Question

$aA{l_2}{\left( {{C_2}{O_4}} \right)_3}\left( {\text{s}} \right)\xrightarrow{\Delta }bA{l_2}{O_3}\left( {\text{s}} \right) + cCO\left( {\text{g}} \right) + dC{O_2}\left( {\text{g}} \right)$
According to the equation for the reaction represented above, what is the mole of $CO$ to $C{O_2}$ that is produced by the decomposition of aluminum oxalate?
A.1 mole ${\text{CO}}$ ; 1 mole of $C{O_2}$
B.1 mole ${\text{CO}}$ ; 2 moles of $C{O_2}$
C.1 mole ${\text{CO}}$ ; 3 moles of $C{O_2}$
D.2 mole ${\text{CO}}$ ; 1 mole of $C{O_2}$
E.3 mole ${\text{CO}}$ ; 1 mole of $C{O_2}$

Answer 1

Here we have to first balance the reaction to obtain the value of c and d from the reaction. Balancing the reaction means the number of atoms present on the reactant side should be equal to the number of atoms on the product side.

Complete step by step answer
By looking at the unbalanced reaction we can say that:
$A{l_2}{\left( {{C_2}{O_4}} \right)_3}\left( {\text{s}} \right)\xrightarrow{\Delta }A{l_2}{O_3}\left( {\text{s}} \right) + CO\left( {\text{g}} \right) + C{O_2}\left( {\text{g}} \right)$
The number of Aluminum atoms present on the reactant side is equal to the number of aluminum atoms present on the product side.
The number of carbon atoms on the reactant side is 6 and the total number of carbon atoms on the product side is 2.
The number of the oxygen atom on the reactant side is 12 and the total number of the oxygen atom on the product side 6.
So, we can write the balanced chemical reaction as:
$A{l_2}{\left( {{C_2}{O_4}} \right)_3}\left( {\text{s}} \right)\xrightarrow{\Delta }A{l_2}{O_3}\left( {\text{s}} \right) + 3CO\left( {\text{g}} \right) + 3C{O_2}\left( {\text{g}} \right)$
From the balance reaction we can say that:
a is equal to 1
b is equal to 1
c is equal to 3
d is equal to 3
But in the question, we are asked to write the moles associated with $CO$ and $C{O_2}$ .
So by taking the ratio of the number of moles of $CO$ and $C{O_2}$ we get:
$\dfrac{c}{d} = \dfrac{3}{3} = \dfrac{1}{1}$

Therefore, we can conclude that the correct answer to the question is option A.

Note: Here we must focus on the balancing of the reaction and as the number of moles of both $CO$ and $C{O_2}$ is 3 that is produced by the decomposition of aluminum oxalate we can take the ratio of their stoichiometric constant.