Please show work for me to follow along thanks 4 A Container

Please show work for me to follow along, thanks!

4. A Container A with a volume of5.0Land a container B with a volume of 2.5Lare connected with a thin tube with a switch in between as shown in the figure below. Initially, the switch is closed, and the container A is set at a temperature of 27°C and a pressure of 2.5atm. The container B is set at a temperature of 27°C and a pressure of 1.0atm. Ignore the volume of the thin tube and the heat expansion of the containers. A) Determine the number of moles n of the air in both container A and B. B) Find the pressure when the valve is open. C) For B), how many number of moles of the air moved from A to B? D) While the switch is left open, the temperature of the container A is raised to 77 oC, and the temperature of the container B is kept 27°C. Find the air pressure and the ratio ofthe number of moles for A and B nA nH)

Solution

(A) Applyinng Gas equation: P V = n R T

for A:

(2.5 x 101325 Pa) (5 x 10^-3 m^3) = nA (8.314) (273 + 27)

nA = 0.508 mol

for B:

(1 x 101325) (2.5 x 10^-3) = nB (8.314) (273 + 270)

nB = 0.101 mol

number of moles, n = nA + nB = 0.610 mol

(B) when valve is opened,

n = 0.610 mol

V = 5 + 2.5 =7.5 L Or 7.5 x 10^-3 m^3

T = (273 + 27 ) K

P V = n R T

P (7.5 x 10^-3) = (0.610)(8.314) (300)

P = 202861.6 Pa

P(in atm) = 202861.6/101325 = 2 atm

(C) nA\' = PV / RT = (202861.6)(5 x 10^-3) / (8.314 x 300) = 0.407 mol

so 0.508 - 0.407 = 0.101 mol moved from A to B.

(D)
Pressure remains constant.

nA = P V / R T

nA /nB = (VA / TA) / (VB / TB) = VA TB / VB TA

= (5 x (273 + 77)) / (2.5 x (273 +27))

= 2.33 Or 7/3