Answer to Question #189273 in General Chemistry for gerarld

Question

Coal as fired contains 2.5% moisture. On a dry basis the coal analysis is C 80%, H 6%, O 8%, ash 6%. The flue gas analyzes CO2 14.0%, CO 0.4%, O2 5.6%, N2 80.0%. The air used has a dew point of 50°F. The barometer is 29.90 in. Hg. Calculate the dew point of the stack gas.

Answer 1

Ans:-

Antoine equation can be used to determine the vapor pressure of the substance,

$p=10^{(A-\dfrac{B}{T+C})}$

Since the coal contained the $2.5$ %moisture and the basis is $100 lb mol$ , the water or moisture entering the system can be calculated as follows:

$H_2O_{in}=2.5$

$= \dfrac{2.5}{100}\times 100$

$=2.5 mol$ in F

Therefore, the coal entering the system is

$Coal_{in}= 100-2.5$

$= 97.5 mol$ in F

Further, F and A can be determined using material balances as follow:

$C_{in} =80\% =0.80 mol$

$C_{out}= CO_2(out) +CO_{out}$

$=14\%+0.4\%\\ =0.140+0.004\\=0.144mol$

Thus, to determine F

$0.80F \times \dfrac{1}{12}=(0.144)\times (100)\\ 0.080F=14.4\\ F=18lb mol$

The molar mass of the carbon is$12 lb/mol$ . So,

Mass of F$=$ Number of moles$\times$ Molar mass

$= 18lb mol \times 12lb/mol\\ =216lb$

Nitrogen

$N_2(in)=79\%=0.79mol\\ N_2(out)=80\%=0.80mol$

Thus, to determine A

$80=(A)\times(0.79)\\ A=101.26lb mol$

Now, the moles of hydrogen in dry cola and water is determined as follow:

Moles of H in dry coal$=(\dfrac{Mass of H in F}{Molar mass of H})$

$=12.86 moles$

From the ideal gas equation we find the temperature of Coal gas

$T=\dfrac{P\times V}{n\times R}\\ =\dfrac{29.9\times 100}{12.86\times 62.363}\\ =3.728K$

Dew point will be 12