Question

__Fe203(s)+__C(s)---> __ Fe(s)+ CO2(g)
A. 2,3,2,3 B. 2,3,4,3. C.1,1,2,3

Answer 1

Option A.

`\rm 2\; Fe_2O_3\, (s) + 3\; C\, (s) \to 2 of hte \; Fe\, (s) + 3\; CO_2\, (g)`.

Step-by-step explanation:

Balance by the conservation of atoms

In a chemical reaction, the left-hand side of the equation should contain as many atoms of one element as the right-hand side does.

Start by assuming that the coefficient of the most complex species (e.g.,
`\rm Fe_2O_3\, (s)` is
`1`.

`\rm 1\; Fe_2O_3\, (s) + ?\; C\, (s) \to ? \; Fe\, (s) + ?\; CO_2\, (g)`.

`\rm Fe_2O_3\, (s)` is the only species with iron and oxygen atoms on the left-hand side. On the left-hand side of the equation, it can be confirmed that there are

• 2 units of Fe atoms, and
• 3 units of O atoms.

By the conservation of atoms, the right-hand side should also contain that many atoms of Fe and O, respectively. Since on the right-hand side,
`\rm Fe\, (s)` is the only species with Fe atoms, the coefficient of
`\rm Fe\, (s)` should be 2. Similarly,
`\rm CO_2\, (g)` is the only species with O atoms. Additionally, each unit of
`\rm CO_2\, (g)` provides two units of O atoms. Hence, the coefficient of
`\rm CO_2\, (g)` should be
`\displaystyle (3)/(2)`.

`\displaystyle \rm 1\; Fe_2O_3\, (s) + ?\; C\, (s) \to 1\; Fe\, (s) + (3)/(2)\; CO_2\, (g)`.

There are
`\displaystyle (3)/(2)` units of
`\rm CO_2\, (g)` on the right-hand side. Besides, each unit of
`\rm CO_2\, (g)` contains one C atom. Hence, it can be concluded that each side of the equation should contain

• 
  `\displaystyle (3)/(2)` units of C.

All the C atoms on the left-hand side of the equation are in the form
`\rm C\, (s)`. Hence, the coefficient of
`\rm C\, (s)` should also be
`\displaystyle (3)/(2)`.

`\displaystyle \rm 1\; Fe_2O_3\, (s) + (3)/(2)\; C\, (s) \to 1\; Fe\, (s) + (3)/(2)\; CO_2\, (g)`.

Coefficients should preferably be whole numbers. Hence, multiply all coefficients by the denominator (or the gcd of the denominators in case there are more than one of these) to get rid of the fraction. In this case, multiply all coefficients by
`2` to obtain:

`\rm 2\; Fe_2O_3\, (s) + 3\; C\, (s) \to 2 \; Fe\, (s) + 3\; CO_2\, (g)`.