Question

A mixture of A and B is capable of being ignited only if the mole percent of A is 6 %. A mixture containing 9.0 mole% A in B flowing at a rate of 800 kg/h is to be diluted with pure B to reduce A concentration to the lower flammability limit. Calculate the required flow rate of B in mol/h and the percent by mass of Oz in the product gas. (Note: B may be taken to consist of 21 mole% O2 and 79% Nz and to have an average molecular weight of 29.0.) MA = 16.04 g/mol.

Answer 1

Explanation:

As it is given that mixture (contains 9 mol % A and 91% B) and it is flowing at a rate of 800 kg/h.

Hence, calculate the molecular weight of the mixture as follows.

             Weight = $0.09 \times 16.04 + 0.91 \times 29$

                          = 27.8336 g/mol

And, molar flow rate of air and mixture is calculated as follows.

                    $\frac{800}{27.8336}$

                     = 28.74 kmol/hr

Now, applying component balance as follows.

                $0.09 \times 28.74 + 0 \times F_{B} = 0.06F_{p}$

                   $F_{p}$ = 43.11 kmol/hr

                   $F_{A} + F_{B} = F_{p}$

                          $F_{B}$ = 43.11 - 28.74

                                      = 14.37 kmol/hr

So, mass flow rate of pure (B), is $F_{B}$ = $14.37 \times 29$

                                                    = 416.73 kg/hr

According to the product stream, 6 mol% A and 94 mol% B is there.

             Molecular weight of product stream = $Mol. weight \times 43.11 kmol/hr$

                                  = $0.06 \times 16.04 + 0.94 \times 29$

                                  = 28.22 g/mol

Mass of product stream = 1216.67 kg/hr

Hence, mole of $O_{2}$ into the product stream is as follows.

                    $0.21 \times 0.94 \times 43.11$

                      = $8.5099 kmol/hr \times 329 g/mol$

                      = 272.31 kg/hr

Therefore, calculate the mass % of $O_{2}$ into the stream as follows.

                 $\frac{272.31}{1216.67} \times 100$

                     = 22.38%

Thus, we can conclude that the required flow rate of B is 272.31 kg/hr and the percent by mass of $O_{2}$ in the product gas is 22.38%.