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A quantity of 0.020 mole of a gas initially at $0.050 \mathrm{L}$ and $20^{\circ} \mathrm{C}$ undergoes a constant-temperature expansion until its volume is 0.50 L. Calculate the work done (in joules) by the gas if it expands (a) against a vacuum and (b) against a constant pressure of 0.20 atm. (c) If the gas in (b) is allowed to expand unchecked until its pressure is equal to the external pressure, what would its final volume be before it stopped expanding, and what would be the work done?

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(a) $0 \mathrm{J}$(b) $-9.11 \mathrm{J}$(c) $2.4 \mathrm{L},-48 \mathrm{J}$

Chemistry 101

Chapter 6

Thermochemistry

Drexel University

University of Maryland - University College

University of Toronto

Lectures

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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.

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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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So for this question, we have a certain gas that is allowed to expand and need to calculate the work done and jewels as it expands under some Sercan dish in So throw against each individual part. We know that the governing equation to solving these kinds of questions with work and gases going to be work equals negative pressure. Times change in volume. So that is going to be main formula that we use for all three parts. So for part, a party says that it's allowed to expand against the vacuum. Well, any vacuum pressure zero. And if pressures euro, no matter what the change in volume is, the work must be zero. So that's the answer. Pretty simple. Party, Part B. It says it's allowed to expand against a constant pressure of point to a T M. So we just plug in the numbers into the equation. Executive point to a T M, and we know that the final volume it's half a leader. But the initial volume is 0.5 of a leader, and so that will get us the work over. We can't just plug this into our calculator, calculate the final answer because if you notice the units that we will get our leader times a t m. But the question access for the units to be done. You Jules. So we need to rewrite this expression so that it'll give us. Jules has finally unit, so trade this little smaller. That's what we have right now. So we need to find some conversion factor that gives us the jewels that we want His final unit in the numerator. So naturally we think of the gas. Constant are which says there's 8.314 Jules Permal Kelvin. So that gives us her first part. But we still have a problem here and that we still have leader of a team that we need to cancel out. We need to multiply by mole Kelvin, but we already know that That's another form of our you know, that that the other form of our maybe divide by it says this. And so this is a very useful conversion because that cancels out all of the units. So we want to counsel out for us. So instead, we know that from here, and I'll put in red leaders a t m. Those cancel out no more Calvin. Cancel out. And the only thing that we have left is the jewels like you wanted. So that's an example of how you would use to different conversion factors in order to get the final unit. When you plug all of that into the calculator, you get final work that is done is the negative 9.11 tool, part C. So for part C, it tells us that the gas allowed to expand unchecked until it's pressure is external pressure. So the first thing we need to do is we need to find its final volume. And so, in order to do that running Jozy Ideal Gas Law says that PV equals NRT. But we can rewrite this so that it solves for volume would be V equals and our t overpay. And we know all those numbers and we can just plug it in into the equation, for example, you know, But the number of moles of the asset we have is point oh, two animals, You know that are, as always, is you're appointed euro needs to one. You know that the temperature is 20 degrees Celsius, but nor did from worth at Kelvin meet ad to 73 and then we divide all that by the pressure which we know to be points to a kim. The reason why we know that to be pointed to a T M is because we know that it says that the pressure has to it expands until the pressure is going to be able to the external pressure. So you simply use the same pressure as part beat. When you plug all of that inter calculator, you will get the final volume of the gases 2.4 leaders that solves this. The first part of part C now I'll have to do is do the exact same thing we did for part B. You know that the pressure this point to a team, you know that the final volume was two point for Mr Truck, the initial volume to get the change in volume and just like last time, we need to multiply by two constants. First is 8.314 ticketus the jewels that we needed just like last time. So, Jules, over more okay, and then we have to divide by our, which will help us cancel out the market And that units, of course, is leader 10 feet. So plug that into calculator. You'll get that the work is negative. 48. Jules Night is the final answer.

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