Answer: The coefficients for the given reaction species are 1, 6, 2, 3.
Step-by-step explanation:
The given reaction equation is as follows.
![Cr_(2)O^(2-)_(7) + Cl^(-) \rightarrow Cr^(3+) + Cl_(2)](https://img.qammunity.org/2022/formulas/chemistry/college/v12qjv8nt05jg64fr2uyuk29e82lwiqsh4.png)
Now, the two half-reactions can be written as follows.
Reduction half-reaction:
![Cr_(2)O^(2-)_(7) + 3e^(-) \rightarrow Cr^(3+)](https://img.qammunity.org/2022/formulas/chemistry/college/3belzkezcvezqygnje484u2xs58d5qgbm5.png)
This will be balanced as follows.
... (1)
Oxidation half-reaction:
![Cl^(-) \rightarrow Cl_(2) + 1e^(-)](https://img.qammunity.org/2022/formulas/chemistry/college/5pce88flrweey605uvnb3awuvs2nrc2xxj.png)
This will be balanced as follows.
... (2)
Adding both equation (1) and (2) we will get the resulting equation as follows.
![Cr_(2)O^(2-)_(7) + 14H^(+) + 6Cl^(-) \rightarrow 2Cr^(3+) + 3Cl_(2) + 7H_(2)O](https://img.qammunity.org/2022/formulas/chemistry/college/e66x3qw5wx4sysl9j1tb80m9jpeyrt8stt.png)
Thus, we can conclude that coefficients for the given reaction species are 1, 6, 2, 3.