Question

In: Chemistry

A spherical bulb with a volume of 500 cm3 is evacuated to a negligibly small residual...

A spherical bulb with a volume of 500 cm3 is evacuated to a negligibly small residual gas pressure and then close off. One hour later, the pressure in the vessel is found to be 2.00 × 10-7 atm because the bulb has a tiny hole in it. Assume that the surroundings are at atmospheric pressure, T = 300 K, and the average molar mass of molecules in the atmosphere is 28.8 g mol-1.

a) Please calculate the radius of the hole on the bulb surface, assuming the tiny hole to be circular

b) assume that the surroundings contain only N2 (molar mass 28 g/mol) and O2 (molar mass 32.0g/mol)and the mole fraction ratio between the two species is X(N2):X(O2) = 4:1. when the pressure in the bulb is found to be 1.00 x10^-7 atm, the mole fraction ratio X(N2):X(O2) inside the bulb should be higher , equal to, or smaller than 4:1? Why? Explain your answer by calculating the enrichment factor for N2

Solutions

Expert Solution

(b): Given the initial mole fraction ratio X(N2):X(O2) = 4:1

The mole fraction ratio X(N2):X(O2) inside the bulb will be higher than the outside 4:1 ratio.

This can be explained from the following calculation.

The rate at which gas molecules enters inside the bulb can be calculated from the following formulae

Reff = (1/4) x (X/V) x Vavg

where Vavg = average velocity.

For N2 gas:

R1 = (1/4) x [X(N2)/V)]x underroot(8RT / PixM(N2)) ------- (1)

For O2 gas:

R2 = (1/4) x [X(O2)/V)]x underroot(8RT / PixM(O2)) ------- (2)

Dividing eqn(1) by (2) we get

R1/R2 = [X(N2) / X(O2)]x underroot[M(O2) / M(N2)]

=> R1/R2 = 4 x underroot(32/28) = 4.276 which is higher than 4.


Related Solutions

An electric light bulb is made of an evacuated, i.e. no air inside the bulb, glass...
An electric light bulb is made of an evacuated, i.e. no air inside the bulb, glass bulb containing a long thin tungsten filament. The resistivity of tungsten is is 6.87x10 -7 Ohm meters at the temperature of the filament. The filament can be modeled as a 580 mm long thin cylinder with 0.046 mm diameter. The light bulb is plugged into a 120 V wall outlet. The power dissipated by the filament is radiated away as black body radiation with...
value unit spherical volume (in^3) spherical volume (m^3) spherical volume (gallons^3) x in ? ? ?...
value unit spherical volume (in^3) spherical volume (m^3) spherical volume (gallons^3) x in ? ? ? So I'm being assigned the task of creating a custom conversion table that utilizes logical statements for the purpose of converting the given values from the input units into the other listed units within excel. I've tried a few, however, I don't know how to list multiple statements. For example, if B2, the user writes "m", then each of the corresponding spherical volume units...
Three bulbs are connected by tubing, and the tubing is evacuated. The volume of the tubing...
Three bulbs are connected by tubing, and the tubing is evacuated. The volume of the tubing is 40.0 mL. The first bulb has a volume of 72.0 mL and contains 6.00 atm of argon, the second bulb has a volume of 250 mL and contains 2.42 atm of neon, and the third bulb has a volume of 21.0 mL and contains 9.88 atm of hydrogen. If the stopcocks (valves) that isolate all three bulbs are opened, what is the final...
A system undergoes a change in volume from 100 cm3 /mol to 225 cm3 /mol. The...
A system undergoes a change in volume from 100 cm3 /mol to 225 cm3 /mol. The pressure of the model is predicted by, P = aT + B/T^3, where a = 2.13x10-3 bar/K and ß = 2.6x10-5 bar^3K^3. Calculate AS at 350 K (in J/mol-K) b. What is the heat required at 350 K (in J/mol)? c. Calculate AU for the system described (in J/mol-K) SHOW ALL WORK.THANKS
Two containers of the same volume are evacuated. Container 1 is maintained at a temperature of...
Two containers of the same volume are evacuated. Container 1 is maintained at a temperature of 400 K and filled with oxygen gas to a pressure of 750 mm Hg. Container 2 is maintained at a temperature of 200 K and filled with hydrogen gas to a pressure of 750 mm Hg. Compare the two samples of gas quantitatively with regard to: a. Number of molecules b. Mass c. Average molecular kinetic energy d. Average molecular speed (rms)
Imagine a gas of N spherical particles that are free to distribute throughout either a large volume or a small one.
Imagine a gas of N spherical particles that are free to distribute throughout either a large volume or a small one. Why does the gas spread out into a large volume? The tendency to spread out is pressure and can be explained in terms of multiplicity or increased probability. To illustrate this, let's create a simpler model that we can visualize, solve exactly, and will illustrate the essence of the problem without the mathematical complexity. For each of the following,...
A rigid tank of volume 0.75 m3 is initially evacuated. A hole develops in the wall,...
A rigid tank of volume 0.75 m3 is initially evacuated. A hole develops in the wall, and air from the surroundings at 1 bar, 30°C flows in until the pressure in the tank reaches 1 bar. Heat transfer between the contents of the tank and the surroundings is negligible. Determine the final temperature in the tank, in °C.
An adiabatic tank, 0.5 m3, is initially evacuated and charged with steam at 500 kPa and...
An adiabatic tank, 0.5 m3, is initially evacuated and charged with steam at 500 kPa and 300 C. The final tank pressure is 500 kPa. Determine the final temperature and the entropy production.
Solution A contained 40 cm3 volume of wine diluted to 100 cm3 using deionized water. Solution...
Solution A contained 40 cm3 volume of wine diluted to 100 cm3 using deionized water. Solution B contained 1 cm3 taken from Solution A and diluted to 10 cm3 with deionised water.  After running Solution B through the GC it was found it contained 0.045 cm3 of ethanol. What is the % alcohol by volume (ABV) in the original wine sample?
A four-cylinder petrol engine has a swept volume of 2000 cm3, and the clearance volume in...
A four-cylinder petrol engine has a swept volume of 2000 cm3, and the clearance volume in each cylinder is 60 cm3. Calculate the air standard cycle efficiency. If the introduction conditions are 1 bar and 24 ?C, and the maximum cycle temperature is 1400 ?C, calculate the mean effective pressure based on the air standard cycle. ANSWERS(59.1%; 5.30 bar)
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT