Process Calculations GATE-2008

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Q 1: Air (79 mole % nitrogen and 21 mole % oxygen) is passed over a catalyst at high temperature. Oxygen completely reacts with nitrogen as shown below.

0.5N_2(g)+0.5O_2(g)\rightarrow NO(g) 0.5N_2(g)+O_2(g)\rightarrow NO_2(g)

The molar ratio of NO to NO2 in the product stream is 2:1. The fractional conversion of nitrogen is   





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Q 2: A 35 wt% Na2SO4 solution in water, initially at 50º C, is fed to a crystallizer at 20º C. The product stream contains hydrated crystals Na2SO4.10H2O in equilibrium with a 20 wt% Na2SO4 solution. The molecular weights of Na2SO4 and Na2SO4.10H2O are 142 and 322, respectively. The feed rate of 35% solution required to produce 500 kg/hr of hydrated crystals is  





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Q 3: Carbon black is produced by the decomposition of methane:

CH_4(g)\rightarrow C(s)+2H_2(g)

The single-pass conversion of methane is 60 %. If the fresh feed is pure methane and 25 % of the methane exiting the reactor is recycled, then the molar ratio of the fresh feed stream to the recycle stream is





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Q 4: A tank of volume 0.25 m3 and height 1 m has water flowing in at 0.05 m3/min. The outlet flow rate is governed by the relation

F_{out}=0.1h

Where h is the height of the water in the tank in m and Fout is the outlet flow rate in m3/min. The inlet flow rate changes suddenly from its nominal value of 0.05 m3/min to 0.15 m3/min and remains there. The time (in minutes) at which the tank will begin to overflow is given by





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Common data for Q 5, 6 & 7:

Methane and stream are fed to a reactor in a molar ratio of 1:2. The flowing reactions take place,

CH_4(g)+2H_2O\rightarrow CO_2(g)+4H_2(g) CH_4(g)+H_2O\rightarrow CO(g)+3H_2(g)

Where CO2 is the desired product, CO is the undesired product and H2 is a by-product. The exit stream has the following composition

SpeciesCH4H2OCO2H2CO
Mole %4.3510.8815.2167.392.17

Q 5: The selectivity for a desired product relative to an undesired product is





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Q 6: The fractional yield of CO2 is (Where fractional yield is defined as the ratio of moles of the desired product formed to the moles that would have been formed if there were no side reactions and the limiting reactant had reacted completely)





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Q 7: The fractional conversion of methane is





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