Answer :
(1) The number of grams needed of each fuel
are 19.23 g and 20.41 g respectively.
(2) The number of moles of each fuel
are 0.641 moles and 0.352 moles respectively.
(3) The balanced chemical equation for the combustion of the fuels.
![C_2H_6+\frac{7}{2}O_2\rightarrow 2CO_2+3H_2O](https://tex.z-dn.net/?f=C_2H_6%2B%5Cfrac%7B7%7D%7B2%7DO_2%5Crightarrow%202CO_2%2B3H_2O)
![C_4H_{10}+\frac{13}{2}O_2\rightarrow 4CO_2+5H_2O](https://tex.z-dn.net/?f=C_4H_%7B10%7D%2B%5Cfrac%7B13%7D%7B2%7DO_2%5Crightarrow%204CO_2%2B5H_2O)
(4) The number of moles of
produced by burning each fuel is 1.28 mole and 1.41 mole respectively.
The fuel that emitting least amount of
is ![C_2H_6](https://tex.z-dn.net/?f=C_2H_6)
Explanation :
<u>Part 1 :</u>
First we have to calculate the number of grams needed of each fuel
.
As, 52 kJ energy required amount of
= 1 g
So, 1000 kJ energy required amount of
= ![\frac{1000}{52}=19.23g](https://tex.z-dn.net/?f=%5Cfrac%7B1000%7D%7B52%7D%3D19.23g)
and,
As, 49 kJ energy required amount of
= 1 g
So, 1000 kJ energy required amount of
= ![\frac{1000}{49}=20.41g](https://tex.z-dn.net/?f=%5Cfrac%7B1000%7D%7B49%7D%3D20.41g)
<u>Part 2 :</u>
Now we have to calculate the number of moles of each fuel
.
Molar mass of
= 30 g/mole
Molar mass of
= 58 g/mole
![\text{ Moles of }C_2H_6=\frac{\text{ Mass of }C_2H_6}{\text{ Molar mass of }C_2H_6}=\frac{19.23g}{30g/mole}=0.641moles](https://tex.z-dn.net/?f=%5Ctext%7B%20Moles%20of%20%7DC_2H_6%3D%5Cfrac%7B%5Ctext%7B%20Mass%20of%20%7DC_2H_6%7D%7B%5Ctext%7B%20Molar%20mass%20of%20%7DC_2H_6%7D%3D%5Cfrac%7B19.23g%7D%7B30g%2Fmole%7D%3D0.641moles)
and,
![\text{ Moles of }C_4H_{10}=\frac{\text{ Mass of }C_4H_{10}}{\text{ Molar mass of }C_4H_{10}}=\frac{20.41g}{58g/mole}=0.352moles](https://tex.z-dn.net/?f=%5Ctext%7B%20Moles%20of%20%7DC_4H_%7B10%7D%3D%5Cfrac%7B%5Ctext%7B%20Mass%20of%20%7DC_4H_%7B10%7D%7D%7B%5Ctext%7B%20Molar%20mass%20of%20%7DC_4H_%7B10%7D%7D%3D%5Cfrac%7B20.41g%7D%7B58g%2Fmole%7D%3D0.352moles)
<u>Part 3 :</u>
Now we have to write down the balanced chemical equation for the combustion of the fuels.
The balanced chemical reaction for combustion of
is:
![C_2H_6+\frac{7}{2}O_2\rightarrow 2CO_2+3H_2O](https://tex.z-dn.net/?f=C_2H_6%2B%5Cfrac%7B7%7D%7B2%7DO_2%5Crightarrow%202CO_2%2B3H_2O)
and,
The balanced chemical reaction for combustion of
is:
![C_4H_{10}+\frac{13}{2}O_2\rightarrow 4CO_2+5H_2O](https://tex.z-dn.net/?f=C_4H_%7B10%7D%2B%5Cfrac%7B13%7D%7B2%7DO_2%5Crightarrow%204CO_2%2B5H_2O)
<u>Part 4 :</u>
Now we have to calculate the number of moles of
produced by burning each fuel to produce 1000 kJ.
![C_2H_6+\frac{7}{2}O_2\rightarrow 2CO_2+3H_2O](https://tex.z-dn.net/?f=C_2H_6%2B%5Cfrac%7B7%7D%7B2%7DO_2%5Crightarrow%202CO_2%2B3H_2O)
From this we conclude that,
As, 1 mole of
react to produce 2 moles of ![CO_2](https://tex.z-dn.net/?f=CO_2)
As, 0.641 mole of
react to produce
moles of ![CO_2](https://tex.z-dn.net/?f=CO_2)
and,
![C_4H_{10}+\frac{13}{2}O_2\rightarrow 4CO_2+5H_2O](https://tex.z-dn.net/?f=C_4H_%7B10%7D%2B%5Cfrac%7B13%7D%7B2%7DO_2%5Crightarrow%204CO_2%2B5H_2O)
From this we conclude that,
As, 1 mole of
react to produce 4 moles of ![CO_2](https://tex.z-dn.net/?f=CO_2)
As, 0.352 mole of
react to produce
moles of ![CO_2](https://tex.z-dn.net/?f=CO_2)
So, the fuel that emitting least amount of
is ![C_2H_6](https://tex.z-dn.net/?f=C_2H_6)