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Consider the reaction $$\begin{aligned}\mathrm{H}_{2}(g)+\mathrm{Cl}_{2}(g) \longrightarrow & 2 \mathrm{HCl}(g) \\\Delta H &=-184.6 \mathrm{kJ} / \mathrm{mol}\end{aligned}$$ If 3 moles of $\mathrm{H}_{2}$ react with $3$ moles of $\mathrm{Cl}_{2}$ to form $\mathrm{HCI}$, calculate the work done (in joules) against a pressure of $1.0 \mathrm{atm}$ at $25^{\circ} \mathrm{C}$. What is $\Delta U$ for this reaction? Assume the reaction goes to completion.

$-553.8 \mathrm{kJ} / \mathrm{mol}$

Chemistry 101

Chapter 6

Thermochemistry

Rice University

Drexel University

University of Maryland - University College

Brown University

Lectures

05:27

In chemistry, a chemical reaction is a process that leads to the transformation of one set of chemical substances to another. Both reactants and products are involved in the chemical reactions.

06:42

In chemistry, energy is what is required to bring about a chemical reaction. The total energy of a system is the sum of the potential energy of its constituent particles and the kinetic energy of these particles. Chemical energy, also called bond energy, is the potential energy stored in the chemical bonds of a substance. Chemical energy is released when a bond is broken during chemical reactions.

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Consider the reaction$…

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Consider the reaction $$\b…

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Consider the reaction at $…

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Calculate $\Delta H_{\math…

So here we have a fun little chemical reaction taking place where we have hydrogen gas and chlorine as chloride in its gas form are reacting to form hydrochloric acid in its gas form. And we see their uh equations balance, which is great. We have two hydrogen is to chlorides. There's two coefficient applies to the hydrogen and chlorides, meaning that equation is perfectly balanced. We have two hydrogen to chlorides on both sides of the reaction. And we're told a few things about this reaction. So first of all, the entropy which we can think of as being uh the heat released. That that's a good thing to think about Is negative, 184.6 kg per mole. And if it's negative, that normally implies that he is being released. Okay, So we're also told some of the other units of different measurements that are going on. The pressure is one atmosphere And the temperature is 25°C.. We're also told that in this reaction we have three moles of hydrogen reacting with three moles of chloride. So how do we progress from here? Because the first thing it asks us to do is calculate the work done in jewels. So how do we actually calculate work? Well in a physics con context, we understand work is being some force with some displacement, and we can apply this with chemistry as well because we think about the movement, this is going to be the volume, because if something is changing and it's the size it occupies, there's going to be a change in the distance that something is covering and then pressure is going to be our our force here. So that would mean the force that is being exerted against the outside of a container. For example, if we have a bike tire, it was gonna be a certain pressure in the tire due to the gas that is pushing against the the actual tire that was in, that the rubber parts on the outside. So this is how we define work and actually solve for it. So how do we progress from here? Well, we're given the pressure at one atmosphere, were given the temperature which is not really relevant for this part of the question. So we have the pressure. That's something good to think about and then we can think about the volume. That's only other thing. We really need to solve this problem. So one of the best ways to go about solving for volume is using an ideal gas law or we have PV equals N. R. T. And just for a really quick review, he is equal to pressure. V. Is equal to volume and malls are is it constant and T. Is temperature. So let's rearrange the equation to solve for V. So V equals and our T divided by P. So how do we progress from here? Well, we know the moles of the reactant. We have three moles of H2 and three moles of cl two. So let's just write the volume of the reactant trying to find the change in volume. Remember? And change is always ah it's a comparative term. So the change of volume here is just going to equal VF minus V. I. Because we're looking to change the difference. So the volume of the reactions, which let's just use our let's make a little more easy on us. Lower case R It's the volume of the reactant Is equal to end, which is six miles in total. Right? Three plus three. Let's just write as three plus three for moles. Just so we're not just skipping things mentally and we don't get confused on the line. We can keep our as it is. I'll recommend doing so because it's a constant right Temperature, we're told it's 25 as well. Okay. And then the pressure is going to be one. That's how we find the volume of their accents. But before we solve this, let me just point something very interesting out to you. Now, if you look at the final, we have to look at what the variables will be. So we're setting it up the same, it's the same equation we have end for the moles. So we're told that we have three moles of H two and three moles of cl two. But if we look at the reaction, If this is three and this is three, then to balance this, There's two. Here, we have to change is to be a six because we have to have the same amount of elements on one side or the other. So it really turns out we'll have six moles of hcl. So just before we even solve for this, just see what is going on here and I'd like you to try and predict what is actually going to go now, we can just cross off are from this equation, because it's the same in both, it's a constant. We could even cancel out the rest of this as well if you wanted to because it's the same for both equations. So if we were to set him equal to another, these would cancel out. So if we would apply things, so Delta V Physical too, VF, which is six Course It's not six, but this is just, I'm just trying to prove something to very quickly minus six. Now, it could be a 100 -100, it could be 10,000 10,000 to the point I'm trying to get across is it doesn't matter because even if we plugged in our as its official value, we plugged in the 25 be divided by one, which of course divided by one, doesn't do anything. Meaning if we actually didn't cross these off and just solved the equation by plugging everything in manually and you get any more accurate relevant numbers, it was still equal zero for change in volume, it's still zero. Now if we know anything about arithmetic, we know that Anything multiplied by zero is 0. So the pressure is one time 0 zero. So what is the work done in killing tools? Zero killer jewels is the amount of work done here because we don't have any change in volume. So there can be no work done. It doesn't matter how hard that pressure is pushing against uh the container it's in. If there's no change in volume, there's no work done. So that is the first part of the problem. The work is zero kill rituals. Okay. So that was a little bit of a conceptual test. So it makes us think we're gonna do a big calculation. But if we understand the terms and the concepts applied here, we can just understand that work is going to be zero. There's no actual calculation. It's more of a conceptual understanding. So now we need to calculate dealt to you. That's the next part. So Delta U. Of the reaction is what now we have to know some other equations to proceed here. And in case you're wondering, there's some textbooks which refer to dealt to you as delta E. They're both just referring to the energy in a system internally in a system before it's being acted on buy whatever else. So, and this is the change, right? Delta the triangle means change. So what are some equations that would be very useful? Well we know that delta your delta E. Let's just use DELTA you because that's what the problem asks for. Same term though to be like spelling gray with an E R N. A. It's the same thing. An equation would be Q plus W. Now here's where things get a little bit fun. Here is where we have some fun. This is a fun thing because we don't actually do very much arithmetic and thought anymore hints. I'm going to give you another equation where we have the entropy is delta H. But there's another equation that we know. So delta H is equal to delta E. We always use dealt to you that it doesn't really matter again. But let's just try and make things a little less confusing is equal to delta you. That's you plus pressure, multiplied by the change in volume. Now this is where we going to do a little bit of substituting, This is where we can see that pressure most of the by the change volume is just W. So this is just equal to dealt to you plus work. Alright. We're just substituting working for this variable here. That's all We're doing. Just a little bit substitution because we see that things equal and we already know the work is zero. So we know that delta H is equal to the work down in the system, which makes perfect sense. So delta delta you is equal to the same as our our entropy given to us at the very beginning of the problem negative 148.6 kg per mole. It's that simple for this problem. It makes it seem like it's more uh hard and there's more than its correct out to be. But there's no actual change in pressure or temperature given to us the beginning of the problem and because it's set up the way it is, everything has to stay the same as far as uh the volume is concerned. So this is going to be our second answer. Or we can just know that entropy will be the same thing as ah the internal energy or internal energy of the system which is dealt to you.

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