# The Universal Gas Constant is 8.314 J mol−1 K−1. Express

Question

. Answer ALL parts of this question.

a) The Universal Gas Constant is 8.314 J mol−1 K−1. Express this value in units of

atm·ft3 (lb-mol)−1 °R−1. [4 marks]

b) A fuel with a composition 89 mol% methane, 7 mol% ethane and 4 mol% carbon

dioxide is supplied to a boiler at a temperature of 68ºF and a gauge pressure of 98

mm Hg. Determine:

(i) the composition of the fuel in % w/w, [4 marks]

(ii) the average molecular weight of the fuel, [4 marks]

(iii)the theoretical air required to burn the fuel (in kg of air per m3 of fuel), if

the atmospheric pressure is 754 mm Hg, [7 marks]

(iv)the composition of the flue gas in mol% if the fuel is burned with 30%

excess air, assuming complete combustion. [6 marks]

c) Mesitylene (trimethyl-benzene) can be reduced by reaction with hydrogen to

produce xylene (dimethyl-benzene) with methane generated as a by-product.

Unfortunately, valuable xylene can be further reduced by hydrogen to the less

valuable toluene (methyl-benzene), again producing methane as a by-product.

A reactor feed contains 40 mol% mesitylene and 60 mol% H2. If the conversion

of mesitylene is 60% and the selectivity is 2.2, determine the composition of the

product leaving the reactor and the yield. [15 marks]

DATA:

1 atm = 1.013 ×105 N m−2

1 m3 = 35.31 ft3

1 mol (g-mol) = 2.205×10-3 lb-mol

1 N m−2 = 7.50×10-3 mm Hg

T(ºF) = 1.8 T(ºC) + 32

T(K) = T(ºC) + 273

T(ºR) = T(ºF) + 459

The ideal gas constant R = 8.314 J mol−1 K−1.

Assume air has a composition of 79 mol% N2 and 21 mol% O2.

Relative atomic mass: C=03.0, H=1.0, O=16.0 and N=14.0.