Question

Fe₂O₃ + H₂ → Fe + H₂OBalance this equation: How many grams of iron will be produced from 9 moles of hydrogen gas?

Answer 1

Balanced equation: Fe₂O₃ + 3H₂ → 2Fe + 3H₂O

The grams of iron produced = 335.07 grams

Step-by-step explanation

Given:

The unbalanced equation is: Fe₂O₃ + H₂ → Fe + H₂O

The moles of hydrogen gas that reacted = 9 moles.

What to find:

The balanced question and the mass in grams of iron produced.

Solution

Step 1: Balance the equation.

The equation can be balanced by adding 3 as the coefficient of H₂ on the reactant side and 2 and 3 as the coefficients of Fe and H₂O respectively.

Fe₂O₃ + 3H₂ → 2Fe + 3H₂O

Step 2: Determine the moles of Fe produced.

Using the mole ratio of H₂ and Fe in the balanced equation in step 1 and the given moles of H₂ that reacted; then the moles of Fe produced is

`\begin{gathered} 3mol\text{ }H₂=2mol\text{ }Fe \\ \\ 9mol\text{ }H₂=x \\ \\ Cross\text{ }multiply\text{ }and\text{ }divide\text{ }both\text{ }sides\text{ }by\text{ }3mol\text{ }H₂ \\ \\ x=\frac{9mol\text{ }H₂}{3mol\text{ }H₂}*2mol\text{ }Fe \\ \\ x=6\text{ }mol\text{ }Fe \end{gathered}`

Step 3: Covert the 6 moles of Fe produced in step 2 to grams.

From the periodic table; the molar mass of Fe = 55.845 g/mol.

So, using the mole formula, the mass of Fe produced is

`\begin{gathered} Moles=\frac{Mass}{Molar\text{ }mass} \\ \\ Mass\text{ }of\text{ }Fe=Moles* Molar\text{ }mass \\ \\ Mass\text{ }of\text{ }Fe=6\text{ }mol*55.845\text{ }g\text{/}mol \\ \\ Mass\text{ }of\text{ }Fe==335.07\text{ }grams \end{gathered}`

Therefore, the grams of iron that will be produced from 9 moles of hydrogen gas is 335.07 grams