Given the following sets of values for three of the gas...

Given the following sets of values for three of the gas variables, calculate the unknown quantity. a. $P=782.4 \mathrm{mm} \mathrm{Hg} ; V=? ; n=0.1021 \mathrm{mol} ; T=$ $26.2^{\circ} \mathrm{C}$ b. $P=? \mathrm{mm}$ Hg; $V=27.5 \mathrm{mL} ; n=0.007812 \mathrm{mol}$ $T=16.6^{\circ} \mathrm{C}$ c. $P=1.045$ atm; $V=45.2 \mathrm{mL} ; n=0.002241 \mathrm{mol} ;$ $T=?^{\circ} \mathrm{C}$

Transcript

00:01 All righty, so today we're going to be talking about using the ideal gas law to find unknowns in ideal gases.

00:06 And so our ideal gas law is pv equals nrt, and i have our r constant value written out over here at 0 .08206 liters atmospheres per mole kelvin.

00:15 So we start out with this one, and the first thing we notice is that our units won't cancel because our constants in an atmosphere in kelvin and our pressure is in millimeters mercury and our temperature is in celsius.

00:25 But our celsius temperature, we just add 273 .15 to convert us over to kelvin and we get 299 .4 kelvin.

00:34 So again, we go through and do our pressure conversion, just like we've done earlier in this chapter.

00:39 So we do 782 .4 millimeters of mercury.

00:51 And then we know that there are 760 millimeters of mercury and one atmosphere.

00:58 And so when we divide that out, we get that our pressure is one, 0 .029 atmospheres.

01:08 And then we plug all of this into our ideal gas loss.

01:11 So we have 1 .029 atmospheres.

01:17 Our volume is our x and then that's going to equal our n, so our 0 .1021 moles.

01:27 Our r which is our 0 .08206 liters atmosphere per moles kelvin.

01:37 And then our temperature, which is that 299 .4 kelvin.

01:43 And so we can go ahead and double check that our units cancel.

01:45 So we have atmospheres on both sides, moles on the top and on the bottom, and kelvin on the top and on the bottom.

01:50 So then we just do our algebra here to solve for x, and we get that x is equal to 2 .44 liters.

01:58 So now we'll move on to our next example, and this time we again have our temperature and degree celsius.

02:04 So we go ahead and add our 273 .15, and we get our 289 .8 kelvin.

02:11 So now we plug this in.

02:12 We're looking for pressure.

02:14 We know that our volume is 27 .5 milliliters.

02:17 We know we need it to be in liters for our gas constant, so we'll just plug that conversion factor into our equation here.

02:26 That's something you can do, especially if you're tied on time for exams.

02:30 And then our n is our 0 .0071812 moles.

02:38 Our ideal gas constant is 0 .0826, liters, per mole kelvin, and then our temperature is our 289 .8 kelvin.

02:58 So again, we do all of the math...

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