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Disinfectant and Non-Chlorine Bleach

First, There is not "A non-chlorine bleach" -- there are many.

Second, "chlorine bleach" is not "liquid chlorine". Liquid 
chlorine is the liquid for of the element chlorine which boils at 
about -29F. Do not confuse "chlorine bleach" with "liquid 
chlorine". Chlorine bleach is a solution of sodium hypochlorite, 
and it is the hypochlorite that is the active ingredient.

Third, it depends upon what microbes are the target of the 
disinfection. Some agents work better on some microbes than other 
agents. Note: here I use the term "microbe" as a generic term 
referring to viruses, bacteria, mold, spores, etc. all lumped 
together, even though they are very different. In practice, some 
disinfecting agents may be more effective against some types of 
"microbes", and other agents are more effective against other forms.

There are several readily available substances that are used in place of hypochlorite bleaches.
        Hydrogen peroxide is commonly used as a disinfectant and it 
is very effective against many microbes. Its mechanism is a rather 
complicated decomposition of the hydrogen peroxide into various 
intermediates before ending up as molecular oxygen, which is why it 
foams when you rinse your mouth out with peroxide. Its shortcoming 
is that it tends not to be too stable once the bottle is opened.
       Alcohols: usually ethanol (grain alcohol) or isopropanol 
(rubbing alcohol) are both very effective disinfectants. Their 
shortcoming is flammability and toxicity if ingested.
       There is an entire class of chemical substances with the 
daunting name "quaternary ammonium salts" or "quats" for short. 
There are used in a variety of  hand and body wipes. They are 
relatively non-toxic (to humans), stable (to light and air), and 
effective against a wide range of microbes. They are frequently 
used in combination with an alcohol in hand and body wipes. But 
they are also used in surface cleaners like "Envy" (this is not an 
endorsement, but only used to identify a type of product).
       These are only a few of the substitutes "out there" for 
non-hypochlorite disinfectants. That field is a large area of 
on-going research and development by companies who make those types 
of products.