Question

Bromine (Br2) is produced by reacting HBr with O2, with water as a byproduct. The O2 is part of an air (21 mol % O2, 79 mol % N2) feed stream that is flowing sufficiently fast to provide 25% excess oxygen ("excess" has a precise meaning in process analysis: in this case there is 25% more oxygen than the amount needed to completely react with the limiting reactant). The fractional conversion of HBr is 78%.
a) Show the degree of freedom analysis. Be as specific as possible about labeling the unknowns and completely write out all of the independent equations.
b) Calculate the composition (mole fractions) of the product stream.

Answer 1

Answer:

The mole fractions:

$x_{HBr}=\frac{100mol}{318.5}=0.314$

$x_{Br_2}=\frac{78mol}{318.5}=0.245$

$x_{H_2O}=\frac{78mol}{318.5}=0.245$

$x_{O_2}=\frac{62.5mol}{318.5}=0.196$

Explanation:

The reaction described is:

$2 HBr (g) + 1/2 O_2 (g) \longrightarrow Br_2 (g) + H_2O (g)$

The limiting reactant is the HBr (oxygen is in excess).

a) The mass (in moles) balance for this sistem:

$n_{Br_2}=\frac{ 1 mol Br_2}{1 mol HBr} *n_{HBr}*0.78$

(the 0.78 is because of the fractional conversion)

$n_{O_2}=\frac{ 0.5 mol O_2}{1 mol HBr} *n_{HBr}*1.25$

(the 1.25 is because of the oxygen excess)

$n_{H_2O}=\frac{ 1 mol H_2O}{1 mol Br_2} *n_{Br_2}$

There is only one degree of freedom in this sistem, you can either deffine the moles of HBr you have or the moles of Br2 you want to produce. The other variables are all linked by the equations above.

b) Base of calculation 100 mol of HBr:

$nn_{HBr}=100 mol HBr$

$n_{Br_2}=\frac{ 1 mol Br_2}{1 mol HBr} *100mol HBr*0.78$

$n_{Br_2}=78 mol Br2$

$n_{O_2}=\frac{ 0.5 mol O_2}{1 mol HBr} *100 mol HBr*1.25$

$n_{O_2}=62.5 mol O_2$

$n_{H_2O}=n_{Br_2}= 78 mol$

$n_{total}=(78+78+100+62.5)mol= 318.5mol$

The mole fractions:

$x_{HBr}=\frac{100mol}{318.5}=0.314$

$x_{Br_2}=\frac{78mol}{318.5}=0.245$

$x_{H_2O}=\frac{78mol}{318.5}=0.245$

$x_{O_2}=\frac{62.5mol}{318.5}=0.196$