Useful Constants: 1 Torr = 133.32 Pa; R = 8.3145 J/mol·K You have a thin metal s

Question

Useful Constants: 1 Torr = 133.32 Pa; R = 8.3145 J/mol·K
You have a thin metal sphere of unknown volume that contains helium gas at low pressure. You put the entire metal sphere into a bath of liquid nitrogen, and a pressure gauge on the sphere indicates a pressure of 299 torr.


a) You now place the metal sphere in a mixture of dry ice and methanol. What is the new pressure?
___ torr
b) You now place the metal sphere in ice water. What is the new pressure?
___ torr

c) You now place the metal sphere in a water bath at room temperature (measured to be 25.3 °C). What is the new pressure?
___ torr

d) You now place the metal sphere in boiling water. What is the new pressure?
___torr

e) Given that the volume of the metal sphere, pressure gauge, etc., was 389 mL, how many moles of helium gas would you have?
___mol

Explanation / Answer

Actually , for any gas there is a governing equation, known as the ideal gas equation, which controls the physical quantities such a pressure of gas , volume , temperature etc.
it is written as
P * V = n * R * T , where P = pressure of gas , V= volume , n = number of moles and T = temperature in K

Temperature of Liquid nitrogen = 77 K

So since , voluime of sphere is remaining constant , and gas has a fixed number of moles inside the sphere, Our pressure is proportional to Temperature

Hence P/T = constant

Let this constant be k

k = 299/ 77 torr/K

1) temperature of dry ice cooling bath = -78 degrees celcius = 273 - 78 K = 195 K

Hence P1 = k * T1 = 299/77 * 195 = 757 torr

2 ) temperature of ice water = 273 K

Hence P2 = k * T2 = 299/77 * 273 = 1060 torr

3) temperature of water bath = 298.3 K ( or 25.3 degrees celcius)

Hence P3 = k * T3 = 299/77 * 298.3 = 1158 torr

4) temperature of boiling water = 100 degrees celcius = 373 K

Hence P4 = k * T4 = 299/77 * 373 = 1448 torr

5 )

P =299 torr = 299 * 133.32 Pa = 39826.8 Pa

T= 77 K

V =389 ml = 389 * 10^-3 l = 389 * 10^-6 m3

n = P*V/R*T

n = 39826.8 * 389 * 10^-6/(77*8.314) = 0.024 = 24.2 milli moles.

Hope you get the answer.

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