General Chemistry Applications of Aqueous Equilibria

Hi, welcome back to Educator.com.0000

Today's lesson in general chemistry is applications of aqueous equilibria.0003

We are pretty much going to build upon what we learned in the last lesson when we talked about equilibria for acid base chemistry.0008

We are going to see how it can easily apply to other aspects of general chemistry.0015

We are going to learn how to calculate the pH of an acid base mixture.0020

We are going to learn about a very important system in chemistry which is called buffers.0024

Following buffers, we are going to learn a unique experiment called acid base titrations0030

followed by other aspects of chemical equilibria, namely what we call solubility equilibria and compensation equilibria.0037

We will always wrap up the session as always with a summary followed by a sample problem.0047

When we did equilibria before, every equilibria we have discussed has always involved a direct reaction with water.0054

For example, it has always been the acid HA plus H₂O.0064

Or it has always been a base plus H₂O.0069

But what happens when we react directly a Bronsted-Lowry acid with a Bronsted-Lowry base?0073

When this happens, you don't get equilibrium immediately.0079

Instead the very first step that occurs is going to be a neutralization reaction.0082

Neutralization involves complete consumption of one or both of the reactants.0088

We always get the generic reaction where we have an acid HA reacting0093

with a base aqueous going on to form HB¹⁺ aqueous and A^- aqueous.0099

Once again when we do these neutralization reactions, we use a single arrow only0108

because one or both of the reactants is going to be consumed completely.0116

After neutralization occurs, then we can apply whatever we learned last time.0126

Basically whatever remains is going to be reacting with water in a typical aqueous equilibrium.0134

In that case, it is either going to be the acid HA aqueous plus H₂O liquid.0143

Or it is going to be the base reacting with H₂O liquid.0153

Those are going to be our main reactions after neutralization has occurred.0163

Let's go ahead and take a look at a representative problem and jump right into a calculation.0167

What is the pH of the solution that results from adding 30.0 milliliters0173

of 0.1 molar sodium hydroxide to 45.0 milliliters of 0.100 molar acetic acid?0178

Now we have a strong base reacting with a weak acid here.0187

Step one, step one is to always write out the neutralization reaction.0194

Let's go ahead and write that out.0204

It is going to be hydroxide aqueous reacting with the acetic acid, CH₃CO₂H aqueous.0206

That is going to go on to form water liquid and acetate CH₃CO₂^1- aqueous.0216

We can go ahead and proceed to fill in the ICE table as usual.0226

Here hydroxide is what we want, moles.0230

That is 0.0300 liters times 0.100 molar.0233

That is going to give us 0.00300 moles of hydroxide.0240

The acetic acid we have 0.0450 liters times 0.100 molar.0246

That is going to give us 0.0045 moles of acetic acid.0257

Acetate is going to be zero.0263

Remember we said that one of these reactants or both is going to be completely consumed.0266

We can see that this is a 1:1 ratio here.0271

If we have amounts of both reactants, that is like a limiting reactant problem which we discussed a long time ago.0278

Here because it is 1:1 ratio, the reactant that is present in smaller quantity is going to be consumed entirely.0284

Here if this is I-C-E, this is then going to be -0.0300 moles.0291

This is -0.00300 moles; this is going to be +0.00300 moles.0300

The hydroxide gets completely consumed.0310

Most of the acid is going to be eaten up here and consumed or left with only 0.0015 moles.0314

This is going to be 0.00300 moles.0320

Now step two, step two, we are then going go ahead and proceed on to do...0326

Whatever is left standing is going to react with water; step two, react with water.0335

Now this is going to be like our previous lecture.0341

We are going to go ahead and select the acid, CH₃CO₂H aqueous.0346

That is going to react with water going on to form CH₃CO₂^1- aqueous and H₃O¹⁺ aqueous.0352

We carry everything down.0367

The final values of table one become the initial values of table two.0368

This is now 0.0015 moles; this is 0.00300 moles; this is 0.0372

This is going to be ?x, +x, and +x.0380

At equilibrium, 0.0015 moles minus x, 0.00300 moles plus x, and x.0386

The k for acetic acid is something that should be given to you or you look it up.0395

That is 1.8 times 10^-5 which is relatively small.0400

All of this reduces to 0.00300 times x divided by 0.0015.0404

Because the volume is the same for each of these moles, the liters are really going to cancel out.0416

I can directly just use the moles.0424

We get an x value of 9.0 times 10^-6 molar which is the hydronium ion concentration at equilibrium.0427

The pH is going to be 5.05.0438

Again always make sure your answer makes sense.0443

Here we have an acidic pH which we should have because all we have leftover is acid and no more base.0446

Again this is how you calculate the pH of an acid base mixture.0455

Let's now go ahead and examine how to control a change in pH.0460

When a solution contains both a weak acid/base and its conjugate in appropriate amounts,0467

there is going to be a resistance to small changes in pH.0474

These are solutions that we call buffers.0477

A buffer is going to contain again a weak acid HA plus its conjugate base A^-.0482

Or it is going to contain a weak base B and its conjugate acid BH⁺.0493

These are typically going to be in the form of salts; usually in the form of a salt.0501

Anytime you see these two mentioned in the same sentence, they simultaneously occur in the same mixture.0515

We have what is called a buffer; once again buffers resist small changes in pH.0523

The reason why they work is because of the following.0531

If you disrupt the buffer by say adding acid, the solution is going to resist a drop in pH.0534

The reason is because if we add acid to the buffer, this acid is going to react with any base present.0540

Because we have both acid and base present as a buffer, this is good to go.0549

We are going to form HA aqueous and H₂O liquid.0555

Or it can react with H₃O¹⁺ aqueous and base aqueous.0561

We are going to form BH plus aqueous and H₂O liquid.0568

Right away you see how the buffer can resist change in pH because water is formed0574

as a product which helps to counteract5 the effect of the added acid; dilutes H₃O¹⁺ added.0581

The other way to disrupt the buffer of course is by base, adding base to the buffer.0594

The solution is going to resist a rise in pH.0598

The reason is because if we add base, say hydroxide, that will then react with possibly HA if it is an acid in solution.0601

Or the base can then go ahead and react with the conjugate acid if it is a basic buffer.0611

In either case, we see that we still form water.0619

Again it is the formation of water that helps to counteract the effect of added base; dilutes OH^- added.0626

Let's go ahead and jump right into a calculation.0643

A buffer is prepared by mixing 0.50 molar of acetic acid with 0.50 molar0648

of sodium acetate where the k is given to you for acetic acid.0653

Let's go ahead and calculate the pH first.0657

Let's go ahead and write out the equilibrium.0663

CH₃CO₂H aqueous plus H₂O liquid goes on to form CH₃CO₂^1- aqueous and hydronium aqueous.0664

This is 0.50 molar; this is 0.50 molar; this is 0.0682

This is going to be ?x, +x, +x.0688

This is going to be 0.50 minus x, 0.50 plus x, and x.0692

K_a is given to us to be 1.8 times 10^-5.0698

This is then approximately 0.50 times x divided by 0.50.0702

You see that we can get an x of 1.8 times 10^-5 molar.0708

The pH is going to be 4.74.0717

There is a shortcut it turns out.0724

Anytime we have a buffer, it turns out we don't need to set up an ICE table problem.0726

It turns out that we do have a nice shortcut.0732

This is what we call the Henderson Hasselbalch equation.0735

The Henderson Hasselbalch equation is the following.0753

It is pH is equal to the pKa plus the log base 10 of0756

the concentration of the base initial divided by the concentration of the acid initial.0761

This is going to be for an acidic buffer.0767

If you have a basic buffer, it is still pH is equal to pKa.0772

But this time it is going to be the log of the initial concentration0776

of base divided by the initial concentration of the conjugate acid.0778

The nice thing about this equation is that we don't need equilibrium values for the conjugate base and the acid.0785

We only care about initial values.0791

The Henderson Hasselbalch equation, you must know it is only an approximation.0793

But it does work out many times.0799

We can go ahead and plug in our values here for the previous problem we just did.0802

We are going to get pH is equal to ?log of 1.8 times 10^-5.0807

That is equal to the log of 0.50 divided by 0.50.0814

When all is said and done, we get 4.74.0819

As you can see, this matches up very nicely with the previous problem where we did the ICE table.0822

Once again when you see a buffer problem, think Henderson Hasselbalch equation.0831

Next let's go ahead and see what happens to the pH when we disrupt this buffer by adding strong base.0837

Now we are going to add 0.010 moles of sodium hydroxide to exactly 1 liter of the buffer.0843

Once again because we are adding a strong acid or a base, step one is to do the neutralization step.0853

Because we are adding a strong base hydroxide, this is going to go0861

ahead and react with the weak acid that is already in solution.0866

That is going to go on to form acetate and water.0871

This is going to be 0.010 molar; this is 0.50 molar.0881

This is going to be 0.50 molar; we don't care about water.0886

Because again this is a 1:1 ratio, remember what we always said.0892

Anytime there is neutralization, either one or both of the acid and base are going to be consumed.0895

My 1:1 ratio tells me I am going to choose a smaller amount that is going to get consumed completely.0901

This is -0.010; this is -0.010 molar; this is +0.010 molar.0907

This goes to 0; this goes to 0.49 molar; this goes to 0.51 molar.0916

We can go ahead then and step two...0923

Remember we would set up ICE table like we taught you at the beginning of this session.0926

But because this is a buffer, we can use Henderson Hasselbalch directly which is always nice.0931

It saves us a lot of time.0937

pH is equal to the pKa plus the log of acetate initial divided by the initial concentration of acetic acid.0942

Remember how we said last time, the final values of table one become initial values of table two.0960

That is still going to apply.0964

This 0.51 goes right there; this 0.49 goes right there.0967

When all is said and done, we expect a pH that is going to be0972

greater than 4.74 because we added strong base but not too much greater.0977

When we do this, we get pH of 4.76.0982

As you can see, the buffer was successful in resisting this change in pH.0986

We only went up 0.02 units.0993

The next thing we are going to discuss is how to make a buffer and what we call buffer capacity.0998

Exactly 1.25 liters of a buffer solution is prepared from mixing 23.5 grams of sodium dihydrogen phosphate1003

and 15.0 milliliters of 14.7 molar phosphoric acid where the K_a is given to you.1014

Calculate the pH.1019

Because this is a buffer, again we can use Henderson Hasselbalch equation directly.1020

The pH is equal to the pKa plus the log of the conjugate base initial divided the acid initial.1025

The hardest part of this is just to figure out which one is the conjugate base and which one is the acid.1036

This is going to be equal to pKa plus the log of...1041

the conjugate is going to be the H₂PO₄^1- concentration.1045

Of course the acid is going to be the phosphoric acid initial concentration.1052

We can go ahead and again use this to calculate the pH of this buffer by inserting everything directly in.1062

This 23.5 grams of course we need to get to moles first.1073

This 14.7 molar is going to go right there.1080

Remember the final volume is exactly the same.1084

The 1.25 liters is same for both A^- and HA which means the volume term is going to cancel.1089

All you need is just really the moles.1106

Here is 15 milliliters of 14.7 molar phosphoric acid.1110

Then you can convert the 23.5 grams of the sodium dihydrogen phosphate directly to moles.1114

A buffer can only do so much.1122

A butter can accommodate so much extra base or extra acid.1124

It is what we call buffer capacity.1129

A buffer is considered to be effective when the pH is within 1 unit of the pKa.1132

In other words, pH is equal to +/-1 of the pKa.1138

What that means by going from the Henderson Hasselbalch equation is that the ratio of A^- to HA is less than 10.1145

Anything outside this range, the buffer will not be effective.1153

Why?--because you have too little of either the acid or base to counteract any effect from disturbing the buffer.1157

That is our brief discussion on buffer preparation and buffer capacity.1167

Following buffers is going to be now a specific experiment.1176

This is what we call an acid base titration.1180

In an acid base titration, an acid or base of known concentration is used to determine the concentration of an unknown acid or base.1183

This is known as standardization of the unknown.1192

The solution that is known is what we call the analyte.1195

Excuse me... the solution of known concentration is what we call the titrant.1201

The solution that is unknown, what we are trying to standardize, what we are1209

trying to find the concentration of, this is what we call the analyte.1213

The basic setup is going to be the following.1219

We are going to have a pretty long thin cylindrical tube.1224

This is usually 50.00 milliliter; this is what we call a buret.1229

The burets are very very precise.1236

You notice I use two sig figs after the decimal.1238

This is always two within 0.01 milliliter.1241

There is going to be an Erlenmeyer flask on the bottom.1250

Usually the buret is going to have the titrant.1253

Usually the flask is going to have the analyte.1262

With this flask with the analyte inside the flask, there is also going to be called what is called indicator.1266

Indicator solution is going to change color.1274

When it changes color, this is what we call the equivalence point, also known as the stoichiometric point.1281

At this point, we have complete neutralization.1299

When we have complete neutralization, the moles of HA acid is equal to the moles of the base.1308

You see that we can use mole to mole ratio here between acid and base to backtrack and get the concentration of the unknown.1319

But let's go ahead and go through a typical problem first.1329

Calculate the pH at the equivalence point when so much HClO is titrated with 1 molar KOH.1333

Anytime you see volume and molarity, you have heard me say this before.1342

That is always a good 1-2 combo; you are going to get moles.1347

Let's go ahead and do that.1349

0.250 liters times 0.0350 molar, that is going to give us 0.00875 moles of HClO.1350

Because we are at the equivalence point, this is also the same number1365

of moles with the KOH by definition; by definition of equivalence point.1371

Because we now have both of our amounts, let's go ahead and set up the neutralization reaction.1389

HClO plus OH^1-, that goes on to form H₂O liquid and ClO^1- aqueous.1394

This is 0.00875 moles; this is 0.00875 moles; this is going to be 0.1406

Remember last time how when we have an acid and base neutralization reaction,1415

we said that either one or both of the reactants is going to get consumed entirely.1419

This is a good example where both of them gets consumed entirely.1424

Why?--because we have a 1:1 ratio.1427

Because this is the equivalence point, we have equal amounts.1430

This is going to go -0.00875 moles; this is going to be -0.00875 moles.1433

This is going to be +0.00875 moles.1444

This goes to 0; this goes to 0; this goes to 0.00875 moles.1448

Final values of table one become initial values of table two.1457

But this is not a buffer anymore; why?--because we have zero amount of HClO.1460

Let's go ahead and do our second setup; it is the last man standing.1465

The only thing remaining is ClO^1- aqueous plus H₂O liquid going on to form HClO aqueous plus OH^1- aqueous.1471

When all is said and done, we are going to be using K_b.1486

We are going to use K_b to get the concentration of hydroxide.1491

From there, you can go ahead and get the pH.1496

But don't forget, the important thing is to take this moles amount and get to molarity first.1500

When you get to molarity, you need to divide by the total volume; very very important.1509

This is a typical type of question to calculate the pH at an equivalence point of a titration.1523

During a titration, something that is done that is very typical is to monitor the pH yielding what is known as a titration curve.1532

When we look at a typical titration curve, it is going to be the following: pH versus volume of titrant added.1541

We can have different types of titration curves.1556

Each one is going to be a different experiment.1558

We can have a curve that looks like this.1561

We can have a curve that looks like this.1569

In each of these cases here, the pH is going to be greater than 7 here.1575

Here the pH is going to be less than 7 here.1583

Of course the final situation is pH equal to 7.1587

Of course you can have the mirror image right here, pH equal to 7.1599

Let's go ahead and discuss what each of these means right now.1607

The first situation, here the pH is acidic.1610

The only thing you have initially is your acid.1615

This is going to be a weak acid titrated with strong base.1619

Here you see that the initial pH when no titrant has been added is basic.1629

This is going to be a weak base titrated with strong acid.1635

Let's go back one.1645

When the weak acid is titrated with a strong base, the pH is always going to be basic at the equivalence point.1647

When the weak base is titrated with strong acid, the pH is going to be acidic at the equivalence point.1655

Here pH is neutral.1662

When the pH is neutral at the equivalence point, you have one of two possibilities.1665

Either a strong acid titrated by strong base or you have a strong base titrated by strong acid.1670

A titration curve typically can be broken up into four regions.1693

I am going to choose the weak acid titrated with a strong base as our typical example.1699

Here is region one, region two; region one, region two, region three, and region four.1706

At the end of this lesson, you are going to be able to calculate the pH along any point of the titration curve.1719

You are basically in one of four regions.1725

Each region is going to have little own strategy.1727

Let's go ahead and go over them.1730

In region one, which is basically the y-intercept; in other words, zero base added.1732

The equilibria that you would use is an equilibrium from last lecture which is the1747

weak acid HA reacting with water going on to form H₃O¹⁺ aqueous and A^- aqueous.1755

It is a typical ICE table setup problem; you use K_a to solve for pH.1768

Region number two, you notice that in region number two, the pH doesn't change that much.1777

It is really a plateau.1784

The pH doesn't change that much because we have a functioning buffer.1787

Region two is what we call the buffer region.1790

Again you don't need an ICE table setup to calculate the pH in the buffer region.1797

You simply use the Henderson Hasselbalch equation.1802

pH is equal to pKa plus the log of the concentration of A^- initial divided by the concentration of HA initial.1806

There is special point of interest in the buffer region.1818

It is right here; that is what we call the midpoint.1821

That is what we call the midpoint of the titration.1828

At the midpoint of the titration, we have this very special relationship where pH is equal to the pKa.1831

In other words, the concentration of A^- initial equals the concentration of HA initial.1836

It is called the midpoint because we are exactly halfway done with the titration in order to get to the equivalence point.1847

In other words, the moles of hydroxide added is going to be equal to half the moles of HA present.1853

Again the moles of hydroxide added is half the moles of HA present.1866

We are halfway to the stoichiometric point; halfway to equivalence point.1870

Region number three, in region number three, we get a sudden spike in pH.1885

That is because the buffer no longer is functioning.1894

We are beyond the capacity of the buffer.1897

The point of interest is of course the equivalence point.1901

We went over already how to calculate the pH at the equivalence point.1908

Remember it is going to be here.1912

Remember the acid is completely gone; the base is completely gone.1916

All you have left is the conjugate base A^- reacting with water going on to form HA aqueous and hydroxide aqueous.1919

For this one, you are going to use K_b.1933

As you can see, that is why pH is going to be greater than 7.1938

Finally region number four, region number four, you have nothing but excess hydroxide added, nothing more than that.1941

That is going to be a typical pH is equal to ?log of H₃O¹⁺ equation.1957

We are going to go through a problem later on at the end of this lecture discussing that.1967

That is our basic introduction to titration curves.1973

The four regions, each require a different strategy to compute the pH.1979

Let's now take a look at another application of aqueous equilibria.1984

It is what we call solubility equilibria.1988

Remember a long time ago at the beginning of the first couple of presentations, we went over our table of solubility rules.1991

We said that some salts were relatively soluble; we said that some salts are insoluble.2000

It turns out that a really all solid salts are going to be soluble in water to a measurable degree.2006

Some of course more so than others.2014

Salts that are very soluble will have the following equilibrium lie far to the right.2016

We can go ahead and imagine an ionic solid of the formula MX solid2021

dissolving into the respective cation and anion, M⁺ aqueous and X^- aqueous.2029

The equilibrium expression for this type of reaction would be the concentration of M⁺ times the concentration of X^-.2041

We give this equilibrium constant a very specific name.2051

This is what we call the K_sp or the solubility product constant.2055

Basically as you can see, the larger this constant, the more ions you get.2063

In other words, the more soluble the solid is; solubility increases with K_sp.2069

Salts that are relatively insoluble such as carbonate will have the equilibrium lie to the left instead.2082

These are going to have smaller K_sp values.2090

We can use K_sp to predict if a solution will form a precipitate2099

of the ionic solid given initial amount of the cation and anion.2103

This is done by simply assessing the reaction quotient Q, something we discussed in a previous lecture.2108

We compare it to K_sp.2114

Just like Le Chatelier principle, we are going to use the same principles here.2116

If Q is less than K_sp, we have the reaction shifting to the right because we don't have enough product.2121

Because it shifts to the right, that is away from the solid.2129

Precipitation will not occur.2132

However if we find and calculate that Q is greater than K_sp,2135

the reaction will shift to the left because we have too much product.2140

Because we are going toward the solid, this is the same as saying that precipitation will occur.2144

Now that we have gone through solubility equilibria and the solubility product constant K_sp,2154

let's go ahead and examine some factors that affect solubility.2159

When a solid salt is dissolved in a solution that already contains either the cation or2164

anion of the salt, its solubility will be found to be lower than in pure water.2169

This is what we call the common ion effect.2176

Let's go ahead and look at an example.2178

The solubility of lead(II) chloride in water is 3.9 grams per liter.2181

Calculate its solubility in 0.55 molar sodium chloride solution.2186

We have solubility in water to be 3.9 grams per liter.2192

We are asked to calculate the solubility in salt water.2197

Let's go ahead and set it up.2203

Remember we must always write out the proper equilibrium.2205

In this case, because it deals with solubility, it is going to show the ionic solid dissolving water into cation and anion.2209

PbCl₂ is going to go ahead and form Pb²⁺ aqueous plus two Cl^1- aqueous.2218

You see that we do have an initial amount of sodium chloride.2229

It is 0.55 molar and zero Pb²⁺; this is going to be +.2233

We don't use x anymore; instead we use s as a convenience to indicate solubility.2241

This is going to be +2s; this is going to be s.2247

This is going to be 0.55 plus 2s.2250

The K_sp for the lead(II) chloride is going to be given to you.2253

Or you look it up in your textbook; that is 1.7 times 10^-5.2257

That is going to be equal to the concentration of Pb²⁺ times the concentration of Cl^1- squared.2262

That is going to be equal to s times 0.55 plus 2s squared.2269

Because K_sp is relatively small, the approximation rule still applies.2275

That is s times 0.55; we can go ahead and solve for s.2281

That is going to be equal to 2.81 times 10^-5 moles per liter.2287

That is in salt water; in pure water, the solubility was 3.9 grams per liter.2298

You can easily convert grams per liter to moles per liter.2305

We get 0.015 moles per liter here.2308

As you can see, the solubility in salt water is much less than the solubility in pure water.2313

In other words, the common ion effect reduces the solubility of an ionic salt.2321

Common ion effect reduces solubility.2329

The common ion effect is one factor that affects solubility.2344

Another factor is when the solid salt contains the conjugate of a weak acid.2348

It is found that these salts are going to be more soluble when in acidic solution.2353

The typical example is going to be for example a metal carbonate, MgCO₃ for example.2359

MgCO₃ solid goes on to form Mg²⁺ aqueous plus CO₃^2- aqueous.2366

Something that can drive the reaction to the right is addition of acid.2379

Why?--because H₃O¹⁺ aqueous will want to go ahead.2384

It is going to react with the conjugate base of carbonic acid.2390

CO₃^2- aqueous plus H₃O¹⁺ aqueous is going to go ahead and reform part of the carbonic acid.2398

We are going to first bicarbonate aqueous and H₂O liquid.2410

As you can see, because hydronium is going to react with carbonate, it reduces the amount of carbonate.2417

That is going to drive the equilibrium to the right.2423

CO₃^2- will be consumed by acid driving the dissolution of magnesium carbonate.2427

Finally the last factor that influences solubility is of course temperature.2443

This is going to be true for all ionic solids.2449

Solubility is always enhanced with increasing temperature.2451

Basically the reason is because the thermal energy is going to become sufficient enough that2456

you can overcome the electrostatic attraction between the cation and anion in the ionic solid.2462

The last type of equilibria is what we call complexation equilibria.2473

Aqueous solutions that involve transition metal cations can also form from their aqueous cation and anion counterparts.2477

Can also form... excuse me... from their aqueous cation and anion counterparts.2488

Let's go ahead and show a representative equilibrium showing the formation of what we call a complex ion.2494

For example, Fe³⁺ aqueous can react with six equivalents of carbon monoxide gas.2499

That can go ahead and form Fe(CO)₆³⁺ aqueous.2512

We are going to get into these types of compounds in a later presentation.2523

But this is what we call a complex ion.2529

Basically it involves a transitional metal and what we call a ligand.2535

In this case, the ligand is going to be carbon monoxide.2543

The extent to which the complex ion forms can be described by its equilibrium constant.2547

In this case, K is equal to the concentration of Fe(CO)₆³⁺ divided by the2552

concentration of Fe³⁺ times the concentration of carbon monoxide raised to the sixth power.2562

Because this is involving complex ion formation, we don't just call this K_eq anymore.2571

But instead this is what we call K_f or the complex ion formation constant.2576

The main difference between K_sp and K_f is that they are opposite.2584

K_sp represents a breakup of a compound.2588

K_f represents the formation of a compound from its constituent ions.2594

While K_sp values tend to be very small, K_f values actually tend to be2599

just the opposite--quite large, several orders of magnitude, much much much larger.2605

Again that is what we call complexation equilibria.2611

Let's go ahead and summarize this very important part from general chemistry.2616

Equilibrium can be applied to various systems including acid base mixtures, buffers, titrations, solubility, and complex ion formation.2620

We found a very nice shortcut that we call the Henderson Hasselbalch equation.2631

This can be used to approximate the pH of a buffer system.2636

We found that during a titration, we can monitor the pH to yield or generate what is called a titration curve.2641

Finally we also saw that solubility product constants can quantify the extent to which an ionic solid is going to be soluble in water.2650

Let's now go ahead and jump into a representative sample problem.2660

This sample problem is quite long.2665

I have chosen an acid base titration on purpose because this is where students tend to trip up.2667

I want to go through how to calculate the pH along a titration curve in each of the four regions that we pointed out.2675

Exactly 1.36 grams of trimethyl amine is going to be dissolved in 250 milliliters of water.2683

Then 23.6 milliliters of hydrochloric acid was required to reach the equivalence point.2691

Basically we are asked to calculate the following.2698

The pH at the beginning of the titration which is region one.2700

The pH at the midpoint or halfway point... sorry about that... this should read or.2707

Because we are at halfway point, this is going to be region two.2718

The pH at the equivalence point which is region three.2724

Finally the pH after 27.50 milliliters of acid was added.2728

You notice that this 27.50, that is greater than the 23.60 which means we are after the equivalence point.2734

We are out of region three; we are into region number four.2742

Let's go ahead and do this.2748

When we go ahead and calculate the pH at the beginning of the titration, remember no titrant has been added yet.2751

Initially we only have the trimethyl amine; this is a weak base.2757

Let's get the 1.36 grams into molarity right away, 1.36 grams of the trimethyl amine.2765

We are going to go ahead and divide this by its molar mass which is approximately 59 grams.2777

That is going to give us 0.023 moles of the trimethyl amine.2783

We are going to go ahead; we are going to divide this, 0.023 moles.2792

We are going to divide it by the total volume at that point which is 0.250 liters.2800

We get the initial molarity of the base to be 0.092 molar.2804

Now it is just a typical equilibrium problem with direct reaction with water.2812

Let's go ahead and write out the equilibrium then.2819

Trimethyl amine aqueous plus H₂O liquid goes on to form HN¹⁺(CH₃)₃ and hydroxide aqueous.2821

Let's go ahead and plug in all our values.2841

That is 0.092 molar and 0 and 0; -x, +x, and +x.2843

This is going to be 0.02 minus x, x, and x.2851

Of course we are going to use K_b to go ahead and get x.2855

X is then going to give us the concentration of OH^-.2862

From there, we can go ahead and get the pH.2867

Of course we expect a basic pH greater than 7 because we only have base present in solution.2870

No titrant has been added in the form of strong acid yet.2878

That is part A; part B is very simple, the pH at the midpoint.2883

Because we can use the Henderson Hasselbalch equation, the pH at the midpoint is simply equal to pKa.2891

That is a very quick calculation there; not bad.2900

Part A is done; part B is done; region one and region two.2903

Let's go ahead and do part C now, the pH at the equivalence point, region three.2907

At region three, at the equivalence point, the moles of the base is going to be equal to the moles of the added acid.2915

Let's go ahead and get the moles of the acid then.2933

0.02360 liters times 0.974 molar, that is going to be equal to 0.0230 moles of HCl.2936

The acid is monoprotic; we don't have to worry about diprotic or triprotic.2951

Then it is a 1:1 ratio with this amine.2957

This is going to be equal therefore to 0.0230 moles of the trimethyl amine that we had initially.2960

Let's go ahead and write out the neutralization reactions.2970

That is going to be HCl aqueous plus the trimethyl amine aqueous.2973

That is going to give us HN¹⁺(CH₃)₃ and then Cl^1- aqueous.2983

Let's go ahead and plug in all our values--0.0230 moles, 0.0230 moles, and then 0 and 0.2992

Again this neutralization reaction, 1:1 ratio, we have the identical amounts of each reactant.3004

All the reactants are going to be consumed entirely; this is -0.0230 moles, -0.0230 moles.3010

This is going to be +0.0230 moles and +0.0230 moles.3020

This goes as 0; this goes as 0.3029

This is 0.0230 moles; this is 0.0230 moles; the neutralization step is done.3033

Now we can go ahead and proceed on to write the equilibrium with direct reaction with water.3043

You have to choose: is it going to be the conjugate acid or is it going to be Cl^-?3049

We already know from a previous lecture that Cl^- is the conjugate of HCl.3056

It will not react with water to reform HCl.3063

Therefore you are going to select the conjugate acid of the amine.3066

HN(CH₃)₃¹⁺ aqueous direct reaction with water goes on to form H₃O¹⁺ aqueous and the trimethyl amine weak base.3071

This is going to be 0.0230 moles, 0, and 0.3092

Remember final values of table one become initial values of table two.3100

This is ?x, +x, and +x; this is 0.0230 minus x, x, and x.3103

You are going to use K_a for this expression.3113

K_a is going to be equal to the following expression: x squared over 0.0230 moles minus x.3116

Again we need to get moles into molarity.3128

This is simply going to be 0.0230 moles divided by the total volume at the equivalence point which is going to be 0.2736 liters.3132

When all is said and done, you can go ahead and solve for x.3143

X will give you the hydronium ion concentration which will then get you to pH.3148

As you can see, this titration was a weak base with a strong acid.3154

We had better expect the pH to be acidic or less than 73159

as we saw in the previous slide where we introduced the graphs.3163

That is going to be the case because we only have hydronium being formed with no hydroxide.3168

That is region three.3175

Finally let's go ahead and solve how to do region four.3177

In region number four, we have nothing but excess titrant added; region four, extra HCl added in this case.3181

What you need to calculate is the amount of HCl remaining after neutralization.3194

Need to determine amount of HCl leftover after neutralization has occurred; after neutralization.3201

We know that 23.6 milliliters was required for neutralization.3222

Here we are given a total of 27.5 milliliters; we are just going to subtract.3227

That tells us that 3.9 milliliters of HCl still remains after neutralization.3234

Because this is a strong acid, we can use the pH equation directly.3243

Right now we need to get this into molarity.3248

We are going to say 0.0039 liters of the HCl.3255

We are going to multiply that by the molarity which is 0.974.3259

That is going to give us moles.3265

To get the molarity, we are going to divide by the total volume at that point.3267

The total volume at this point is actually 0.2775 liters.3271

That is going to give us our concentration of HCl which because HCl is monoprotic, gives us the concentration of H₃O¹⁺.3279

From there, we can go ahead and calculate the pH.3289

Again because this is region four of this titration curve, the pH had better be3293

much less than 7 because this is the titration of a weak base by a strong acid.3299

At this point, we have nothing but strong acid remaining.3304

Again this as you can see, each of the four different regions of3311

a titration curve require its own different strategy for solving the pH.3315

I want to thank you for your time; I will see next time on Educator.com.3321