How To Find Equilibrium Pressure

2E-one :	Equilibrium Pressure When Two Gases Are Mixed								5 pts

Ii storage tanks are connected and their contents mixed. Tank A initially contains 5 kg of nitrogen gas at 150 o C and 150 KPa. Tank B initially contains 2 kg of oxygen gas at 100 o C and 75 KPa. Can either gas be treated equally an ideal gas? If both tanks somewhen cool to room temperature (20 o C) afterwards mixing, what will the final pressure level be at equilibrium?

Read :	The primal here is to assume that both the pure gases and the final mixture of gases behave as ideal gases. Nosotros tin immediately verify that the pure gases in their initial state are ideal gases, just nosotros cannot verify that the final mixture of gases is platonic until we solve the problem and determine the final pressure.




	Cull the contents of both tanks as the system. The fact that links the initial and final states of this organisation is that the total number of moles in the system does non modify. This is a closed system.



Given:	mN2 =	5	kg				Notice:
	TA =	150	oC =	423.15	K		Pequ =	???	kPa
	PA =	150	kPa
	mO2 =	2	kg
	TB =	100	oC =	373.15	K
	PB =	75	kPa
	Tequ =	20	oC =	293.15	K

Assumptions :
	- Both pure gases, as well as the last mixture, conduct as platonic gases.

Solution :	A diatomic gas tin can be considered ideal when the post-obit benchmark is satisfied:								Eqn 1

	VN2 =	23.45	L/mol			Where:	R =	viii.314	J/mol K
	VO2 =	41.36	L/mol

	Since both tooth volumes are much greater than 5 L/mole, it is condom to consider both gases to be platonic gases.


	The fundamental to solving the problem is to ASSUME that the equilibrium mixture will be an ideal gas:								Eqn 2

	Let'south begin by determining how many moles of gas are initially in each tank.								Eqn iii

	And so we can decide the total moles of gas in the system :								Eqn 4

	MWN2 =	28.01	g/mol		nN2 =	178.v	mole N2
	MWO2 =	32.00	grand/mol		nO2 =	62.5	mole O2
					ntotal =	241.0	mole total

	The total number of moles in the system does not changes as the gases mix !
	The system, consisting of both tanks, is closed.

	Next, we tin can use the IG EOS to make up one's mind the volume of each tank and then the total book of the system.


			Eqn 5	Where (for platonic gases) :					Eqn 6
							and :
	5A =	4.19	k3						Eqn seven
	VB =	ii.59	one thousand3
	5tot =	half-dozen.77	chiliad3

	From the IG EOS we derive the following equation for the equilibrium pressure :								Eqn eight

Answer :							Peq =	86.seven	kPa

Verify :	Now, summate the molar book at the equilibrium land, just to be sure information technology is still prophylactic to care for the gas as an platonic gas !


				Veq =	28.10	Fifty/mol

	Since Veq is greater than 5 L/mole, nosotros were justified in using the ideal gas EOS for the equilibrium state every bit well.