Gases problems

hoay SG

Two glass vessels M and N are connected by a closed valve.

M contains helium at 20 °C at a pressure of 100000 Pa. N has been evacuated, and has three times the volume of M. In an experiment, the valve is opened and the temperature of the whole apparatus is raised to 100 °C.

What is the final pressure in the system?

solution:

T1 = 20oC = 293 K ; P1 = 100000 Pa ; T2 = 373 K ; P2 = ??

P1V1 /T1 = P2V2 /T2

Placing 3 in palce of V1 and 1 in palce of V2

100000 x 3 / 293 = P2 x 1/393

P2 = 127303 Pa

Is it correct ?

UltimaOnline SG

Two glass vessels M and N are connected by a closed valve.

What is the final pressure in the system?

BedokFunland JC Solution :

Before valve is opened :

PV=nRT

(100000 Pa) (V1) = (n) (R) (293 K)

This implies nR = 3.413 x 10^2 V1

where V1 = volume of container M

After valve is opened :

PV=nRT

(Y Pa) (V2) = (n) (R) (373 K)

where V2 = combined volume of both containers

Substituting nR = 3.413 x 10^2 V1 into new scenario (since total moles of gas remains the same)

(Y Pa) (V2) = (3.413 x 10^2 V1) (373 K)

(Y Pa) (V2 / 3.413 x 10^2 V1) = (373 K)

Since V2 is (1 + 3 = 4) times the volume of V1,

(Y Pa) (4 / 3.413 x 10^2) = (373 K)

Y Pa = 3.1826 x 10^4 Pa

hoay SG

Thank you for the comprehensive answer. But is there any other way of doing this and secondly how u know we have to use PV= nRT and other gas relationships as i mentiond.

UltimaOnline SG

Thank you for the comprehensive answer. But is there any other way of doing this and secondly how u know we have to use PV= nRT and other gas relationships as i mentiond.

Boyle's Law, Charles' Law, Gay-Lussac's Law and Avogadro's Law, are all combined into the Ideal Gas Law PV=nRT. Which means (for A level Chemistry, in which we always assume ideal gas behavior for calculation purposes, unless of course when Cambridge occasionally provides in the exam question, info on the more advanced Van der Waals equation, and requires the candidate to apply this in the exam question, as has been asked before in Singapore JC Prelim exams, and makes for an excellent higher order question) you can always just use PV=nRT and ignore the individual sub-laws (and leave other variables alone to cancel out in the later stages of the calculation), like what I did.

hoay SG

okay sir that is a satisfactory answer.

blackyblue SG

May I please know why in this particualr step

Substituting nR = 3.413 x 10^2 V1 into new scenario (since total moles of gas remains the same)

the number of moles remain the same .isnt this nR only for M

UltimaOnline SG

May I please know why in this particualr step

Substituting nR = 3.413 x 10^2 V1 into new scenario (since total moles of gas remains the same)

the number of moles remain the same .isnt this nR only for M

M was simply the container that the gas previously occupied. Now the same moles of gas occupies both containers, so pressure and volume are different, but no. of moles of gas, remains the same.

blackyblue SG

Oh now i understand .Thanks for the reply

Metanoia SG

Two glass vessels M and N are connected by a closed valve.

What is the final pressure in the system?

solution:

T1 = 20oC = 293 K ; P1 = 100000 Pa ; T2 = 373 K ; P2 = ??

P1V1 /T1 = P2V2 /T2

Placing 3 in palce of V1 and 1 in palce of V2

100000 x 3 / 293 = P2 x 1/393

P2 = 127303 Pa

Is it correct ?

I think your method is fine except for some minor mistakes.

1) V2 is four times of V1

2) You subbed T2 = 293 instead of 273

-------------------------------------------------------

P1V1 /T1 = P2V2 /T2

Substitute V2 = 4*V1

P1V1 /T1 = P2(4*V1) /T2

P1 /T1 = P2(4) /T2