Balanced chemical formulas

An email question:
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I just had some confusion regarding the homework for Chapter 2. I am confused about how to get the ions for the balanced chemical formulas. An example that I got incorrect was: 

The balanced chemical formula for magnesium chlorate contains___magnesium ion(s) and___chlorate ion(s)

I'm not sure how to go about getting the answer for this example. 

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Balancing chemical formulas is a critical skill, but it's also one that many students struggle with until that magic moment when it clicks. Let's see if we can break this question apart a bit...

Many monoatomic ions have charges that can be reasonably predicted based upon where they are on the Periodic Table. Basically, we know from observation that noble gases have very stable numbers of electrons (we'll get deeper into that later in the semester...), so other elements in the Periodic Table tend to lose or gain electrons to get to the same number of electrons as a noble gas. This is especially true when the neutral element has a number of electrons that's pretty close to the number in the noble gas.

Metals:

The alkali metals (lithium, sodium, potassium, etc) almost always lose 1 electron to become +1 in ionic formulas, the alkaline earth metals (beryllium, magnesium, calcium, etc) are almost always +2, aluminum and gallium are almost always +3.

Transition metals and the metals toward the bottom of the B/C/N/O/F columns can have more than one common charge, so those usually have to be specified with a roman numeral; nickel(III) is +3, ruthenium(II) is +2, manganese(V) is +5, etc. The one common exception is zinc, which is (almost) always +2 in ionic compounds.

Non-Metals:

These have similar trends, but now as anions. Halogens (fluorine, chlorine, etc) gain an electron to become -1 charged halides in ionic formulas; chalcogens (oxygen, sulfur, etc) gain 2 electrons to become -2; pnictogens (N, P, As, etc) gain 3 electrons to become -3.

In the context of this specific problem, it's reasonable to assume that the magnesium is Mg⁺².

The other half of this specific problem is a polyatomic ion. There are a number of trends that we could explore in polyatomic ions, but at this point in this course, this is something you should just memorize. Find the list of polyatomic ions in your book, make up some flashcards, and just drill these into your brain. Chlorate is ClO₃^-1.

When writing balanced ionic formulas, the "balance" refers to the balance of charge... nature does not allow random positive or negative charges to be running loose, so for every positive charge in an ionic formula, we must have a corresponding negative charge. Since we have a +2 cation and a -1 anion, we need two anions so the +2 charge of the cation is "balanced" by two negative charges from the anions.

Balance in all things. A yin for every yang.

Working with ammonia

From my perspective, aqueous ammonia is a fascinating reagent to use in the lab. As a type of matter, it is a gas dissolved in a liquid, which seems pretty wild. In many cases, aqueous ammonia is just a fairly typical weak base that's nothing all that special as long as you're using the Bronsted-Lowry definition of a base. Those are great features of aqueous ammonia, but they really pale in comparison to what we see when we start combining aqueous ammonia with metal ions, especially transition metal ions. The key to thinking about aqueous ammonia in these situations is to remember that aqueous ammonia is always involved in a K_b-type equilibrium:

NH₃(aq) + H₂O(l) <=> NH₄⁺¹(aq) + OH^-1(aq)

This means that in any solution of aqueous ammonia, there are both ammonia molecules and hydroxide ions. If we think about the Lewis definitions of acids and bases, this means that floating around in every solution of aqueous ammonia, there are nitrogen-based lone pairs of electrons on ammonia molecules and oxygen-based lone pairs of electrons on hydroxide ions. Different metal ions have different affinities for different types of lone pairs, so sometimes when a metal ion is added to aqueous ammonia it forms complexes with ammonia while other times it forms complexes with hydroxide.
How do we tell which is which? Whenever possible, by comparison with know reactions. If the observed reaction between a metal ion and aqueous ammonia looks identical to the reaction of that same metal ion with a known hydroxide source {like NaOH(aq)}, then the metal ion is probably more attracted to oxygen lone pairs and is reacting with the hydroxide ions in the aqueous ammonia. If, however, the observed reaction between a metal ion and aqueous ammonia is different from the reaction of that same metal ion with NaOH(aq), then the metal ion is probably reacting with the ammonia molecules in the aqueous ammonia solution.
Differential affinities between metal ions (Lewis acids) and different Lewis base donors is a very diverse field and was a driving force in chemistry before newer instrumental methods were developed. It's still an important consideration in chemistry and physics and biology... Biology? That's right! Every biological system that contains metal ions (especially transition metal ions) relies heavily upon differential binding affinities to function correctly. And that's just one of the many reasons why biologist need to understand chemistry...

Qualitative analysis of metal cations

This week in lab, you'll be using the chemical tests you observed last week to separate (and identify) the metal cations in an unknown mixture of cations. It's probably better to think about this as a separation rather than just an identification because you will be given 1 sample and through a series of chemical (or physical) steps you will end up with up to 5 different metals in 5 different container. Some tips:
1. Flow chart - You have to organize your procedure to do well. The logical way to do this is with a flow chart for this type of a problem... a sequence of steps with decision points and branches along the way. You might not be a "flow chart person", but it makes it MUCH easier to follow through on a logical set of tests if you become a bit of a flow chart person for this experiment. Here's an example of a flow chart for separating and identifying anions if you're looking for an example: http://chemlab.truman.edu/chemlab_backup/CHEM131Labs/QualFiles/Figure2.gif
2. Assume you have all 5 metals - OK, there's not much chance that you'll get the sample that has all 5 metals, but you might. Even if you don't, design your flow chart and approach so that it will work for any possible unknown in this experiment.
3. The first step is the key! - Any step in which you are potentially making 2 or more precipitates represents a potential problem because you need to be able to separate those solids from one another. If you can't separate the solids from one another, it's not a useful test. For example, chromate makes a BUNCH of precipitates with the metals we are using, but there's no way (in our list of chemical tests) to separate those solids from one another. Adding chromate would be a horrible first step in your flow chart, but it might be handy later on when you only have to test for the presence of a single metal cation.
4. Positive tests - You need to have a positive confirmation test for all the metals, do not try to infer the presence or absence of a specific metal cation based upon negative results.
5. Chemical equations - If you come to lab prepared with a good plan, the "wet" part of this lab will not take three hours. This is a lab report experiment and as part of your lab report, you will have to write out balanced chemical equations for ALL of the tests you performed in the first week of the experiment. {quit rolling your eyes, it's not that hard and it's good practice!} Take advantage of your time in lab to make sure you understand the chemical equations and ask your instructor and lab assistant for feedback.

Good luck on your unknowns. One final note on your flow chart: this is one of those experiments where there is not a single correct answer. There are probably half a dozen or more variations on the "correct" flow chart that all work well.

Qualitative Analysis of Metal Cations - Week 2

This week in lab you're going to be analyzing an unknown mixture of the metal cations you studied last week.  To do this, you need to look over the tests you did last week and find a way to sequentially use some or all of those tests to separate the cations.  This is NOT a "run all the tests and figure it out later" experiment, you have to have a plan.
To develop your plan, assume you are starting with a mixture of all 5 cations, and you want to separate them into 5 different containers.  The key to developing a good flow chart is the ability to separate solids from each other when multiple things precipitate.  For example, if the first step of your flow chart is "add chromate", you will precipitate all 5 cations as their chromate salts.  You have no way to separate these solids from each other, so this would be a VERY bad first step.  Look over some of the multi-step tests you did last week.  If adding some reagent causes 2 or 3 of the cations to form precipitate, and you have a way to separate those precipitates from each other (with another step in the multi-step test you performed last week), then that might be a good place to start.
As an example, what if you had a mixture of NaCl, NaNO₃, sand, and sawdust.  How could you separate them?  If you added water, the NaCl and NaNO₃ would dissolve, the sand would sink, and the sawdust would float.  That accomplishes some of the separation, but what about the dissolved salts?  If there was a reagent you could add to make chloride ions form a precipitate, like maybe Pb²⁺(aq), you would be able to separate the chloride from the nitrate.
{OK, picky people in the crowd, that doesn't exactly separate "NaCl" from "NaNO₃", but it illustrates the point!}
Given the tests you performed, there are a few different flow charts that will work to separate the 5 cations you're working with, so if you have something that's a little different from someone else, that's OK.  It would be great if you compared your flowchart to someone else's and had a discussion about the similarities and differences, it might lead you BOTH to make better flowcharts/plans.