Coefficients Party, Part 8
When liquid octane
(
C
X
8
H
X
1
8
)
combusts, it forms carbon dioxide and water vapor. The reaction can be modeled by the following, where
α
,
β
,
γ
,
and
δ
are positive coprime integers,
α
C
X
8
H
X
1
8
(
l
)
+
β
O
X
2
(
g
)
→
γ
C
O
X
2
(
g
)
+
δ
H
X
2
O
(
g
)
Find
α
+
β
+
γ
+
δ
.
Image Credit: Wikimedia Jynto .
The answer is 61.
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4 solutions
By given rules we get series of equations: 8 α = γ 1 8 α = 2 δ 2 β = 2 γ + δ
Considering it has infinite number of solutions (3 equations, 4 variables), we are looking for smallest integer solution. Solving for α , γ , δ results in: α = 2 5 2 β γ = 2 5 1 6 β δ = 2 5 1 8 β Therefore β = 2 5
This question itself is wrongly framed as it not mentioned whether we have to take the smallest integer coefficients.
see basically this was an easy according to this formula. if take as aC8H18+bO2-------------> cCo2 + dH2o now equate the same elements from lhs to rhs for ex. 8a=c here in lhs carbon has 8 atom and on RHS carbon has 1 atom so u can equate
The balanced formula is: 2 C 8 H 1 8 + 2 5 O 2 − > 1 6 C O 2 + 1 8 H 2 O Thus we have: 2 + 2 5 + 1 6 + 1 8 = 6 1