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Euter Jour answer in the provided box: container of volume 2.50 L aud at 4 temperature of 25PC exerts sample of nitrogen gas kept of4.90 atm. Calculate the number o...

Question

Euter Jour answer in the provided box: container of volume 2.50 L aud at 4 temperature of 25PC exerts sample of nitrogen gas kept of4.90 atm. Calculate the number of moles of gas present: pressuremol

Euter Jour answer in the provided box: container of volume 2.50 L aud at 4 temperature of 25PC exerts sample of nitrogen gas kept of4.90 atm. Calculate the number of moles of gas present: pressure mol



Answers

A sample of nitrogen gas kept in a container of volume $2.3 \mathrm{L}$ and at a temperature of $32^{\circ} \mathrm{C}$ exerts a pressure of 4.7 atm. Calculate the number of moles of gas present.

This is question 34 from chapter 16 and we have a 19 gas at 4.5 leaders and 27 degrees so excused, and we're going to see how much most of gases emit. So we're gonna be seeing the ideal gas accordionists PV is equal to in our tea. Okay, Now too soft. Resigned from moles of gas and the equation is gonna be rearranged to look like in its pressure times volume divided by oh, are t So when you put these in, the numbers in pressure is for 0.1 promise your pressure times of all you four point five leaders divided by the costs and are which is 0.0 a Teoh six. And the temperature and temperature in this equation has to be expressed by Kelvin. So if we have 27 degrees associates to get the coven temperature, we have to add 273 which comes out temperature of 300 come in. And this only goes for n to be zero 0.0 seven by most

Street forward. Ideal cast looks a problem, except for we're given degrees Celsius instead of degrees. Coffin. We just take the number of degrees Celsius. We had 273 point on 500 to get Calvin. Then we put it in. Multiply pressure from defying, then multiply. Then, um, the great constant time temperature divide you get 6.85 each. The negative three walls or 100868 vitals.

In this problem, we're being asked to find the amount of moles of the gas given its temperature, the volume of its container and the amount of atmospheres of pressure that it is exerting on its environment. All of these conditions should remind you of the ideal gas law whose equation looks like this. The pressure of the gas that it is. The pressure that the gas exerts on the environment is equal to the volume of the container times the moles of gas times the gas constant times the temperature. Now we want to find the moles of gas. So we're going to rearrange this expression so that n is at the beginning. That's what we have, is and equals the pressure divided by the volume, the gas constant and the temperature in this case, the gas constant, which is represented by the Capital Letter R is going to be 0.8205 leaders atmospheres, um, divided by more Kelvin. So now what we can do is plug in all of our given values to this new equation. So what we have is and eagles the pressure which was given to us as 3.81 atmospheres divided by the volume of the container, which is 0.44 leaders times the gas constant, which we found as 0.8 to 5 leaders atmospheres over more Calvin. And if we look att tthe e units that we have here, we need to find temperature and Kelvin. But we were given it as 25 degrees Celsius. That's what we need to do now is convert this value into Calvin by adding 273. So what we get is 298 Calvin. Now we can make sure that we have all our correct units by trying to cancel them out. Take away the leaders, the atmosphere's and the Calvins. And what we're left with is moles, which is exactly what we want to find. So you put all these numbers into our calculator and we get 3.54142 etcetera, which needs to be rounded down to the correct amount of significant figures. We find the correct amount by seeing the smallest amount of significant figures in the values that we plugged in, which happens to be this volume here. It only has two significant figures. Therefore, the answer to this problem is going to be 3.5 moles of gas.

We're gonna do this equation two different times for two different temperatures, one for 25 degree Celsius. And then when we increase, you could get 40 93 Celsius from both cases ever. Interesting thing, but I'll walk through them separately. So for 25 degrees Celsius are we need to convert that into Calvin in order to kill Castle off. So we do. 25 post 3 73 which is 298 Calvin. Well, then take our ideal gas law, which is PV equals energy. And we divide by our key. So you have end number moles by itself. That's PV equals party, which is this right here. Now we just blood things in were given. That is 3.5 team When won't buy that bike that, given two leaders divide that by the great points. You're 821 times temperature t. So everything's gonna cancel E t m. Any team cancel leaders and leaders canceled. Calvin, I'm comin. Cancel. Which did you just moves left? So you multiply the 1st 2 together want by the last two together. And if I talked my bottom and you get 2.86 miles number under the exact same thing. But for temperature we have our 49 degrees Celsius. I need to convert again. Asked me that 2 73 You get 300 when you do Kelvin. So 24 degrees Calvin in Qatar. We're going to use that same equation and equals P v rt and everything that you're plugging in to repeat the same, except for the number of Calvin at the end. So once again, everything's kind of cancel. Multiply that same way by multiplying the two and the denominator and the 21 numerator together before the fighting. And when you have 322 Calvin and instead of 2 98 we have slightly last malls, 0.265 moles told. So just to clarify at 25 degrees Celsius or 298 Calvin were expected to get 0.26 moles. But when we increase the temperature 48 Govan 48 degree Celsius 322 Calvin, we have a slightly lower number of moles of Europe went to 65


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