Best Answer:
there is no reason to use the "combined gas law" for this problem. that is a roundabout way to get the answer. Anytime you use "roundabout" ways, you add risk of making errors. Your goal should be simplicity and consistency and the lowest # of calculations possible. So just use PV = nRT and solve directly.

PV = nRT

T = PV/(nR) = (5.4atm) x (120L) / [(0.08206 Latm/moleK) x (4 moles) ] = 1974 K

this should be reported as 2000 K with 1 sig fig.

*** update ***

so let's look a the two types of answers you have here.

T = PV/(nR) = (5.4atm) x (120L) / [(0.08206 Latm/moleK) x (4 moles) ] = 1974 K

advantages...

• straighforward logical approach. you have an equation, plug in the values

• 1 equation to use

• easily derived from the ideal gas law. it's a simple algebraic rearrangement

• easy to know what variables are what values

• easy to watch units cancel

• easy to follow sig figs.

dissadvantages.

• you must remember the value of R. (and there are two that you need to memorize for chemistry. R = 0.08206 Latm/moleK = 8.314 J/moleK)

• you may need to convert units.

*******

now look at this.

4.0 moles of gas at STP (273K and 1.0atm) occupy 4mol x 22.4L/mol = 89.6L.

Using the combined gas law:

P1V1T2 = P2V2T1.

1.0atm x 89.6L x T2 = 5.4atm x 120L x 273K.

T2 = (5.4 x 120 x 273) / 1 x 89.6 = 1,974.4K - 273 = 1,701.4°C

advantages.

• you don't need to remember R

dissadvantages

• complicated approach (assume that number of moles is at STP - not the given T and P, then calculate volume @STP, then convert volume at STP to volume at the given T and P). Some might call this "spaghetti logic" because of it's complexity

• you do have to remember 22.4 L / mole.

• you do have to remember P1V1T2 = P2V2T1 (usually written P1V1/T1 = P2V2/T2)

• you have 6 variables, P1, V1, T2, P2, V2, and T1 to decipher and plug in values for. huge opportunity for errors. is P1 = 1 atm or 5.4 atm? Is T1 = 273 or is T2 = 273? Am I solving for T1 or T2? is V1 = 120L or is V2 = 120L?

• you have to do the math correctly. you have to convert correctly in the first step and solve for V2 correctly in the second. And plug all the numbers into your calculator correctly. There are literally 5 x and / steps in this method vs 3 in the other.

• you have lower precision. You have rounding errors in the first step that carry over into the second.

• It's nearly impossible to watch units cancel without carrying them along

• it's difficult to track sig figs. That first step should have 1 extra carried over into the second. then how many should be in the final answer?

*******

I know that there are some here without any training in this subject matter that will argue differently. And that's ok. Let them. They're not taking the class. They're not responsible for learning this material. You are. So you will have to make decisions about how you want to go about learning this material and handling test questions. Make good ones because this is YOUR future, not mine nor anyone elses.

My opinion, have taken ALL the chemistry classes, having obtained my Ph.D. in chemical engineering, having taught this subject matter to undergraduate university students, and having worked as a professional chemical engineer for a long time now is this. The simplier = the better. The more straightforward = the better. The less probabilty of errors = the better. And this problem can and therefore should be solved directly.

T = PV/(nR)

except in the case where you cannot remember "R"

*** update for Norrie ***

some additional comments for you to think about

1) the thumbs down Jacob and I received were from YOU! YOU are the dreaded "thumbs downer". You give thumbs down ratings to answers for reasons other than the intended reasons of the thumbs up and down. Which is peer review of the quality of the answer. YOU rate for retaliation. vindication. I rate because an answer is good or bad. So which one of us is the grown up here?

2) I gave your answer 1 thumbs down for using the combined gas law to solve this. It is NOT the best approach. It is NOT what I recommend. It is prone to errors. As you have demonstrated frequently in the past.

3) the NUMBER you calculated is the same as mine. That is TRUE. But your approach is NOT. And you must be blind to think it is.

4) my rating is based on my educational experience. I have taught this material to students at the university where I obtained my Ph.D. I have watched and graded countless students as they completed homework assignments, quizzes and tests. And of course, I've taken the classes and the tests. And without a doubt, the students who sit there sorting through spaghetti logic like your answer here during exams are the ones who fail. They waste too much time solving SIMPLE problems that could be solved DIRECTLY. The A students are the ones who practice simplicity. And if you have ever taken a university level chemistry exam, or even an AP exam, you would know exactly what I'm talking about.

Which is exactly my point. The METHOD of solving all of these problems posted here on YA is more important than the actual calculated value. Your method is not the method I recommend. So your answer gets a thumbs down from me.

do you understand now?

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