gas law_F6 CHEM 問題

3.
(b)
Pressure on sea level
= 1 atm

Pressure at the seabed
= 1 + 1 x (20/10)
= 3 atm

(c)(i)
Consider the gas in the cylinder on the sea level:
Volume, V1 = 0.02 m3
Pressure, P1 = 18 atm
Temperature, T1 = 273 + 27 = 300 K

Consider the gas in the cylinder at the seabed just before the diver inflates the balloon:
Volume, V2 = 0.02 m3 (unchanged)
Pressure, P2 = ?
Temperature, T2 = 273 + 21 = 294 K

PV = nRT
P/T = nR/V
Since n, R and V are constant, thus P/T = constant
P1/T1 = P2/T2
18/300 = P2/294

Gas pressure in the cylinder just before the diver inflates the balloon, P2
= 294 x (18/300)
= 17.64 atm

(c)(ii)
Consider the gas originally in the cylinder used to inflate the balloon:
Volume, V3 = 0.02 m3
Partial pressure, P3 = ? atm
Temperature, T = 294 K

Consider the gas in the inflated balloon:
Volume, V4 = 0.01 m3
Pressure, P4 = 3 atm
Temperature, T = 294 K (unchanged)

PV = nRT
Since n, R and T are constant, thus PV = constant
P3V3 = P4V4
P3 x 0.02 = 3 x 0.01
P3 = 1.5 atm

Gas pressure in the cylinder just before the diver inflates the balloon
= 17.64 - 1.5
= 16.14 atm

c(iii)
According to Dalton's law of partial pressure,
fraction of the gas originally in the cylinder used to inflate the balloon
= 1.5/17.64
= 0.085

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