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



Since the coal contained the 2.52.5% %moisture and the basis is 100lbmol100 lb mol , the water or moisture entering the system can be calculated as follows:

H2Oin=2.5H_2O_{in}=2.5%

=2.5100×100= \dfrac{2.5}{100}\times 100

=2.5mol=2.5 mol in F

Therefore, the coal entering the system is

Coalin=1002.5Coal_{in}= 100-2.5

=97.5mol= 97.5 mol in F

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

Cin=80%=0.80molC_{in} =80\% =0.80 mol

Cout=CO2(out)+COoutC_{out}= CO_2(out) +CO_{out}

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

Thus, to determine F

0.80F×112=(0.144)×(100)0.080F=14.4F=18lbmol0.80F \times \dfrac{1}{12}=(0.144)\times (100)\\ 0.080F=14.4\\ F=18lb mol

The molar mass of the carbon is12lb/mol12 lb/mol . So,

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

=18lbmol×12lb/mol=216lb= 18lb mol \times 12lb/mol\\ =216lb

Nitrogen

N2(in)=79%=0.79molN2(out)=80%=0.80molN_2(in)=79\%=0.79mol\\ N_2(out)=80\%=0.80mol

Thus, to determine A

80=(A)×(0.79)A=101.26lbmol80=(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=(MassofHinFMolarmassofH)=(\dfrac{Mass of H in F}{Molar mass of H})

=12.86moles=12.86 moles

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

T=P×Vn×R=29.9×10012.86×62.363=3.728KT=\dfrac{P\times V}{n\times R}\\ =\dfrac{29.9\times 100}{12.86\times 62.363}\\ =3.728K

Dew point will be 12


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