Why are some conditionals regarded false even if the antecedent is false? In the Mendelson's logic book, there are 2 conditionals which Mendelson says they are regarded false even if their antecedent is false. One of them is the following:

If this piece of iron is placed in water at time $t$, then the iron will dissolve.

Why is it considered false even if its antecedent is false - that is, the iron is not placed in water at time $t$?
 A: Mendelson is after the fact that the conditionals we use in everyday language are often not at all like material implication ($\to$) in logic.
The example sentence (intuitively) expresses that iron has a certain disposition (click) rather than being a regular implication.
Example: Let "$x$ is lethally poisonous" be defined as "If someone eats $x$, then he will die". Then, surely, you wouldn't agree that everything that noone ever tried to eat is lethally poisonous. So, despite being of If-then-form, the example definition (intuitively) doesn't express a material implication here. Rather, we take the definition to mean that $x$ has a certain property, a disposition to kill us when eaten.
Another example of commonly used conditionals that are entirely unlike $\to$ are of course counterfactual conditionals like "If you hadn't asked this question on math.SE, someone else would have". Because, well, who knows what would have happened?
You can ignore Mendelson's remark for the rest of the book, just be aware that (as often) the colloquial understandings and the mathematical understanding diverge.
The Stanford Encyclopedia of Philosophy also has something on conditionals and their classification, but it's a long read.
A: 

If this piece of iron is placed in water at time t , then the iron will dissolve.

Why is it considered false even if its antecedent is false - that is, the iron is not placed in water at time t ?

Because when we express such a statement in natural language, it is often implicitly a modal logic statement; a claim of the necessity of the implication. 
We can express the statement as: "In all possible worlds, the iron will dissolve whenever it is placed in water at time t, (for a given definition of "possible")"   So, if there are possible worlds where the iron is placed in water at time t, and in any of those worlds the iron does not dissolve, then the given statement is falsified.
If it is not necessary that the iron would have dissolved if we had placed the iron in the water at that time, then the implication is not necessarily true.
