There is a laboratory room which measures 5 m times 5 m and has a 4 meter high c
ID: 537121 • Letter: T
Question
There is a laboratory room which measures 5 m times 5 m and has a 4 meter high ceiling. The wall of the lab is rigid and cannot be destroyed by any means. An observation window made of bullet-proof glass that can withstand a pressure of 5 atmospheres and 2000 degree C is installed on the south side of the wall. A researcher produces 5 kg of liquid ethane (C_2 H_6) in the reactor. (a) She accidentally left the reactor open when she left the lab. What would be the size of the cloud of ethane that forms? Assume 20 degree C. Ans.____m^3. (b) Next morning, she comes to work and turns the light switch on before entering the lab. If the cloud of ethane (C_2 H_6) mixed with just the right (stoichiometric) quantity of oxygen from the air, and was ignited by the light switch, assuming a final temperature of 1500 degree C, will the observation window break? ExplainExplanation / Answer
This can be solved by applying Gas Law, as -
PV = nRT,
where P is rhe pressure, V is the Volume, n is the no. of moles, R is the universal gas constant and T is the Temperature in K.
Mass of ethane produced = 5 kg, or 5000 g
MW of Ethane = 30 g/mol
No. of moles of Ethane = 5000/30 mol, or 500/3 mol
(a) This needs to be approached assuming pressure remains constant at 1 atm, and that entire room is not covered -
Thus, T = 293.15 K, R = 0.0821 L/atm.mol.K, P = 1 atm, n = 500/3
Plugging these values, we get -
V = 4.011 x 103 L = 4.011 m3, since 1 m3 is 1000 L
Since, the total volume is 5 x 5 x 4 m3 i.e. 80 m3 and the volume determined is lesser than that, the Pressure assumption stands correct, else if the volume determined would have been greater than that there would have been a compression of the gas and the Volume would have been 80 m3 which is the maximum that can be achieved.
(b) Now, the ethane reacts with O2 in the room and forms CO2 and H2O, by the reaction -
C2H6 + 3.5 O2 ----> 2 CO2 + 3 H2O,
thus producing 7 times the moles of ethane in gases which is 2500/3 mol, n.
Now, assuming that the entire volume is occupied - V = 80 x 103 L
And, T is 1773.15 K.
Plugging in the above values -
P = 1.5 atm
The window can withstand 5 atm, and this is way below that, hence it remains intact.
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