Answer to Question #189273 in General Chemistry for gerarld

Question #189273

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.


1
Expert's answer
2021-05-05T07:13:22-0400

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\\%\\\\\n\n =0.140+0.004\\\\=0.144mol"

Thus, to determine F

"0.80F \\times \\dfrac{1}{12}=(0.144)\\times (100)\\\\\n\n 0.080F=14.4\\\\\n\nF=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\\\\\n\n =216lb"

Nitrogen

"N_2(in)=79\\%=0.79mol\\\\\n\nN_2(out)=80\\%=0.80mol"

Thus, to determine A

"80=(A)\\times(0.79)\\\\\n\nA=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}\\\\\n=\\dfrac{29.9\\times 100}{12.86\\times 62.363}\\\\\n=3.728K"

Dew point will be 12


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