Question

In the balanced equations, the values of \(a\), \(b\) and \(c\) are respectively
\[ aFe_3O_4(s)+bAl(s)\longrightarrow Fe(s)+Al_2O_3(s) \] \[ V_2O_5(s)+cCa(s)\longrightarrow V(s)+CaO(s) \]

• A. \(4,5,5\)
• B. \(3,4,5\)
• C. \(3,8,5\)
• D. \(4,8,5\)

Hint:

While balancing chemical equations, first balance atoms that appear in complex compounds, then balance metals, and finally check oxygen atoms.

Answer 1

The Correct Option is C

Step 1: Balance the first equation.
The given equation is \[ aFe_3O_4+bAl\longrightarrow Fe+Al_2O_3 \] This is an aluminothermic reduction reaction.
To balance oxygen atoms, take \[ 3Fe_3O_4 \] Then the number of oxygen atoms is \[ 3\times 4=12 \] To get 12 oxygen atoms on the product side, we need \[ 4Al_2O_3 \] because \[ 4\times 3=12 \] Now, \(4Al_2O_3\) contains \[ 4\times 2=8 \] aluminium atoms.
So, \[ b=8 \] Also, \(3Fe_3O_4\) contains \[ 3\times 3=9 \] iron atoms.
Hence, the balanced equation becomes \[ 3Fe_3O_4+8Al\longrightarrow 9Fe+4Al_2O_3 \] Therefore, \[ a=3,\qquad b=8 \]

Step 2: Balance the second equation.
The given equation is \[ V_2O_5+cCa\longrightarrow V+CaO \] In \(V_2O_5\), there are 5 oxygen atoms.
Each \(CaO\) contains 1 oxygen atom.
Therefore, to balance oxygen atoms, we need \[ 5CaO \] This requires \[ 5Ca \] So, \[ c=5 \] Also, \(V_2O_5\) contains 2 vanadium atoms, so the balanced equation is \[ V_2O_5+5Ca\longrightarrow 2V+5CaO \]

Step 3: Combine the values.
From the first balanced equation, \[ a=3,\qquad b=8 \] From the second balanced equation, \[ c=5 \] Thus, \[ a,b,c=3,8,5 \]

Step 4: Final conclusion.
Therefore, the required values of \(a\), \(b\), and \(c\) are \[ \boxed{3,8,5} \]