AP Chemistry Acid-Base Reactions

Welcome back to Educator.com; welcome back to AP Chemistry.0000

In our last lesson, we talked about precipitation reactions, which is when you mix soluble salts, one solution with another.0004

Some combinations of cation and anion might actually be insoluble, so they bind together and they drop to the bottom like a stone, as a solid.0012

Well, today, we're going to be talking about the second class of really, really important reactions in chemistry, acid-base reactions.0021

This particular topic, acid-base reactions, and the next one, oxidation-reduction, really constitute the heart and soul of the most important chemistry that you're going to be working on in your career.0030

So, if nothing else, do your best to understand acids and bases really well, and oxidation-reduction really well, and I promise it will pay handsome dividends as you go on in your career, whether it's in biology or chemistry or even in physics, believe it or not.0041

Let's go ahead and get started.0057

Let's define what we mean by an acid.0061

Now, I have to warn you: if some of what we discuss today is not altogether clear, don't worry about it; acid-base chemistry is something that we will revisit again in great detail when we discuss the mathematics of acid-base chemistry--when we quantify some of what we discuss more qualitatively today.0064

So, again, as we do more and more problems, this whole acid-base, oxidation-reduction theme will come up over and over and over again, and as we do the problems, we will be discussing theory.0083

That is what I tend to do: as I'm doing the problems, I will go over theory; so don't feel bad if you don't immediately understand what is happening.0094

Let's define an acid--very, very simple: an acid is a compound that ionizes to form a hydrogen ion.0101

Ionizes--you can also substitute the word dissociates.0125

You can think of an acid--you remember when we were naming acids; we did it a little differently than the ionic compounds--well, hydrogen is in the first column of the periodic table, on the left; right below it, you have the lithium, potassium, and things like that.0130

Well, even though hydrogen is not a metal, in many ways, it actually behaves like a metal.0143

So, if I have something like HCl, even though we named it as an acid, it's not inappropriate to call it hydrogen chloride, which is exactly what it is when we make it in the lab.0149

It only turns into an acid when we drop it in water.0158

When we drop it in water, that is when it dissociates, and it gives up its hydrogen ion; it's soluble, like anything else.0161

But, because it's so important, we have just given it a different name; but the chemistry is actually the same--you drop something like lithium chloride in water; lithium and chloride break apart; well, you drop something like hydrogen chloride in water--the hydrogen and the chloride break apart.0169

What makes it different is that, where lithium doesn't react with anything, and chloride doesn't react with anything, hydrogen--very, very reactive.0185

Probably the most important single thing in chemistry is that hydrogen ion.0193

So, that's it; it's just a compound that ionizes, that dissociates to form a hydrogen ion, as one of its free ions.0198

Another way of looking at it, if you want to, is a compound that actually has a hydrogen to give up.0206

More often than not, it will give it up when it's actually involved in some chemistry.0215

A compound that has H⁺ to give up--that's all; there is nothing mysterious about it.0219

And, when we talk about an acid, we're talking about the hydrogen ion.0229

That is what an acid is; that is the most important part of the acid.0232

Let's see what we're looking at.0235

If we had hydrogen chloride, and we drop it in some water, well, the hydrogen and the chloride come apart, like ionic compounds tend to.0237

You have H⁺ floating around, and you have Cl^- floating around.0246

You're welcome to put _(aq) if you want; it just means that they are floating around in solution.0250

This is dissociation; this is the acid part--this is what does the damage, if you were to put your hand in some acid--this H⁺, not the Cl^-.0256

OK, this is called a monoprotic acid, and as you know, if you take hydrogen (it has one proton and one electron), well, you rip off that electron, and now you have a hydrogen ion; it's the same as a proton.0267

You might have energy levels there that electrons can occupy, but essentially, it's just a free proton--that's all it is.0280

That is why a hydrogen ion is also referred to as a proton; monoprotic means an acid that only has one proton to give up--one hydrogen ion to give up; monoprotic.0289

Let's do an example of a polyprotic acid.0299

The most popular: sulfuric acid, H₂SO₄.0301

When that one dissociates--it is also a strong electrolyte--it doesn't give up both hydrogens simultaneously; acids only give up one hydrogen at a time.0305

It breaks up into one hydrogen, and what is left over--HSO₄^-, the bisulfate ion.0314

Notice, this is actually--it has another H that it can give up.0322

It does so, to some extent, which is why, when we write this reaction, we use a double arrow.0329

It breaks up into H⁺ + SO₄^2-.0338

This dissociates, but it actually doesn't dissociate completely; it depends on the circumstance--what is going on in the reaction.0343

This one is a single arrow because it gives up that hydrogen completely--it just doesn't want it.0351

It wants to be this way and this way; we just call this polyprotic, and again, just fancy words for a chemistry that you completely understand.0356

One hydrogen to give up; a second hydrogen to give up; phosphoric happens to have three hydrogens that it will give up.0365

Very important, phosphoric acid, by the way--which is how the acidity inside of your cells is actually regulated--by the phosphate buffer system.0374

So, those of you who are in biology: that will be a big part of the work that you do.0381

OK, I'm going to write another representation; generally, when we do these acid-base problems, this is really what we're concerned with--the dissociation of the acid and the stoichiometry involved.0385

There is an alternative way that has become fashionable in the last fifteen to twenty years, and well, let me just write it out.0399

We can also write this this way: HCl + H₂O goes to H₃O⁺ + Cl^-.0407

Now, this thing right here is exactly the same as this thing right here.0417

H⁺ is the same as H₃O⁺; they write it this way--it has become fashionable--because it's a little bit more consistent with the idea of acid-base.0421

So, we said above that an acid is something that has a hydrogen to give up; well, a base is something that actually takes that hydrogen.0432

So, acid-base reactions, like oxidation-reduction later on, come in pairs; you have something that acts as an acid, something that acts as a base--the acid is the thing that gives up the hydrogen ion; the base is the thing that takes the hydrogen ion.0438

Here, what has happened is: water (if I rewrite water as HOH, which I'll do in the examples that follow, because I think it's a little bit more clear)--well, this H is actually given over to this; HCl gives up the H; the H₂O, or the HOH, takes the H; and now, it becomes H₃O⁺, since now it's carrying that extra ion, a plus charge; and then you are left with Cl^-.0451

This is just an alternate way to write it.0479

I'll just put that there; sometimes, depending on the problem and what it is that we want to emphasize, how we want to look at it, we might use different versions of it; but as long as you know that this H⁺ hydrogen ion and this H₃⁺ are the same thing...it is called the hydronium ion.0484

Again, it's just a name; it's just the same species--it's really just the H⁺ that is reacting here.0501

OK, now let's talk about a base.0508

We'll give a couple of definitions for base, because there are a couple of different types of bases.0511

A base is just a compound that dissociates to produce a hydroxide ion, OH^-.0517

And when we say "dissociates," it can be partial dissociation; it can be complete dissociation; there is always some little bit of dissociation.0533

Or, we could say it's a compound that takes or accepts a hydrogen ion.0541

So, let's go back up to this one right here: in this particular case, HCl was the acid; it gave the H⁺.0555

In this case, H₂O acted as the base; it took, it accepted, the hydrogen ion to form this and this.0562

An example of a base that dissociates to form hydroxide directly is sodium hydroxide.0570

We dissolve it in water; what you end up with is sodium ion floating around and hydroxide ion floating around; this is a base.0578

Base chemistry, acid chemistry--even though they come in pairs, they actually behave differently--they do different things.0585

Another example would be calcium hydroxide: Ca(OH)₂.0595

Drop some of that in water, and what you get is a calcium 2+ ion and these two hydroxides; they come apart completely; they don't come apart one at a time, like H⁺ does.0600

You're going to end up with 2 free hydroxide ions.0610

OK, now we'll give an example of a base that doesn't dissociate to release hydroxide ion; it actually does something else, but in the process produces hydroxide ions.0615

So, the net effect is hydroxide ion floating around in solution that wasn't there before.0628

Here, the base has hydroxide that it released into the solution; now, we'll do something...the most common base is ammonia.0635

So, NH₃; this time, I'm going to write it like I did before--the H₂O--instead of on top of the arrow, and I'll tell you why in a minute.0644

It's going to be NH₄⁺ + OH^-; so you notice, the OH^- still showed up, but it showed up indirectly.0652

In this case, now, the NH₃ is acting as the base; it's going to take a hydrogen from this H₂O, which I will write as HOH.0661

It's going to take this hydrogen to become NH₄⁺, and it's going to leave behind this OH^-.0672

This is one of the reasons why they started writing acids the way we did a minute ago--acid + H₂O.0679

It shows the acid-base behavior; in the last equation, the water was behaving as the base; it took the hydrogen from the acid, HCl.0685

Here, water is acting as the acid; it is giving up one of its hydrogens to the base, ammonia.0694

There is a consistency here; that is why they started doing that about 15 or 20 years ago.0700

OK, so now that we have just a nice, general idea of what acids and bases are, let's talk about acid-base reactions.0705

When we talk about acid-base reactions, we are talking about neutralization reactions.0715

Neutralization reaction: any time you put an acid together with a base, you always get a salt plus water, HOH, or H₂O.0720

Salt: again, salt is just a fancy word for ionic compound.0733

So, if I had an acid, which is dangerous; if I had a base, which is also dangerous; if I mix them together in the appropriate amount, and there was neutralization, and the salt wasn't too unpalatable, I could actually drink that solution, and it wouldn't harm me, because most of it would be water with some dissolved salt.0737

Or maybe not necessarily dissolved salt--maybe the salt would have precipitated, and I could filter it out, and I could drink just plain old water.0755

It's kind of extraordinary, when you think about it.0763

Well, here is what is happening: in neutralization reactions, this is going to be the net ionic reaction.0765

An acid, as we said, was something that has H⁺ floating around.0774

A base is something that has OH^- floating around.0778

When I put H and OH^- together, they really, really, really want to form water--liquid water.0782

And that is exactly what they will do; any time there is H⁺ and OH^- in the vicinity of each other, they will bind very quickly, very strongly, to form liquid water.0790

OK, that's it; this is your basic neutralization reaction; this is neutralization.0803

H is dangerous alone; OH^- is dangerous alone; put them together; they form water--not dangerous.0808

Let's do some examples.0816

We have HCl, hydrochloric acid; we'll put an _(aq) here to let you know that it's actually just floating around in solution.0818

Right now, we're writing the molecular formula; this whole molecular, total ionic, net ionic--it applies to acid-base reactions, as well.0826

Plus sodium hydroxide: again, _(aq); well, let's switch partners: HOH (well, actually, let me do the Na and the Cl first).0834

NaCl +HOH (I hope it doesn't bother you that I write HOH; it just helps me to think about it like this, instead of writing H₂O): well, this is the molecular equation, so let me write "molecular" here.0848

Let's see what is going on.0865

Well, HCl is fully dissociated; it's a strong electrolyte: HCl, minus...oh, I'm sorry; let's make sure it's balanced...it is; yes, not a problem.0867

Sodium hydroxide, a strong electrolyte, fully dissociates; so I have sodium and hydroxide floating around.0877

Remember, everything on the left hand of the arrow is everything before something happens; it's a description of the system before a reaction takes place.0884

Everything on the right hand side of the arrow is a description of the reaction after something has taken place; really, really important.0892

Nothing is going on over here; it's kind of nice--everything is just freely floating.0899

Well, like we said, any time H and OH are in the vicinity of each other, they bind to form water--liquid water.0903

Plus the NaCl...well, NaCl is...again, back to the Solubility Guidelines--you're always checking that--NaCl is fully soluble.0912

Therefore, it doesn't precipitate out; it just stays, sodium ion and chloride ion, floating around in solution.0921

This is our total ionic equation.0928

Now, we write our net ionic; we cancel the things on the right that are the same on the left; what we are left with is H⁺ + OH^-.0930

Those two...HOH, liquid.0943

Molecular formula; total ionic formula; net ionic; and remember, the net ionic is the actual chemistry that takes place; the chemistry that took place here was the hydrogen ion from the acid, and the hydroxide ion from the base, came together to form liquid water in a neutralization reaction.0946

In other words, the two ions neutralized each other--a profoundly important reaction.0968

Let's do another example here.0978

We'll call this one Example 1, because it's our formal example.0982

All right, molecular, total ionic, and net ionic equations for the reaction of (let's see...) carbonic acid, H₂CO₃, and potassium hydroxide, KOH.0987

So, we want molecular, total ionic, and net ionic equations for the reaction of carbonic acid and potassium hydroxide.1029

Carbonic acid: the other important acid in biological systems--it is how the blood...basically, the fluid outside of your cells regulates the acid content of your blood.1035

Your normal blood pH hovers around 7.3 or 7.4, or somewhere in that range.1050

Well, it needs to stay in that range, and carbonic acid--the carbonate buffer system--is what controls it; that is why you exhale CO₂, because if you didn't exhale CO₂, your blood would start to get very acidic, and some very bad things would start to happen.1055

So, outside the cell--carbonate buffer system; inside the cell, phosphate buffer system.1070

Let's see; well, let's just write it out!1075

We have H₂CO₃, carbonic acid, plus potassium hydroxide, and we are doing a molecular here.1082

So, we'll switch partners: we have H and OH; we know that we have an acid and a base--we know that we're going to get salt and water, always; it always happens.1092

We have HOH (actually, you know what--I think I'll put my water second; so I'll do potassium carbonate); I'll do K₂CO₃ first--it's just more traditional; we tend to put...HOH.1104

Now, let's balance it: 2 potassium on the right; I put a 2 there; I have 2 hydroxide--let me put a 2 here; that is 2 hydroxide, and now I have 2 H's; 2 H's.1121

This is one of the reasons why I write it as HOH instead of H₂O; when I'm dealing with polyatomic ions and balancing, I like to balance polyatomic ions completely; hydroxide on the left, hydroxide on the right.1131

Think of water as hydrogen hydroxide--how is that?1142

OK...well, let's see what we can do.1146

H₂CO₃; now, we have to check solubility; H₂CO₃, carbonic acid, is one of those acids that is actually a weak electrolyte; it does not dissociate completely--in fact, it's not very soluble at all.1151

It's soluble in the sense that, if you dropped carbonic acid in water, you wouldn't be able to tell the difference; you would get a homogeneous mixture, so it dissolves, but it doesn't dissociate--meaning the H₂CO₃...the H doesn't really leave.1164

A little bit of it does, but most of it does not.1179

So, we actually don't write it as free ionic species; we leave it as H₂CO₃.1182

Does that make sense?--I hope that makes sense; so just because something dissolves, like sugar (let's just say glucose, C₆H₁₂O₆), you can drop glucose in water, and it will dissolve--you won't be able to see the difference between the glucose and the water--but the carbons, the hydrogens, and the oxygens that make up sugar don't come apart.1191

That is different; that is dissociation--it dissolves, so carbonic acid, H₂CO₃, dissolves in water, but it doesn't dissociate in water the way that, say, hydrogen chloride does.1212

OK, so I leave it like this, and I put a little _(aq) here to let me know that it's dissolved.1223

Well, potassium hydroxide--absolutely, it is a strong electrolyte, so it comes apart completely into free hydroxide and free potassium.1228

And now, potassium carbonate: let's see, what is potassium carbonate?1237

Potassium carbonate, actually, is an alkali metal with a carbonate, so it is soluble; therefore, I do get 2K⁺ + CO₃^2-.1242

Water, of course, is, well...water is water.1253

So, let's cancel this; so the second one is your total ionic; now, let's cancel on the left and right--the only thing that cancels is the potassium.1257

Now, I have to write what is left over.1269

H₂CO₃, plus 2 hydroxide ions, goes to CO₃^2- + 2 waters.1272

That is my total ionic; this is my chemistry, right here.1284

The total ionic represents the chemistry.1287

One molecule of carbonic acid reacts with two molecules, if you will, of hydroxide ion, to produce one carbonate ion and two molecules of water.1290

That is kind of extraordinary, when you think about it; it happens just like this.1302

And, with a 2- charge on the right and a 2- charge on the left, charge balances; mass balances; everything is good.1306

OK, let's do another one; let's do Example 2.1315

This time, I'll just go ahead and write down what it is that we're mixing; we are going to mix lead (2) hydroxide plus (oops, I'll balance it in a minute) hydrochloric acid, and I want to know what happens.1321

Well, OK; I know that I have lead hydroxide, which is a base; and I have HCl, which is an acid; I switch partners--I know I'm going to get a salt plus water.1340

Well, the water comes from the HOH; the only salt left over to make is the PbCl.1352

So, I write PbCl₂, because this is lead (2), and I write HOH, and now I have to balance it.1357

2 hydroxides; 2 hydroxides gives me 2 H's; I put 2 H's; 2Cl, 2Cl; I'm balanced.1365

Now, I check for solubility; that is my next step--that's how I come up with my total ionic equation.1372

Lead hydroxide is not soluble; it stays as a solid.1377

Lead hydroxide, lead (2) hydroxide, is a solid; it does not come apart.1384

Very, very little of it dissociates, which is why the reaction actually proceeds (we'll talk about that later, when we talk about Le Chatelier Principle, solubility equilibria, things like that).1389

But, for right now, it is a solid; it does not break up into free ions; but HCl does: 2H⁺ + Cl^-1399

PbCl₂...now notice, this is a product; this is something that is formed.1410

Well, lead chloride is also insoluble; therefore, I'm going to put a little down arrow, showing that it falls out of solution as a solid, a precipitate.1414

That stays the same (oops, I have all those stray lines showing up again): PbCl₂, down arrow, is a solid, and then of course water is just water: 2HOH.1422

Notice, there is nothing on the left and nothing on the right that is the same; therefore, this total ionic is the same; or I should say, the net ionic is the same as the total ionic.1438

This is the chemistry, right here; in this particular case, we have a mixture of what we talked about before and now--there is an acid-base reaction going on, in the sense that hydrogen ion and hydroxide ion form water.1451

But, there is also a precipitation reaction going on; there is lead ion and chloride ion, come together to form the solid, lead chloride.1464

So, that is also a possibility; and again, you just kind of deal with it systematically--deal with each thing that comes up.1475

It's not a problem if you have an acid-base reaction together with a precipitation reaction; there is no law that says they have to be separate things.1480

They can happen together.1487

Now, I want to introduce a concept called molarity, and it is used to discuss aqueous solutions.1494

After I introduce it really briefly, I'm going to actually do a stoichiometry problem, because we are talking about stoichiometry, and it's going to be a mixture: it's going to be an acid-base neutralization, and it's going to basically just take us through a pretty standard stoichiometry problem, so you get an idea of what it is that we're looking for--how to handle the equations.1505

That is the really important part of the stoichiometry here: Which equations do I use?1524

If you understand the chemistry, I promise, the math is easy; very, very easy; so let's get started.1528

Molarity: it is defined as the moles of solute (the thing that you're dissolving) over the liters of solution (the thing you're dissolving in).1536

And, since most of the time we'll be talking about water, normally our solute will be an acid or a salt dissolved in some kind of water.1554

Now, the symbol for molarity--I'm going to use two symbols: the common symbol, that has been popular for about the last 15 or 20 years, is the capital M, Molarity.1561

I learned it as an m with a line over it; so I'm going to...I'll use both, but in your book, you'll see, of course, the capital M; but just know that an m with a line over it is also another symbol for molarity.1576

You'll see it in the older literature.1586

OK, so moles of solute, liters of solution: the unit is moles per liter--that's it.1589

So, molarity is moles per liter--very, very important--that is a new unit; you have already had grams per mole; you had particles per mole (Avogadro's number); now, you have moles per liter.1595

So, three units that involve mole; clearly, the mole is very important.1606

Let's just do an example here.1611

We'll call it Example 3: I have 14.6 grams of potassium chloride, and it is dissolved in 400 milliliters of water.1618

What is the molarity of this solution?1638

Molarity--another word for concentration: what is the concentration of this solution in moles per liter--what is the molarity?1642

Well, what is our definition of molarity?1649

Molarity is equal to the moles of solute (which, in this case, is KCl) divided by the liters of solution (which, in this case, is water).1654

So, all I need to do is find a denominator, find a numerator, do my division, and I'm done!1664

Well, I know that the volume is the easiest one--it's 400 milliliters--but since the unit is in liters, I'll just convert that to liters, which is 0.400 liters.1671

Now, I need to find how many moles of potassium chloride.1680

I wasn't given moles--I was given grams--but of course, I can convert by using the molar mass.1686

Let's do that: 14.6 grams of KCl times (1 mole of it happens to weigh) 74.55 grams, and when you do that division, you end up with 0.1958 mol of KCl.1691

This is the number that goes up there: 0.1958 mol of KCl, dissolved in .4 liters.1711

I do the division, and I end up with (what is my number?) 0.49; 0.49 moles per liter, or I can put 0.49 Molar (we often say Molar solution).1721

That's it; molarity is just a way of talking about how many moles of something there are floating around in liquid, in a solution (more often than not, water).1741

Because when I drop something in water, more often than not, it will dissolve, I want to know how many moles are actually floating around.1752

If I keep the volume the same, but I dump in five times as many moles, now I'm five times as concentrated--which is why they also refer to molarity as concentration.1759

How concentrated is this particular solution?1768

This .49 tells me that, in 1 liter of solution, I have .49 moles of potassium chloride floating around.1772

"Potassium chloride floating around"--potassium chloride is made of one atom of potassium, one atom of chloride, so I have one mole of potassium floating around and one mole of chloride floating around.1781

So, stoichiometry is really, really important.1795

Again, this dissolves.1798

So, let's jump into a problem here.1803

This will be Example #4.1806

How many grams of PbCl₂ will precipitate when 10 grams of lead (2) hydroxide is dropped into 50 milliliters of a 0.50 Molar HCl solution?1815

Wow, it seems like there is a lot going on here; don't worry about it--we'll deal with it systematically.1864

I have a 50-milliliter beaker; actually, I have 100--let's say a 100-milliliter beaker, about half full--50 milliliters; and it is a hydrochloric acid solution, .5 Molar hydrochloric acid solution.1869

That means, for every liter, there is .5 moles of hydrochloric acid floating around.1883

That's reasonably strong--it will certainly do some damage if you allow it to; not terribly strong, but certainly there is enough acid floating around.1888

So, what we do is: we take 10 grams of lead hydroxide; we drop it into this acid solution; and we know, from the example that we just did when we did lead hydroxide plus the hydrochloric acid, that we're going to get lead chloride plus water.1897

Lead chloride is insoluble, so some of it is just going to drop to the bottom like a stone.1909

We want to know how much lead chloride is actually going to fall out, based on this.1914

So, we have an acid-base reaction; we have a precipitation reaction; this is a stoichiometry problem that involves limiting reactant.1918

All of these things come together now: limiting reactant, acid-base, precipitation.1928

Fortunately, in this case, we're not worried about the water; we're not worried about the acid-base portion; we're worried about the precipitation, so we can narrow our focus.1932

Let's write our equation again, so we know what we're dealing with.1941

That is the most important--always start your chemistry with an equation; that is what chemistry is--it's about things that come together and change.1945

If you don't have an equation, you might be able to do the math, but it's not really going to make much sense; you need an equation.1951

Start with the equation.1956

Pb(OH)₂ + 2HCl goes to PbCl₂ as a precipitate +2HOH.1959

Now, I have my equation that I'm working with; let's get started.1974

Since I'm talking about (let me do this in red) lead chloride, and that is what I'm looking for here--lead chloride--let me take a look at that reaction individually.1979

Lead chloride comes from the following (and again, this is what you're going to be doing in the stoichiometry--write out all of the equations that you need; this is what it's all about--the equations will guide your mathematics).1990

We have lead ion; it comes together with 2 chloride ions to form PbCl₂ as a precipitate; that is my equation for the formation of lead chloride.2001

Well, this says that one mole of lead produces one mole of lead chloride.2014

Two moles of chloride ion produces one mole of lead chloride.2021

Again, it's basic stoichiometry.2024

The first thing we want to do is: we want to find out how many moles of lead ion there are.2028

Then, we're going to find out how many moles of chloride ion there are, because it's a solution of HCl; and then it's going to be a limiting reactant problem.2032

Whichever is the limiting reactant--that is going to control how much PbCl₂ precipitates.2041

So, we have extracted the important information; this equation right here--this is the equation we're dealing with, because we want to know the PbCl₂.2046

Moles of Pb(OH)₂; well, we have 10 grams of the Pb(OH)₂, and one mole of it is 241.2 grams; therefore, we have 0.0414 mol of Pb(OH)₂.2055

Again, in stoichiometry, you're going to always be working in moles; so immediately, if you do nothing else, just convert it to moles.2086

Well, each molecule of lead hydroxide is made up of one atom of lead; therefore, one mole of lead hydroxide produces 1 mole of lead of ion; so .0414 mol of lead hydroxide produces (I'll do a little double arrow)--it implies 0.0414 mol of lead ion, which is what we were interested in; this is our equation.2093

Do you see what I did?--I hope you do.2127

I started with a whole molecule, but each one of these molecules--one molecule releases one molecule of lead, so .0414 mol of the molecule releases .0414 mol of lead ion.2129

That is what is going to react with the chloride to give me the PbCl.2143

Let me put a little bracket around that; I'm going to use that in a minute.2148

Now, let's see...well, let's just go ahead and do the moles of...now, I need to know the number of moles of chloride ion I'm dealing with.2154

Well, the moles of HCl--I have liters, and I have moles per liter.2167

That is why molarity is used, because we often deal with solutions; so we need to know the number of moles to be able to extract it from solutions.2172

For a solid, you use molar mass; but for solutions, you have to use molarity.2182

So, here we go: I have 0.050 liters of solution, and the molarity is 0.5 moles per liter.2187

The units cancel, and I end up with 0.025 mol of HCl floating around.2201

Well, HCl is not floating around; it's dissociated; but every molecule of HCl produces one molecule of H⁺ ion and one molecule of Cl^-.2208

Therefore, I have 0.025 mol of Cl^- floating around; that is my other thing.2217

I hope that made sense; again (oops, these lines just show up out of nowhere, don't they)...2228

Now that I have .0414 mol of Pb, and .025 mol of Cl, now I can find out which one is the limiting reactant.2239

So, let me draw a little bit of a line here; let me go back to blue ink; and I'm going to do the limiting reactant part.2247

I hope I have enough room here; yes, I think I do; actually, you know what--that is fine; let me just move forward.2260

So, let me write that again; this is going to be the limiting reactant part of the calculation.2269

Now, I can choose either one; I can either choose the .025 moles of chloride to start with, or I can choose the .0414 moles of lead ion to start with--it doesn't matter which one.2278

I'm just deciding which one is going to run out first.2289

I'm going to choose the lead.2292

.0414 moles of lead ion (let me rewrite the equation, by the way, so we have a reference here: Pb²⁺ + 2Cl^- goes to PbCl₂ as a precipitate.2295

PbCl₂...there we go.2316

.0414 moles of Pb, moles of lead; moles of chloride; the mole ratio of lead and chloride is 2:1; that is 2:1; that is what I'm doing here.2320

This tells me that, if I have .0414 moles of lead, .0818 moles of chloride are required to react with it.2336

That is what this equation tells me: for every mole of lead, I need 2 moles of chloride to produce a molecule of lead chloride.2350

Well, if I have .0414 moles, and the mole ratio is 2, I multiply by 2; I get .0818--that is moles of Cl^- required.2357

Do I have .0818 moles of Cl^-? No.2365

I only have 0.025 moles of Cl^-; that is what I just calculated; so therefore, Cl^- is limiting.2373

So, the Cl^- is going to control how much lead chloride I have; I'm going to end up with excess lead ion floating around.2386

This is my limiting reactant; now that I have my limiting reactant, I can go ahead and perform my actual reaction.2394

This is the reaction part.2402

Well, I have 0.025 moles of Cl^- (it's my limiting reactant, so I start with that--that is what is going to control it).2409

Now, the relationship--the mole relationship--between Cl^- and PbCl₂ is 2:1.2420

I have mol of Cl^- on the bottom, because it's on top here; mol of PbCl₂, so it is going to be 2:1; that cancels, and I get 0.0125 mol of PbCl₂ produced.2427

Now, I take 0.0125 mol of PbCl₂, and I multiply by its molar mass, which happens to be 278.1, and I end up with 3.48 grams of PbCl₂ that have precipitated.2451

That is my final answer.2473

Let's see what I did: I had 10 grams of lead hydroxide that I dropped into (how many milliliters was it?--I forgot the actual volume amount; let me double-check here; how much was my volume? Yes, it was 50 milliliters) 50 milliliters of a .5 Molar hydrochloric acid solution.2476

I asked for lead chloride; lead chloride precipitates; therefore, I dealt with that equation: one lead ion plus two chloride ions gives me one molecule of lead chloride.2501

I first found the number of moles of lead ion, and then I found the number of moles of chloride ion.2511

Then, it became a limiting reactant problem; I found out that chloride was my limiting reactant--it's the one that is going to run out first--therefore, it is going to control the reaction.2517

I used chloride and the mole ratio of chloride to lead chloride to find out that I'm going to end up producing .0125 moles of lead chloride, which I then convert to grams, and I end up with 3.48 grams of PbCl₂.2526

So, as you see, everything is starting to come together.2543

Stoichiometry, acid-base, precipitation, all of these things are going to play into the problems that you solve on the AP exam.2546

Yes, both in the multiple-choice section, which are going to be no calculator--but you will have to still do the math; the math mostly simple numbers; but particularly in the free response section.2557

It isn't going to be just "Give me this, give me this, give me this"; it's going to be a whole slew of things happening.2567

As long as you understand the chemistry, these other things are just techniques; that is what is going on here.2572

This is a very, very characteristic problem that you will see on the AP exam.2579

You have an acid-base, a precipitation reaction, and you have some stoichiometric calculations.2583

This is the heart and soul of chemistry.2588

Everything happens simultaneously.2590

OK, thank you for joining us here at Educator.com for our discussion of acid-base and solution stoichiometry.2592

Next time, we'll talk about oxidation-reduction; take good care--goodbye.2598