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Limiting Reagent or Reactant

A mixture of ...

Question

A mixture of ferric oxide $(F e_{2} O_{3})$ and aluminium ( $A l$ ) is used as a solid rocket fuel which reacts to give $A l_{2} O_{3}$ and $F e$ . No other reactants and products are involved. On complete reaction of $1$ mole of $F e_{2} O_{3}$ , $200$ units of energy is released. The energy released when $16$ kg of $F e_{2} O_{3}$ reacts with $2.7$ kg of $A l$ is $x \times 10^{3}$ units. Value of $x$ is :

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Solution

The balanced reaction is as follows:
$F e_{2} O_{3} + 2 A l \to A l_{2} O_{3} + 2 F e + E n e r g y ↑$

According to this reaction, if their mole ratio is $1 : 2$ , then the energy released will be maximum.

Given:
$16$ kg of $F e_{2} O_{3}$ and $2.7$ kg of $A l$

Moles of $F e_{2} O_{3}$ $=$ $\frac{16000}{160}$ $=$ $100$

Moles of $A l =$ $\frac{2700}{27}$ $=$ $100$

As $A l$ is limiting reagent, so only $50$ mol of $F e_{2} O_{3}$ reacts with $100$ mol of Al and energy released will be $50 \times 100$ $=$ $5000$ units.

$∴$ value of $x$ is $5$ .

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Q. an intimate mixture of ferric oxide and aluminium is used as solid rocket fuels.calculate fuel value per gram and fuel value per cc of the mixture.heats of formation and densities are as follows;

dHf al2o3= 399 kcal/mole
dhf fe2o3=199kcal/mole density of fe2o3=5.2g/cc density of al=2.7gm/cc

soln;-
2al +3/2 o2 -->al2o3 eq 1
2fe + 3/2 o2---- fe2o3 eg 2
2al +fe2o3= al2o3 + 2fe

1*eq 1 - 1*eq 2
dh=-399-(-199)
= -200 kcal

fuel value/gram
2 moles of al + 1 mol fe2o3
2*27 + 1 * 160
214gm

; fuel value /gram = 200/214= 0.93kcal/gm
fuel gram/ cc
2 mole of al= 54/2.7= 20cc
1 mole of fe2o3 = 214/5.2=30.7cc // here ,1 mole of fe2o3 = 160 ...... and 214gm is the sumation of both al
and fe2o3 ..... while if we multiply 30.7*5.2 =159.64 which is near about 160

Q. An intimate mixture of ferric oxide,

F e_{2} O_{3}

, and aluminium, Al, is used in solid fuel in rockets. Calculate the fuel value (in Kcal) per cc of the mixture. Heats of formation and densities are as follows :

H_{f} (A l_{2} O_{3}) = 399

H_{f} (F e_{2} O_{3}) = 199

Kcal/mol, density of

F e_{2} O_{3} = \frac{16}{3} g m / c c

, density of Al = 2.7 gm/cc,

Q. How much thermal energy released when 36.0 g of Al reacts with excess of

F e_{2} O_{3}

:

F e

reacts completely with 0.65 mole of

O_{2}

to give a mixture of only

F e O

F e_{2} O_{3}

.
The mole ratio of ferrous oxide to ferric oxide is x: y, then (x+y) is

1 m o l

(F e)

reacts competely with

0.65 m o l O_{2}

to give a mixture of only

F e O

F e_{2} O_{3}

. Mole ratio ferrous oxide to ferric oxide to ferric oxide is:

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