PS4KEYF07 - Chemistry 391 PS4 KEY 1 Fall 2007 a The gas is...

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1 Chemistry 391 Fall 2007 PS4 KEY 1. a) The gas is heated from 300 K to 450 K at a constant external pressure of 1.00 bar. -1 -1 -2 3 5 1 mol 8.314 J mol K 300 K 2.49 10 m 10 Pa i i i nRT V P × × = = = × -2 3 -2 3 450 K 2.49 10 m = 3.74 10 m 300 K f f i i T V V T = = × × × ( ) 5 -2 3 -2 3 3 10 Pa 3.74 10 m 2.49 10 m 1.25 10 J external w P V = − Δ = − × × × = − × -1 -1 3 , 3 8.314 J mol K 1 mol 150 K = 1.87 10 J 2 V m U nC T × Δ = Δ = × × × 3 3 3 1.87 10 J + 1.25 10 J = 3.12 10 J q H U w = Δ = Δ = × × × -1 -1 -1 , 3 450 K ln 1 mol + 1 8.314 J mol K ln = 8.43 J K 2 300 K f P m i T S nC T Δ = = × × × b) The gas is heated to 450 K at a constant volume corresponding to the initial volume. w = 0 because Δ V = 0. -1 -1 3 , 3 8.314 J mol K 1 mol 150 K = 1.87 10 J 2 V m U q nC T × Δ = = Δ = × × × -1 -1 3 , 5 8.314 J mol K 1 mol 150 K = 3.12 10 J 2 P m H nC T × Δ = Δ = × × × -1 -1 -1 , 3 450 K ln 1 mol 8.314 J mol K ln = 5.06 J K 2 300 K f V m i T S nC T Δ = = × × × c) The gas undergoes a reversible isothermal expansion at 300 K until the pressure is half of its initial value.
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