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Calculate the expansion work done when 3.70 moles of ethanol are converted to vapor at its boiling point $\left(78.3^{\circ} \mathrm{C}\right)$ and $1.0 \mathrm{atm}.$

Now when we have the value of volume, we can measure the work:\[\mathrm{w}=-\mathrm{P} \Delta \mathrm{V}\]since ethanol was in its liquid phase, the difference between the two volumes is equal to the final volume previously calculated. $w=-1$ atm $x 101325 \frac{P a}{a t m} \times 0.107 m^{3}$$\mathrm{w}=-10841 \mathrm{J}$ The work is approximately $11 \mathrm{kJ}$

Chemistry 101

Chapter 6

Thermochemistry

University of Central Florida

Rice University

University of Kentucky

Lectures

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So for this problem, we're supposed to find the expansion work done when 3.7 rolls of ethanol converted to paper at its boiling point. So already from the problem were given some basic information, you know that end were the moles of ethno is equal to 3.70 We know the pressure is one atmosphere. We also know that the temperature is equal to 78.3 degrees Celsius. But really quickly on this temperature, we know that Celsius isn't the correct unit for wonder using gas equations. So we need to convert this to Calvin. And we know that you want to convert Celsius to Kelvin. Simply add to 73 to do that conversion and you get the temperature. And Calvin is 351.3 degrees. Kelvin. So that's the basic information that we know right after that. Then we'll be wanted. You was taken advantage of two different equations. The first equation we're going to use is that work is equal to negative pressure. Times change in volume. The second is the ideal gas law, which is that PV equals NRT. No, we know P and we know NRT. The only thing that we don't know is volume. So we're going to express the ideal gas so that it produces the volume, which is editor t over Pete. And once you find this value, we do, then plug it into that value and finally work. Done. So first, we're going to find volume via the ideal gas law. So volume equals moles. We already know that the malls is 3.7 because I was given to lessen the problem. They are constant is your point. You're 8 to 1 atmosphere. We're over Kelvin Moore. We know that the temperature is 300 and 51.3 degrees Kelvin. And finally, we know that the pressure is equal to to one atmosphere. When we plug all of that into the calculator, you get the The volume is 106 0.71 leaders. So now we need to convert this. And the reason that we're gonna convert this is because leaders, if the unit isn't going to be very ideal for us instead you want meters cubed and we know that there is 1000 leaders in one cubic meter. And so when you convert this We get that approximately. The volume is one point one or 0.1 of seven meters. Cute. So that's the volume that we're going to use in the equation. So now you're going to do the final step of this problem which is plugging this value back into the the equation for work, which is that work equals negative pressure. Times change in volume. So in this case, the change in volume is this value right here. We already solved that. Now for pressure, we're going to have to use a conversion. We know that the pressure is one atmosphere, but that isn't going to be very useful for us if we're going to find the work done which in the final units that we want his jewels or killer jewels instead, the unit that we're gonna need is Pascal's. So you know that the relationship between when a GM and one Pascal is that there are 101 0.32 pascal in one 18 so that we get that the pressure is equal to one a 1.3 to Pascal and we know that killer jewels were jewels can be expressed as meters Cube ties Haskell, so that essentially solves a problem for us. Now we just need to plug this into the final equation. We get negative pressure. Remember, you get the change in volume Jews 0.107 and when you plug it into your calculator, you'll get. But the final answer is about 10 or negative. 10 point age four one. Jules, our killer, Jal's naturals. That's the core cancer. And so, in this case, because it is negative, we know that the expansion work done must be a positive value. And when you take to count Sig Figs, you get the final answer is 10.8 killed Jules, and that is the final answer. Positive. 10.8 killer jewels.

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