Iron is extracted from fe 2o 3 by a reaction with carbon (c) at very high temperature. if you take 2.86 x 10 4 g of fe 2o 3 to react with 9.05 x 10 3 g of c, how many moles of fe 2o 3 will be used? 2fe 2o 3 + 3c → 4fe + 3co 2

Balance Chemical Equation is as follow,

                             2 Fe₂O₃ + 3 C → 4Fe + 3 CO₂

According to this balance equation 319.38 g (2 moles) of Fe₂O₃ completely converts into product when reacted with 36 g (3 mole) of C.

Calculating amount of C required to consume 2.86 × 10⁴ g of Fe₂O₃,

As,
                       319.38 g Fe₂O₃ was consumed by  =  36 g of C
Then
          2.86 × 10⁴ g of Fe₂O₃ will be consumed by  =  X g of C

Solving for X,
                          X  =  (36 g × 2.86 × 10⁴ g) ÷ 319.38 g

                          X  =  3.22 × 10³ g of C.
So,
3.22 × 10³ g of C is required to consume 2.86 × 10⁴ g of Fe₂O₃, But, we are provided with 9.05 × 10³ g of C, means C is in excess and Fe₂O₃ is Limiting Reagent and will control the amount of product formed.

So,
As,
                    319.38 g of Fe₂O₃ produced  =  223.36 g of Fe
Then
           2.86 × 10⁴ g of Fe₂O₃ will produce  =  X g of Fe

Solving for X,
                                 X  =  (2.86 × 10⁴ g × 223.36 g) ÷ 319.38 g

                                 X  =  20001 g
Or,
                                 X  =  2.0 ×10⁴ g of Fe

The correct answer is b