Learn the toughest concepts covered in your Analytical Chemistry class with step-by-step video tutorials and practice problems.

Chemical Equilibrium

** Gibbs Free Energy** represents the maximum amount of work that can be done by a thermodynamic reaction at constant pressure and temperature.

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Gibbs Free Energy

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When it comes to our understanding of spontaneous versus non spontaneous reactions were gonna say that the variable of gibbs free energy is right in the center of everything. If we know what the sign of delta G is, then we can determine if a reaction is spontaneous, non spontaneous or at equilibrium. Now we're gonna say here spontaneous reactions can occur without any outside energy being invested while non spontaneous reactions cannot occur unless you do put in energy for it to work. Now, we're gonna say here, we have spontaneous non spontaneous and reactions that are at equilibrium when it comes to reactions that are spontaneous. We're gonna say when it comes to our energy diagram, our y axis will be delta G, which is our free energy and then our X axis is just the progress of the reaction itself. We're gonna stay here for a spontaneous reaction. Your products at the end will have lower overall energy, which is meaning it's more stable. Lower energy for your compounds means more stable compounds here, for delta G, delta G. Here would be products minus react ints. And because your products are at a lower level, that means that delta G here will be negative, meaning that it is an Xr organic process. So, for spontaneous reaction, DELTA G will be less than zero. When you're a spontaneous reaction, your reactant go to completion. So you have a solid arrow going forward, meaning that you make 100% of your products. If you're a spontaneous reaction, according to the second law of thermodynamics, the entropy of the universe has to be greater than zero. If you're a spontaneous reaction, it also means that your equilibrium constant, K has to be greater than one. Finally, if you're a spontaneous reaction, it means your reaction quotient Q will be less than K. Now Q is basically a way of determining if you write equilibrium or not wherever Q is, It will shift in a direction necessary to get to equilibrium, which is K. So if you're a spontaneous reaction, Q is less than K. You'll have to move in the four direction to get to K equilibrium over time. So all these things can be said about a spontaneous reaction. We can say that the delta S of the universe is greater than zero gibbs. Free energy is less than zero. The equilibrium constant K. Is greater than one Q. Is less than K. And therefore the ford direction is favored, which is why the arrow goes in the forward direction and being a negative delta G. Means your eggs organic. Now, here, if we look at a non spontaneous reaction, exact opposite for almost everything. So here are entropy of our universe will be less than zero. Gibbs. Free energy will be greater than zero, meaning your products at our are at a higher energy state than your reactant, which is not favorable. So here would be positive, which means that this is an ender gone IQ process where energy has been absorbed. So that's why your products are at a higher energy state and then your equilibrium K would be less than one, Q would be greater than K, which is why our reaction favors the reverse direction. Okay, so we're gonna say here for non spontaneous process, the four direction is not favored. So the four direction is non spontaneous, which is not favored, which means very little product is being formed. Notice the difference in a row sizes, The four direction arrow is much smaller than the reverse direction. That's because if you're non spontaneous in one direction, you're spontaneous in the exact opposite direction. So here going in the reverse direction, we have a larger era to show that the reverse direction is favored. Finally, if you're an equilibrium, we're gonna say The entropy of our universe is equal to zero. Delta G is equal to zero. Therefore the difference in energy between my reactant and products um is zero. There is no difference. The same energy state. K will be equal to one and Q will be equal to K. So there will be no shifting of my chemical reaction in either direction because we've reached equilibrium status. Now, in addition to this, we can say that gibbs free energy can be calculated through the use of various equations here are some of the most common ones here, we have delta G gives free energy equals delta H, which is my entropy minus temperature in kelvin times entropy which is delta S here. It can be under nonstandard conditions or it could be under standard conditions where we have the little zero. Now, standard conditions means that my pressure is one atmosphere, My temperature is 25°C and my concentration is one molar. So that's what standard condition means. And that's when we have these little zeros here. Up top. Now, we can also say we can calculate gibbs free energy under nonstandard conditions. A second way where we use the gibbs free energy under standard conditions plus R. T times L N Q. R is our constant, which is 8.314 jewels over most times K T. Is temperature in kelvin. Que is just simply our reaction quotient. Remember your reaction quotient as well as your equilibrium constant. Both equal products. Overreact ints. Both of them ignore solids and liquids. Finally, we can have Gibbs. Free energy under standard conditions equals negative. R T L N. K. Again, R is the same 8.314 jewels over most times K. Constant. So just remember when it comes to determining spontaneity of a process, gives free energy is a great variable to use to determine the overall spontaneity of everything. It's more useful than taking a look at delta H and delta S alone because it can incorporate both those variables within its equations. Now that we've gotten this out of the way, we'll take a look at the example given below in the next video attempted on your own. But if you get stuck, don't worry, come back and see how we approach that same example question.

2

Gibbs Free Energy

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So, recall that a spontaneous reaction is one that happens naturally without the need of outside energy, whereas a non spontaneous reaction is one that doesn't normally occur unless some outside forces in play. So, if we take a look here, we have to figure out which of the following is an example of a non spontaneous process. Alright, so first we have ice melting at room temperature. Now we know that as long as the temperatures above zero degrees Celsius, which room temperature is, ice will naturally melt because this happens in real world scenarios, it is a spontaneous process. Next sodium metal reacting violently with water. Uh this one probably not as well known, just remember here that when it comes to group one A and two, a metals, because of the low number of valence electrons they have, they will violently react with water in order to lose an electron to become more like a noble gas. So here this is true, because it happens naturally in the real world. It's a spontaneous process here rusting of iron at room temperature. So, old cars when it rains, they can rust. This is a natural process that happens every day. And because of that, it's a spontaneous process, a ball rolling downhill. So a ball can naturally roll down a hill using its momentum as well as gravity to push itself down that hill, we can see that this happens um just by imagining it, you can take a ball and throw it down a hill, you'll see it roll down naturally. So it's a spontaneous process. Now, even if you weren't able to determine if the initial four were spontaneous or not, you should know that E is a non spontaneous process here. It says water freezing at room temperature, Room temperature is much too warm for water to freeze. Water has to be at 0°C or lower in order to begin to freeze. So we should know that this makes no sense. It's not a natural occurrence. It could only happen if we invested some outside energy. For example, we have a refrigerator where we put a nice tray in the refrigerator is in a room at room temperature, but inside the refrigerator it's much lower than that. They're therefore water could freeze. So the last option here, we're going to say, does not naturally occur. Water will not freeze at room temperature under natural conditions. Therefore, it is the process that is non spontaneous. Also remember, as we set up above, spontaneous reactions move in the four directions, they never move in the in the reverse direction, because if it's spontaneous, it's gonna move forward. It is non reversible or irreversible. Non spontaneous processes are not spontaneous in the four direction, so they tend to move in the reverse direction to become spontaneous. So non spontaneous processes are reversible

3

Gibbs Free Energy Calculations 1

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So here it says consider the decomposition of a metal oxide to its elements or M represents a generic metal. So here we have M 304 solid decomposes to give us three moles of em solid plus two moles of oxygen gas were also given the Gibbs free energies of formation. So delta G. F. Here Of these four separate compounds. Now, if we look at Part one, it says what is the standard change and gives energy for the reaction as written in the forward direction. So they're asking us to find delta G of the reaction. And standard here means that we have this little circle here. So remember whether you're looking for delta G of reaction delta S of reaction or delta H of reaction. All of them equal products minus react ints. So products minus react ints, realize here that the gibbs free energy of formation for em solid and oxygen gas are both zero. That's because when an element is in its natural standard state, it's gibbs Free energy will be zero, just like its entropy would be zero. So here we're gonna say we have three moles of em solid which really isn't gonna change anything. And the three comes from here times zero plus two moles. Oh, to each one is also zero minus, we have one mole of em 304. It's gibbs free energy of formation is this negative 9.50 killer jewels per mole. Okay, so all of this here is zero, so we can ignore that and we have a negative of a negative which comes out to a positive. So that's a positive 9.50 killer jewels because you're the most cancel out now for part two, it says what is the equilibrium constant of this reaction as written in the four direction? At 298 kelvin. So from the previous page we've seen that delta G can be connected to our equilibrium constant K. By this formula. So delta G equals negative R. T. L. N. K. But here's the thing, we don't want to find delta G. We already found out in Part one. Now, in part two, we're looking for what our equilibrium constant K. Is finding K means we rearrange the equation now to become K equals E. Which is the inverse of the natural log to the negative delta G. Zero, divided by R. T. So this is the equation we're gonna use now. So it's E to the negative are here has isn't jewels. So we're gonna have to convert the delta julie found earlier also into jewels. So remember, one killer jewel is equal to 1000 jewels. So that's 9500 jewels. So 9500 jewels Per mole here divided by 8.314 jewels over most times K. Which is the value of our our constant. And the temperature here is 298 Kelvin here, Mosul cancel out jewels will cancel out and kelvin's will cancel out, meaning that our equilibrium constant has no units. So this becomes E to the negative 3.8344. And when you plug that into a calculator, that's gonna give you 2.16 times 10 to the negative two for my value for my equilibrium constant. K. So now that we found that we finally figure out the last portion parts part three. So what is the equilibrium pressure of 02 over M solid at 298 kelvin. Alright, so now we're being asked to figure out the equilibrium pressure of this gas now here because they're using the coin, the terminology of equilibrium pressure or equilibrium concentration, that means we're gonna have to use the equilibrium constant. We just found so K equals products. Overreact ints. Remember your equilibrium constant ignores what it ignores solids and liquids. So this is a solid. So it's ignored, this is a solid. So it's ignored. So that means that your equilibrium constant is just equal to 02 Because there's a coefficient of two in front of that 02 in the equation that becomes the power. So it's 02 squared. All we do now is and we're gonna stay here since we're looking for equilibrium pressure. This is actually K. P. Now we're gonna say here K. P. Is the K. That we found here. That's 2.16 times 10 to the negative two equals The pressure, vote two squared. Okay, so technically because we're looking for the equilibrium pressure, we should have done this, We use that those brackets to represent concentration. If we're dealing with finding the equilibrium concentration of 02. So here now all we do is we take the square root of this side and the square root of this side. And what's left will be .147. When we're dealing with K. P. The units are at atmospheres, This represents the equilibrium pressure of 0.2 gas. If we're asked to find equilibrium concentration we would have used K. C. And it would have looked like this in that case when we took the square root of both sides, we have found our answer in polarity but again, we're looking for equilibrium pressure here and not equilibrium concentration. So realize these are the fundamental steps you need to take whether you're looking for the gift free energy of a reaction, your equilibrium constant or either equilibrium pressure or equilibrium concentration of any given compound within your balanced equation. So keep these in mind As you approach questions like this later on now that you've seen this example. Look to see if you can do example to that's given below remember we have the equations that relate Delta G2 different variables on the previous page utilize one of those equations to help answer example to once you've done that you can come back and see how I approach that same example to question

4

Gibbs Free Energy Calculations 1

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So here we're told for the reaction of two moles of carbon graphite reacting with one mole of hydrogen gas produces one mole of ethylene gas. Here we're told that gives free energy under standard conditions is 209.2 killer jewels at 25 degrees Celsius. Now we're also told that if the partial pressure of hydrogen gas equals 100 atmospheres and the partial pressure of ethylene gas equals 0.10 atmospheres, calculate gibbs free energy under nonstandard conditions for the reaction. So here we're dealing with gibbs free energy under standard conditions and nonstandard conditions. So the equation that connects them together is gibbs, free energy under nonstandard conditions equals gives free energy under standard conditions plus R T L N Q. Remember Q is just your reaction quotient, it's equal to products overreacting, just like your equilibrium constant and just like your equilibrium constant, we're gonna ignore solids and liquids. So here this would be C two H two Divided by H two. Here we're gonna plug in their partial pressures, technically again we're dealing with pressure. So technically we should only reserve brackets when we're dealing with concentrations. So technically it's P C two, H two. And then ph two here on the bottom. So here my Q would be 0.10 divided by 100 for Q. Now here are has jewels in its units. So we should convert the 209.2 killer jewels into jewels. So remember, one killer jewel is equal to 1000 jewels. So that's 209,200 jewels. So take that number plug it in. Plus our which is 8.314 jules over moles. Times K Temperature has to be in Kelvin. So to the 25°C, you add to 73.15 Which comes out to 298.15 Kelvin And then Ln of 0.10 divided by 100. So here When you work this out, that's gonna come out to be 19, jules as our units. But all the answers here are in killed jules. So we do one more conversion. So remember one killer jewel is equal to 1000 jewels. So that's 192.077 killer jewels which rounds up to 1 92.1 killer jewels. Making option A are correct choice. So just remember in this question, we're dealing with gibbs, free energy, both under standard conditions and nonstandard conditions. So you just have to recall what equation connects those two variables together and then plugging desired units to find your answer at the end

5

Gibbs Free Energy Calculations 2

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So here it states sodium carbonate can be made by heating sodium bicarbonate here, it says, given that the entropy under standard conditions equals 1 28.9 kg joules per mole. And the standard gibbs free energy is 33.1 kg per mole at 25 degrees Celsius. Above what minimum temperature will the reaction become spontaneous under standard state conditions. All right, So, we're given in this question Delta H delta jean and temperature. We know the equation that can link these variables together is DELTA G equals delta H minus T delta S. They're asking us what minimum temperature. Now, normally for a question like this where they're asking for the minimum temperature or asking for the temperature to make it um spontaneous in general, we would set delta G2 equal to zero. The issue with that is if I said delta G equal to zero, I'm still missing another variable. I'm missing delta S. So, what I need to do first is I need to determine what DELTA S. Will be within this question. So, what we're gonna do first is we're going to figure out what DELTA S. Is. We're gonna input all the values we have for delta H delta G. And temperature right now, realize here we're gonna plug in delta G. Which is 33.1 killer jewels per mole. Delta H is 1 28.9 kg per mole. And remember temperature here needs to be in Kelvin. So, we're gonna add to 73.15 to this. So my temperature becomes to 98.15 Kelvin. And then here we don't know what delta S. Is, That's what we're solving for. So first we're gonna subtract 1 28.9 kg per mole. 1 28.9 killer jewels per mole. This cancels out here, we'll get here negative 95.8 kg joules per mole equals negative 2 98.15 kelvin times delta S Divide Out -298.15 Kelvin. So this cancels out with this. So at this point we'll have with delta S equals so at this point it equals 0.0.0.321315 killer jewels over moles times K. Now that we have, that we have to solve for the temperature needed for this question. So we write the equation again, Delta G equals delta H minus T delta S. This time to find the temperature, we're gonna set delta G equal to zero and we're gonna input the values we have for delta H. And our newly found delta S. So delta H is still 1 28.9 kg joules per mole. We don't know what the new temperature is. That's what we're solving for Delta S. Is 0.321315 killer jewels over moles times k. Like we found, subtract 1 28.9 kg per mole from both sides. So negative 1 28.9 kg per mole equals negative T times 0.321315 kg per mole times K. So divide all this out, so cancels cancels. So right now our temperature equals four. 64 kelvin. Now let's talk about this answer. This question is saying above what minimum temperature? Why exactly does it say above? Why doesn't it say below? Why doesn't it say act well. First thing we're looking forward to be spontaneous, right for us to be spontaneous? That means that DELTA G will have to be less than zero at exactly zero. We are at equilibrium. So at exactly this temperature, our reaction is not spontaneous. In fact it is at equilibrium. Alright, so we know why the answer is not exactly that number. But again, why is it above what minimum temperature? Why is it not below what minimum temperature? Well, if we think about the equation delta G equals delta H minus t minus t times delta S. We're gonna come up with this chart here. So here we're gonna have delta H. And delta H. Here it's positive and it's negative. Delta S. Here is positive DELTA S. Here is negative. Using this punnett square, we're gonna say that if delta H is positive and delta S. Is positive at higher temperatures, your reaction becomes spontaneous and it makes sense because if you think about it mathematically this number here will be positive minus this temperature, which is positive times delta S. Which is positive. Right? So think about it. You have these two numbers multiplying each other. So it's gonna be positive and the bigger this is, and it subtracts from this positive number, the more negative delta G will be. So the more spontaneous are going to be. So you would want the temperature to be as high as possible to make this a larger value, which subtracts from this positive here, if delta H is positive and delta S is negative, then we're non spontaneous at all temperatures, because again, this is positive, this here is positive, but now this is negative. So this is going to be a negative value and a negative minus a negative really means positive. So you're really adding to positive values together, giving you a delta G. That's positive. So there'd be no situation in which delta G could be less than zero here, you'd always be spontaneous. And then here you'd become more spontaneous to lower the temperature gets. So here delta S we found was a positive value, and delta H from the beginning was a positive value, meaning you fall right here, in terms of this punnett square. So the higher the temperature gets, the more spontaneous we get. That's why it says above what minimum temperature. So that that's why above this number, your reaction becomes more spontaneous. So, d would be our answer For to be four. To use the word below. We would have to fall here in the punnett square. That would mean that my delta S would have to be negative and my delta H. Would have to be negative. In that case we'd say the lower your temperature gets. So below what minimum temperature would you become spontaneous? So just remember um, words are important here. It helps us to determine basically if our reaction will be spontaneous or not. Think about what what conditions help to make delta G less than zero. The lower delta G becomes, the more spontaneous it becomes. And remember this punnett square to help you understand how the signs of delta H. And delta S. Have a direct relationship with determining the sign for delta G. Now that we've seen this one, and seeing this punnett Square, look to see if you can solve this question given to us below, recall all the things that we've said in terms of spontaneous reactions, direction that's favored and non spontaneous reactions and what direction is favored. Once you do that come back and take a look and see if your answer matches up with mine

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