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I had a question like below and I've had trouble with similar problems before and how to go about solving for the chemical formula.

What is the chemical formula for lithium aluminum hydride?

The first thing that comes to mind, we have one lithium, one aluminum and one hydride. Then why is the chemical formula $\ce{LiAlH4}$? Where did the four $\ce{H}$ atoms come from? Earlier on in the course we had stuff like

What is the chemical formula for di-arsenic trioxide?

And that one is easy, I have 2 arsenic and 3 oxygen. Given the full name I can easily deduce the formula (or the other way around). But what do you do in situations where you don't get "all the information". Do I go about thinking up how the structure works and see that it somehow logically follows that it needs to be four $\ce{H}$?

I know most basic compounds, e.g. sulphate is $\ce{SO4^2-}$, but I feel like I can't memorize some of the things. There has to be a more general way to do this. It feels like and I must have missed it. Essentially, the full systematic names are no problem, but the trivial names are giving me a rough time and I'm scared if they come up during my finals next week. Any tips regarding that?

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    $\begingroup$ Well, that's by design. Systematic names were designed so that you could easily derive formula from them; trivial names were not. Then again, what is the formula for lithium hydride? Can you tell that? And now what is the formula for aluminum hydride? $\endgroup$ – Ivan Neretin Apr 13 '18 at 13:20
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No you are absolutely right here, but even sulphate or nitrate is wrong. If you take a closer look at what a sulphate essentially is, you will see the following: It is a separate unit, it has a central atom and ligands and the whole unit is negatively charged. If this was a metal we would say it's a complex and name it with some sort of -ate in the name. And this is exactly what you see here. So tetraoxosulfate in short is sulfate. Whit this shorter notation you are just not able to guess it unless it is so common that you should know about it. For lithium aluminium hydride it's the same thing, it should be called lithium tetrahydroaluminate.

Now you may ask yourself how are you supposed to work with these problems? In all scientific cases just google it. That's what we do as well, if this is class or homework related, then your teacher will only give you certain examples. If he doesn't, talk to him about it.

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In many cases, the number of each element in a compound can be fairly easily inferred by the normal oxidation states of the constituent elements. In the case of lithium aluminum hydride, we have lithium, which is almost always at a $\ce{+1}$ oxidation state ($\ce{Li^+}$). Aluminum is typically $\ce{Al^3+}$. Thus, we need $\ce{4}$ hydrogen atoms at a $\ce{-1}$ oxidation state, $\ce{H^1-}$ (i.e. "hydride"). We get $\ce{LiAlH_4}$.

Similarly, magnesium chloride is $\ce{MgCl_2}$ because it can't be anything else. No need to call it magnesium dichloride. (This also gets into the difference in conventions for ionic compounds versus covalent compounds.)

Of course, in other cases it may not be as obvious. What about iron oxide? Well, that's a bit more ambiguous, it could either be $\ce{FeO}$ or $\ce{Fe_2O_3}$. For that reason you're more likely to see iron(II) oxide for the former or iron(III) oxide. Occasionally you'll still see ferrous oxide and ferric oxide, respectively, but that's becoming less common.

As far as the trivial naming schemes, there is a bit of a learning curve, but it really does make things easier. Calling $\ce{H_2O}$ "dihydrogen monoxide" is only useful for trolling people who get scared at anything that sounds "chemical". It's "water", everyone knows water. Even for your original example, $\ce{LiAlH_4}$, Wikipedia says "the preferred IUPAC name" is Lithium tetrahydridoaluminate(III) and the "systematic IUPAC name" is Lithium alumanuide ($\ce{AlH_4^-}$ is apparently alumanuide, I personally did not know that one)

Full systematic names aren't supposed to be "easier". They are supposed to be completely unambiguous. The problem is that in many compounds, especially in organic chemistry, it's not just the number of each elements that are present, it's how those elements are connected, which can get rather complicated. Consider aluminum sulfate: $\ce{Al_2(SO_4)_3}$. Calling it dialuminum disulfide dodecaoxide loses the information on the individual ionic character, never mind the fact that "disulfide" means something else. Meanwhile, "aluminum sulfate" is clear.

For the most part, it really does come done to a matter of practice and exposure. There are a lot of names that exist with a fair bit of historical inertia (bicarbonate comes to mind), but eventually you get comfortable with it. Of course, Google and Wikipedia can come in handy if you see something new, but you'll find yourself resorting to that less and less.

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There is a useful rule of thumb when looking at trivial names. Look at the ending of the anion part of the name.

If the name ends in "ide" then the compound only includes the elements indicated in the name. For example sodium chloride.

If the name ends in "ite" then the compound includes the elements indicated in the name plus some oxygen. For example sodium chlorite.

If the name ends in "ate" then the compound includes the elements indicated in the name plus plenty of oxygen. For example sodium chlorate.

If the anion name starts with "per" and ends with "ate" then it normally means more oxygen than is found in the "ate" anion. Such as sodium perchlorate.

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