# Process Calculations GATE-2004

**Q 1: **A distillation column separates 10,000 kg/h of a benzene-toluene mixture as shown in the figure below.

In the figure, x_{F}, x_{D}, and x_{W} represent the weight fraction of benzene in the feed, distillate, and residue respectively. The reflux ratio is

**Q 2: **The weight fraction of methanol in an aqueous solution is 0.64. The mole fraction of methanol X_{M} satisfies

**Q 3: **80 kg of Na_{2}SO_{4} (molecular weight 142) is present in 330 kg of an aqueous solution. The solution is cooled such that 80 kg of Na_{2}SO_{4}.10H_{2}O crystals separate out. The weight fraction of Na_{2}SO_{4} in the remaining solution is

###### Common data for Q 4 & 5:

One mole of methane undergoes complete combustion in a stoichiometric amount of air. The reaction proceeds as

CH_4+2O_2\rightarrow CO_2+2H_2OBoth the reactants and the products are in the gas phase. \triangle H_{298}^0=-730\;\frac{kJ}{mol\;of\;methane}

**Q 4: **The mole fraction of water vapor in the product gases is about

**Q 5: **If the average specific heat of all the gases/vapor is 40 J/(mol K), the maximum temperature rise of the exhaust gases at ^{0}C would be approximately equal to

**Q 6: **A vessel of volume 1000 m^{3} contains air which is saturated with water vapor. The total pressure and temperature are 100 kPa and 200 C, respectively. Assuming that the vapor pressure of water at 200 C is 2.34 kPa, the amount of water vapor (in kg) in the vessel is approximately

**Q 7: **The vapor pressure of water is given by

Where A is a constant, P^{sat} is vapor pressure in atm, and T is temperature in K. The vapor pressure of water in atm at 50^{0} C is approximately