Answer:
a) molar composition of this gas on both a wet and a dry basis are
5.76 moles and 5.20 moles respectively.
Ratio of moles of water to the moles of dry gas =0.108 moles
b) Total air required = 68.51 kmoles/h
So, if combustion is 75% complete; then it is termed as incomplete combustion which require the same amount the same amount of air but varying product will be produced.
Explanation:
Let assume we have 100 g of mixture of gas:
Given that :
Mass of methane =75 g
Mass of ethane = 10 g
Mass of ethylene = 5 g
∴ Mass of the balanced water: 100 g - (75 g + 10 g + 5 g)
Their molar composition can be calculated as follows:
Molar mass of methane ![CH_4}= 16 g/mol](https://tex.z-dn.net/?f=CH_4%7D%3D%2016%20g%2Fmol)
Molar mass of ethane ![C_2H_6= 30 g/mol](https://tex.z-dn.net/?f=C_2H_6%3D%2030%20g%2Fmol)
Molar mass of ethylene ![C_2H_4 = 28 g/mol](https://tex.z-dn.net/?f=C_2H_4%20%3D%2028%20g%2Fmol)
Molar mass of water ![H_2O=18g/mol](https://tex.z-dn.net/?f=H_2O%3D18g%2Fmol)
number of moles = ![\frac{mass}{molar mass}](https://tex.z-dn.net/?f=%5Cfrac%7Bmass%7D%7Bmolar%20mass%7D)
Their molar composition can be calculated as follows:
![n_{CH_4}= \frac{75}{16}](https://tex.z-dn.net/?f=n_%7BCH_4%7D%3D%20%5Cfrac%7B75%7D%7B16%7D)
4.69 moles
![n_{C_2H_6} = \frac{10}{30}](https://tex.z-dn.net/?f=n_%7BC_2H_6%7D%20%3D%20%5Cfrac%7B10%7D%7B30%7D)
0.33 moles
![n_{C_2H_4} = \frac{5}{28}](https://tex.z-dn.net/?f=n_%7BC_2H_4%7D%20%3D%20%5Cfrac%7B5%7D%7B28%7D)
0.18 moles
![n_{H_2O}= \frac{10}{18}](https://tex.z-dn.net/?f=n_%7BH_2O%7D%3D%20%5Cfrac%7B10%7D%7B18%7D)
0.56 moles
Total moles of gases for wet basis = (4.69 + 0.33 + 0.18 + 0.56) moles
= 5.76 moles
Total moles of gas for dry basis = (5.76 - 0.56)moles
= 5.20 moles
Ratio of moles of water to the moles of dry gas = ![\frac{n_{H_2O}}{n_{drygas}}](https://tex.z-dn.net/?f=%5Cfrac%7Bn_%7BH_2O%7D%7D%7Bn_%7Bdrygas%7D%7D)
= ![\frac{0.56}{5.2}](https://tex.z-dn.net/?f=%5Cfrac%7B0.56%7D%7B5.2%7D)
= 0.108 moles
b) If 100 kg/h of this fuel is burned with 30% excess air(combustion); then we have the following equations:
![CH_4 + 2O_2_{(g)} ------> CO_2_{(g)} +2H_2O](https://tex.z-dn.net/?f=CH_4%20%2B%202O_2_%7B%28g%29%7D%20------%3E%20CO_2_%7B%28g%29%7D%20%2B2H_2O)
4.69 2× 4.69
moles moles
![C_2H_6+ \frac{7}{2}O_2_{(g)} ------> 2CO_2_{(g)} + 3H_2O](https://tex.z-dn.net/?f=C_2H_6%2B%20%5Cfrac%7B7%7D%7B2%7DO_2_%7B%28g%29%7D%20------%3E%202CO_2_%7B%28g%29%7D%20%2B%203H_2O)
0.33 3.5 × 0.33
moles moles
![C_2H_4+3O_2_{(g)} ----->2CO_2+2H_2O](https://tex.z-dn.net/?f=C_2H_4%2B3O_2_%7B%28g%29%7D%20-----%3E2CO_2%2B2H_2O)
0.18 3× 0.18
moles moles
Mass flow rate = 100 kg/h
Their Molar Flow rate is as follows;
![CH_4 = 4.69 k moles/h\\C_2H_6 = 0.33 k moles/h\\C_2H_4=0.18kmoles/h](https://tex.z-dn.net/?f=CH_4%20%3D%204.69%20k%20moles%2Fh%5C%5CC_2H_6%20%3D%200.33%20k%20moles%2Fh%5C%5CC_2H_4%3D0.18kmoles%2Fh)
Total moles of
required = (2 × 4.69) + (3.5 × 0.33) + (3 × 0.18) k moles
= 11.075 k moles.
In 1 mole air = 0.21 moles ![O_2](https://tex.z-dn.net/?f=O_2)
Thus, moles of air required =
= 52.7 k mole
30% excess air = 0.3 × 52.7 k moles
= 15.81 k moles
Total air required = (52.7 + 15.81 ) k moles/h
= 68.51 k moles/h
So, if combustion is 75% complete; then it is termed as incomplete combustion which require the same amount the same amount of air but varying product will be produced.