What will happen if I put this chemical into my water tank?
The product which you have mentioned in your post may have other chemicals like fragrance etc... which may make the water not suitable for washing dishes.
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You can purchase sodium hypochlorite (bleach) which is sold separately as powder or solution and add to the water tank. The concentration added to water tank is crucial.

You can use unscented / fragrance free laundry bleach solution also. This will be easier to find.
If you get solution (6% solution of bleach in water) then you can add 40mL to the 8000L full tank first time and mix.

Then, say after a week when your tank has 2400 Liters full (using 800L per day ); you can add 28-30mL again and then fill up tank to full (8000L). (Approximate ratio is 1-1.5mL per 200 Liters of water).

Preventing algal growth:


To prevent the growth of algae it is always recommended to prevent light exposure of stored water. Dark colored/black tanks do well. You can cover the manholes/ crevices through which light may enter the tank.
Additionally, warm water aids in algal growth, so you can try to cover the tank with some tarpaulin etc... to prevent heating.
Regular cleaning is important. Algae already growing on the inner wall of the tank is difficult to to deal with. Proper regular cleaning will help to remove such growth.