncc2a2cr5ecklxaa96ry3rszzll.png)
Best regards!