Combined gas laws (Boyle's, Charles', Guy-Lussac's, Avogadro's) high school test question

[alpha male]

I was helping my kid study for a high school test tomorrow morning when
one of the fifteen questions confused me to no end.

It's either a badly written question or a well written one because it's
not obvious to us which is P1,V1,T1 versus P2,V2,T2.

Here's the question verbatim:

Q: The volume of a bicycle tire is 1.35 liters and the manufacturer
recommends a tire pressure of 125 PSI. If you want the bicycle to have
the correct pressure at 20 degrees Celsius, what volume of air is
required at STP?

For the life of us, we can't figure out for sure which is P1, V1, T1
versus P2, V2, & T2 simply because we can't fully understand the question.

Of course, the combined gas law to use would be:
P1*V1/T1 = P2*V2/T2

And, given all but one volume, we would get that missing volume using:
P1*V1/T1 * T2/P2 = V2

We can easily plug in the numbers ... but we're not sure if we even
understood the question (as to which is P1, V1, T1 versus P2, V2, T2).

Here's what we "assumed":
P1 = 125 psi
V1 = 1.25 liters
T1 = 293K (which is 273K + 20 degrees C)
---
P2 = 14.7 psi (which is 1 atmosphere at Standard Temperature & Pressure)
V2 = the unknown
T2 = 273K (which is 273K + 0 degrees C at STP)

Given that, we arrived at 10.7 liters for V2.

But, that's assuming we understood the question correctly.

In summary, given that question, what would you interpret P1, V1, T1 and
P2, V2, T2 to be as the starting point?

[Marvin the Martian]

Post by alpha male
I was helping my kid study for a high school test tomorrow morning when
one of the fifteen questions confused me to no end.
It's either a badly written question or a well written one because it's
not obvious to us which is P1,V1,T1 versus P2,V2,T2.
Q: The volume of a bicycle tire is 1.35 liters and the manufacturer
recommends a tire pressure of 125 PSI. If you want the bicycle to have
the correct pressure at 20 degrees Celsius, what volume of air is
required at STP?
For the life of us, we can't figure out for sure which is P1, V1, T1
versus P2, V2, & T2 simply because we can't fully understand the question.
Of course, the combined gas law to use would be: P1*V1/T1 = P2*V2/T2
P1*V1/T1 * T2/P2 = V2
We can easily plug in the numbers ... but we're not sure if we even
understood the question (as to which is P1, V1, T1 versus P2, V2, T2).
P1 = 125 psi
V1 = 1.25 liters
T1 = 293K (which is 273K + 20 degrees C) ---
P2 = 14.7 psi (which is 1 atmosphere at Standard Temperature & Pressure)
V2 = the unknown
T2 = 273K (which is 273K + 0 degrees C at STP)
Given that, we arrived at 10.7 liters for V2.
But, that's assuming we understood the question correctly.

You got it. One state is Standard temperature and pressure with an
unknown volume, the other is in the tire at 20 C.

Post by alpha male
In summary, given that question, what would you inter

pret P1, V1, T1 and

Post by alpha male
P2, V2, T2 to be as the starting point?

Huh. So, they're now screwing around with the definition of STP. I HATE
THAT.

http://en.wikipedia.org/wiki/
Standard_conditions_for_temperature_and_pressure#Past_use

I also hate that they hide the fact that in SR they once taught it as a
rotation in complex space.

[alpha male]

Post by Marvin the Martian
You got it. One state is Standard temperature and pressure with an
unknown volume, the other is in the tire at 20 C.

Thanks.

The trouble I had wasn't plugging in the numbers. It was figuring out
what the question was asking.

I wasn't sure what they were describing as the initial state.

For example, they started off with:
"The volume of a bicycle tire is 1.35 liters and the manufacturer
recommends a tire pressure of 125 PSI."

To me, that merely told me the initial volume (at some as-yet unspecified
temperature and pressure); and it told me the desired ending pressure (at
some as-yet unspecified temperature & volume).

The next half sentence was:
"If you want the bicycle to have the correct pressure at 20 degrees
Celsius ..."

OK. So now they supplied the temperature and pressure at the desired
second state.

At this point, we had (in this order):
V1 (the initial volume) = 1.35 liters
T1 (the initial temperature) = as-yet unspecified
P1 (the initial pressure) = as-yet unspecified
---
V2 (the ending volume) = as-yet unspecified
T2 (the ending temperature) = 20 degrees Celcius
P2 (the ending pressure) = presumably the recommended 125 psi

Given there are 3 missing unknowns, of course the expectation is that two-
of-the-three missing unknowns will be given in the rest of the sentence.

The rest of the sentence was:
"what volume of air is REQUIRED at STP?" (emphasis added)

The first problem I had with the question was the word 'required'. What
did that mean? Did it mean over and above the 1.35 liters which were
already inside the bladder? Or did it mean the total volume of the
bladder at the ending conditions?

But wait! They wanted the volume at STP. That means they wanted the
volume at 0 degrees Celsius (not 20 degrees). And, the ending pressure
was 1 atmosphere at STP (not 125 psi as 'recommended').

This question 'still' confuses me because the ending V2 T2 P2 is not what
I listed above as what the first half of the second sentence intimated.

Apparently, the ending V2 T2 P2 are:
V2 (the ending volume) = the unknown to be found
T2 (the ending temperature) = NOT 20 degrees Celsius but 0 degrees Celsius
P2 (the ending pressure) = presumably the recommended 125 psi

So now, the entire equation was turned upside down. The question made
little sense to me in the manner it was posed. They appeared to be
switching the ending temperature from 20 degrees to 0 degrees at the very
last moment. And they did the same with the pressure.

In the end, I resorted to the brain-dead method of simply plugging in the
numbers. To this moment, I still don't understand the question as it
seems to me the ending temperature is 20 degrees and 0 degrees at the
same time.

Likewise, it seems to me that the ending pressure is both 1 atmosphere
and 125 psi at the same time.

Obviously this is impossible so that's why I resorted to just plugging in
the numbers. Sad. But true.

[PD]

Post by alpha male

Post by Marvin the Martian
You got it. One state is Standard temperature and pressure with an
unknown volume, the other is in the tire at 20 C.

Thanks.
The trouble I had wasn't plugging in the numbers. It was figuring out
what the question was asking.
I wasn't sure what they were describing as the initial state.
"The volume of a bicycle tire is 1.35 liters and the manufacturer
recommends a tire pressure of 125 PSI."
To me, that merely told me the initial volume (at some as-yet unspecified
temperature and pressure); and it told me the desired ending pressure (at
some as-yet unspecified temperature& volume).
"If you want the bicycle to have the correct pressure at 20 degrees
Celsius ..."
OK. So now they supplied the temperature and pressure at the desired
second state.
V1 (the initial volume) = 1.35 liters
T1 (the initial temperature) = as-yet unspecified
P1 (the initial pressure) = as-yet unspecified
---
V2 (the ending volume) = as-yet unspecified
T2 (the ending temperature) = 20 degrees Celcius
P2 (the ending pressure) = presumably the recommended 125 psi
Given there are 3 missing unknowns, of course the expectation is that two-
of-the-three missing unknowns will be given in the rest of the sentence.
"what volume of air is REQUIRED at STP?" (emphasis added)
The first problem I had with the question was the word 'required'. What
did that mean? Did it mean over and above the 1.35 liters which were
already inside the bladder? Or did it mean the total volume of the
bladder at the ending conditions?
But wait! They wanted the volume at STP. That means they wanted the
volume at 0 degrees Celsius (not 20 degrees). And, the ending pressure
was 1 atmosphere at STP (not 125 psi as 'recommended').
This question 'still' confuses me because the ending V2 T2 P2 is not what
I listed above as what the first half of the second sentence intimated.
V2 (the ending volume) = the unknown to be found
T2 (the ending temperature) = NOT 20 degrees Celsius but 0 degrees Celsius
P2 (the ending pressure) = presumably the recommended 125 psi
So now, the entire equation was turned upside down. The question made
little sense to me in the manner it was posed. They appeared to be
switching the ending temperature from 20 degrees to 0 degrees at the very
last moment. And they did the same with the pressure.
In the end, I resorted to the brain-dead method of simply plugging in the
numbers. To this moment, I still don't understand the question as it
seems to me the ending temperature is 20 degrees and 0 degrees at the
same time.
Likewise, it seems to me that the ending pressure is both 1 atmosphere
and 125 psi at the same time.
Obviously this is impossible so that's why I resorted to just plugging in
the numbers. Sad. But true.

While I think the problem was worded with a touch of ambiguity, I think
you've overthought things. My first reaction when I read the problem
was, "OK, starting state is uninflated tire and a volume of air on the
outside. Final state is that air compressed and inside the inflated
tire." From there, it's pretty easy to see what's what.

It does help to actually make a little cartoon sketch of initial and
final states in these kinds of problems to lay it out in the mind.

[alpha male]

Post by PD
It does help to actually make a little cartoon sketch of initial and
final states in these kinds of problems to lay it out in the mind.

While I can't possibly disagree, my diagram showed two containers, the
first with only 1.35 liters of air in it at some unspecified temperature
& pressure.

And the second, erroneously of course, showed a second container, with
BOTH 20 degrees and 0 degrees Celsius written on it. And it had both 125
psi and 1 atmosphere written on it.

Point being if I don't understand the question, I can't possibly draw the
diagram right! :)

Anyway, I'll chalk this one up to ambiguity in the question as it appears
nobody else was as confused as I (still am) about what it was asking.

[PD]

Post by alpha male

Post by PD
It does help to actually make a little cartoon sketch of initial and
final states in these kinds of problems to lay it out in the mind.

While I can't possibly disagree, my diagram showed two containers, the
first with only 1.35 liters of air in it at some unspecified temperature
& pressure.
And the second, erroneously of course, showed a second container, with
BOTH 20 degrees and 0 degrees Celsius written on it. And it had both 125
psi and 1 atmosphere written on it.
Point being if I don't understand the question, I can't possibly draw the
diagram right! :)
Anyway, I'll chalk this one up to ambiguity in the question as it appears
nobody else was as confused as I (still am) about what it was asking.

I believe you were the victim of a common foible in word problems. It's
worth noting that the FINAL state was mentioned FIRST in words in the
problem statement (the filled tire). Lots of students get caught up in
this, writing down the first variables mentioned in the problem as
initial-state conditions.

When I said a sketch, I didn't mean two cylinders. I really meant,
initial state: deflated tire and a big dotted box around a volume of
air; final state, inflated tire. This makes it real and visualizable.
That is important in itself. There are so many times when a student has
come up with an answer for how a baseball travels after being hit, and
I've looked at them and said, "You've seen a baseball game, and you KNOW
how baseballs go," and they look back at me and say, "Yeah, but that's
real life; I thought we were talking about physics."

[alpha male]

Post by PD
I believe you were the victim of a common foible in word problems. It's
worth noting that the FINAL state was mentioned FIRST in words in the
problem statement (the filled tire).

That must be the part we missed.

Because of that, we had 'two' final states, and, as a consequence, an
incomplete initial state.

Luckily, the other 14 word problems didn't cause us as much consternation.

Thanks for the help.

BTW, we weren't sure where to post this. Are you guys responding from the
chemical, education, or physics side of the NNTP house?

[PD]

Post by alpha male

Post by PD
I believe you were the victim of a common foible in word problems. It's
worth noting that the FINAL state was mentioned FIRST in words in the
problem statement (the filled tire).

That must be the part we missed.
Because of that, we had 'two' final states, and, as a consequence, an
incomplete initial state.
Luckily, the other 14 word problems didn't cause us as much consternation.
Thanks for the help.
BTW, we weren't sure where to post this. Are you guys responding from the
chemical, education, or physics side of the NNTP house?

I'm posting from the physics side, but I see some respondents I don't
recognize from that group, so that these may be from other groups.

[Bodo Mysliwietz]

Post by PD

Post by alpha male
BTW, we weren't sure where to post this. Are you guys responding from the
chemical, education, or physics side of the NNTP house?

I'm posting from the physics side, but I see some respondents I don't
recognize from that group, so that these may be from other groups.

I am from the chemical side of the NNTP house :-)

[Wally W.]

Post by Marvin the Martian

Post by alpha male
I was helping my kid study for a high school test tomorrow morning when
one of the fifteen questions confused me to no end.
It's either a badly written question or a well written one because it's
not obvious to us which is P1,V1,T1 versus P2,V2,T2.
Q: The volume of a bicycle tire is 1.35 liters and the manufacturer
recommends a tire pressure of 125 PSI. If you want the bicycle to have
the correct pressure at 20 degrees Celsius, what volume of air is
required at STP?
For the life of us, we can't figure out for sure which is P1, V1, T1
versus P2, V2, & T2 simply because we can't fully understand the question.
Of course, the combined gas law to use would be: P1*V1/T1 = P2*V2/T2
P1*V1/T1 * T2/P2 = V2
We can easily plug in the numbers ... but we're not sure if we even
understood the question (as to which is P1, V1, T1 versus P2, V2, T2).
P1 = 125 psi
V1 = 1.25 liters
T1 = 293K (which is 273K + 20 degrees C) ---
P2 = 14.7 psi (which is 1 atmosphere at Standard Temperature & Pressure)
V2 = the unknown
T2 = 273K (which is 273K + 0 degrees C at STP)
Given that, we arrived at 10.7 liters for V2.
But, that's assuming we understood the question correctly.

You got it. One state is Standard temperature and pressure with an
unknown volume, the other is in the tire at 20 C.

Post by alpha male
In summary, given that question, what would you inter

pret P1, V1, T1 and

Post by alpha male
P2, V2, T2 to be as the starting point?

Huh. So, they're now screwing around with the definition of STP. I HATE
THAT.
http://en.wikipedia.org/wiki/
Standard_conditions_for_temperature_and_pressure#Past_use

STP version 2.0.

Is that progress?

Standards are arbitrary. Why is a new one better?

For whom is a 0°C reference temperature convenient?

(460+70)/(460+32) = 1.08

(460+70)/(460+59)= 1.02

Using a 'standard' based on a 0°C reference temperature without
correction to room temperature results in a 8% error.

Using a 'standard' based on a 59°F reference temperature without
correction to room temperature results in a 2% error.

The latter may be negligible for practical purposes.

59°F and 15°C are exact equivalents in whole numbers. It was a good
compromise for a choice of standard temperature.

32°F and 0°C are also exact equivalent in whole numbers, but no one
wants prolonged exposure to freezing tempeatures. Prolonged exposure
to an air tempeature of 59°F is more tolerable if one wants to perform
an experiment at "standard" conditions.

Are the makers of scientific standards misanthropes? What mythical
creatures do they hope to appease by defining standards without regard
for human convenience?

The redefinition of STP does not appear to help people in the real
world.

http://www.quotationspage.com/quote/473.html
The nice thing about standards is that there are so many of them to
choose from. - Andrew S. Tanenbaum

[jbriggs444]

Post by alpha male
I was helping my kid study for a high school test tomorrow morning when
one of the fifteen questions confused me to no end.
It's either a badly written question or a well written one because it's
not obvious to us which is P1,V1,T1 versus P2,V2,T2.
Q: The volume of a bicycle tire is 1.35 liters and the manufacturer
recommends a tire pressure of 125 PSI. If you want the bicycle to have
the correct pressure at 20 degrees Celsius, what volume of air is
required at STP?

To me, this question asks: "What volume of air at STP would it
take to fill the tire to the indicated condition"

I would take it as an implicit assumption that the tire starts with
no air at all inside.

Equivalently: "If you took all the air in this tire, what volume
would
it occupy at STP".

Post by alpha male
For the life of us, we can't figure out for sure which is P1, V1, T1
versus P2, V2, & T2 simply because we can't fully understand the question.
P1*V1/T1 = P2*V2/T2
P1*V1/T1 * T2/P2 = V2

Sure.

Post by alpha male
We can easily plug in the numbers ... but we're not sure if we even
understood the question (as to which is P1, V1, T1 versus P2, V2, T2).
P1 = 125 psi
V1 = 1.25 liters
T1 = 293K (which is 273K + 20 degrees C)
---
P2 = 14.7 psi (which is 1 atmosphere at Standard Temperature & Pressure)
V2 = the unknown
T2 = 273K (which is 273K + 0 degrees C at STP)
Given that, we arrived at 10.7 liters for V2.
But, that's assuming we understood the question correctly.
In summary, given that question, what would you interpret P1, V1, T1 and
P2, V2, T2 to be as the starting point?

My take on the problem is the same as yours. Your assumptions
are correct.

I am a little disturbed by the way you posed your own question.
Rather than asking about your understanding of the physical
situation, you asked about which numbers to plug into an
equation.

Also, looking up STP, I see that it is taken as 14.5 PSI these
days. It's not atmosphere. It's one bar = 100 kPa.

[alpha male]

I am a little disturbed by the way you posed your own question. Rather
than asking about your understanding of the physical situation, you
asked about which numbers to plug into an equation.

I'm sorry if it sounded that way.

When someone is confused (as I am) about the question ... they're
confused about how to ask for what the question is asking.

I'm embarrassed to say in the end I merely brainlessly plugged in numbers.

The reason I did that was because the question seemed to be saying the
ending conditions were, at the same time, both 20 degrees and 0 degrees
for temperature and both 125 psi and 1 atmosphere for the pressure.

Since I knew that was impossible, I had to make a value judgment as to
what ending temperature and pressure to use - but that doesn't mean I
understood the question.

Googling some more, I found the same question in the handout here:
http://lghs.edlioschool.com/ourpages/users/cmessenger/
CompleteGasLawsPractice.pdf

And, I found a detailed description of the answer here:
science.widener.edu/~svanbram/chem145/ch11/solutions.pdf

But neither explains the question any better (in fact, they just plug in
the numbers - which is exactly what you rightly chastised me for doing!).

[Bodo Mysliwietz]

Post by alpha male
When someone is confused (as I am) about the question ... they're
confused about how to ask for what the question is asking.

I agree.

Post by alpha male
I'm embarrassed to say in the end I merely brainlessly plugged in numbers.

<laugh> I guess _we all_ know such situations.

Post by alpha male
Since I knew that was impossible, I had to make a value judgment as to
what ending temperature and pressure to use - but that doesn't mean I
understood the question.
http://lghs.edlioschool.com/ourpages/users/cmessenger/
CompleteGasLawsPractice.pdf
science.widener.edu/~svanbram/chem145/ch11/solutions.pdf
But neither explains the question any better (in fact, they just plug in
the numbers - which is exactly what you rightly chastised me for doing!).

I try to explain the physical background in another way.

Given is a soap-bubble at a quit high (unreal) atmospheric pressure of
about 125 psi, with an inner geometrical volume of 1,25 liter at 20 °C
(293K).

You know what will happen when the atmosperic pressure drops down to
standard pressure (14,7 psi or 101.325kPa)?! The bubble will expand,
roughly 8.5 times. But the amount of Air-molecules will not changes.

-----------------------------
This gives us the first law:
P*V = c
(c= constant)

At both conditions the amount of air do not change. The amount of air is
constant!
We conclude: P1*V1 = P2*V2
(*Boyle-Mariotte law)
----------------------------


I guess that you allready know that gas volume is temperature depending
(under constant pressure). What will happen when the temperature drop
down, from 20 °C, to 0 °C? The volume of the soap-bubble decrease (the
bubble will shrink).

We could simply say it change with a ratio of 273/293. Even, the bubble
shrinks a little bit, the amount of air does not change - just the
geometrical volume change.
We can say: P*V/T = c
(c = constant)


We conclude: P1*V1/T1 = P2*V2/T2
(--> combination of Boyle-Mariotte and Gay-Lussac law)
================================

Whereas:
P1 = 125 psi
V1 = 1,25 liter
T1 = 293K

after expansion:
P2 = 14,7 psi
T2 = 273K
V2 = ?

(sorry for my bad english)

[alpha male]

I think P1 should be 139.7 PSI.
The manufacturer's recommendation is probably gauge pressure...

I had actually wondered about that myself!

I wasn't sure if the atmosphere exerts a pressure that must be overcome
in order to register a pressure on the gauge.

Are you saying in order to 'read' 125 psi inside the tire, you need to
add 14.7 psi above 125 psi to overcome atmospheric pressure pushing back?

[PD]

Post by alpha male

I think P1 should be 139.7 PSI.
The manufacturer's recommendation is probably gauge pressure...

I had actually wondered about that myself!
I wasn't sure if the atmosphere exerts a pressure that must be overcome
in order to register a pressure on the gauge.
Are you saying in order to 'read' 125 psi inside the tire, you need to
add 14.7 psi above 125 psi to overcome atmospheric pressure pushing back?

Gauge pressure is actually what bike tire pressure gauges read, which is
the DIFFERENCE in pressure between inside the tire and outside the tire.
Does that help?

[alpha male]

Gauge pressure ... is the DIFFERENCE in pressure
between inside the tire and outside the tire.
Does that help?

Yes. Thanks.

[alpha male]

Unknown volume at 14.7 PSI and 273 K
is compressed to 1.35 l at 139.7 PSI and 293 Kelvin...

The way you put it is succinct and understandable.

The whole concept of gauge pressure versus absolute pressure is
interesting as I don't see 'anything' about that in the books.

I think you're saying that we need to treat the pressures as force
vectors, is that right?

That is, the force of the atmosphere is pushing down on the bladder such
that if we started with an empty tire and filled it to just 14.7 psi, it
would register on the gauge at zero psi.

Is that what you're trying to tell me?

[Bodo Mysliwietz]

Post by alpha male
The whole concept of gauge pressure versus absolute pressure is
interesting as I don't see 'anything' about that in the books.

The examination question is not very precise but it doesn't matter from
my point of view, because when you mount a totally deflated tire the
inner volume would be nearly zero. When the volume is zero, the pressure
at initial state (after mounting) does not play a rule.

If you pressurize the tire now (controlled by a normal gauge) you
pressurize it until the gauge reads 125 psi above atmospheric pressure.
Means the pressure difference is still 125 psi - not the mentioned 139,7
psi! Just the tires volume change from 0 to 1,35 liter.

The worst (stupid) case could be, that the manufacturer specifies
absolute pressure but the tire is mounted at atmospheric pressure
(14,7psi absolute), which yields in a pressure difference off
125-14,7=110,3 psi !

But if we consider the idea with the mentioned 139,7 psi we would have
three possible solutions:

A)
============
P1 = 125 psi
V1 = 1,35 liter
T1 = 293K
after expansion:
P2 = 14,7 psi
T2 = 273K
V2 = ?


B)
============
P1 = 110,7 psi
V1 = 1,35 liter
T1 = 293K
after expansion:
P2 = 14,7 psi
T2 = 273K
V2 = ?
--> that is just the additioal volume of air, needed to pressurize the
tire from 14,7 psi absolute to 125 psi absolute.


C)
===========
P1 = 139,7 psi
V1 = 1,35 liter
T1 = 293K
after expansion:
P2 = 14,7 psi
T2 = 273K
V2 = ?
--> that is additioal volume of air, needed to pressurize the tire from
0 psi (vacuum) to 139,7 psi absolute.


The only one who knows how to interprete the question, is the teacher
themself. And you will know it within a few days ;-)
B and C are not very likely.