Iron(III) oxide can be reduced to metallic iron by heating it in the presence of carbon. Balance the following equation, then determine the ratio of C to Fe in the reaction?

Fe2O3 + C → Fe + CO2?

2Fe2O3 + 3C → 4Fe + 3CO2?

C:Fe = 3/2. Look at the coefficients.

To balance the equation Fe2O3 + C → Fe + CO2, we need to ensure that the number of atoms of each element is the same on both sides of the equation.

Balancing the equation step by step:

1. Start by counting the number of atoms for each element on both sides of the equation:
Fe: 2 on the left side, 1 on the right side
O: 3 on the left side, 2 on the right side
C: 1 on the left side, 1 on the right side
CO2: 2 on the right side

2. Begin balancing with the element that appears in the fewest compounds. In this case, carbon (C) appears in only one compound on each side.

Multiply the C on the left side by 2:
Fe2O3 + 2C → Fe + CO2

3. The number of carbon atoms is now balanced, so let's move on to balancing the oxygen (O) atoms.

There are 3 O atoms on the left side and 2 in CO2 on the right side. To balance the number of O atoms, we need to add another CO2 molecule on the right side:

Fe2O3 + 2C → Fe + 2CO2

4. The number of oxygen atoms is now balanced.

5. Finally, count the number of iron (Fe) atoms. There are 2 Fe atoms on the left side and 1 on the right side. To balance them, we need to multiply the Fe on the right side by 2:

Fe2O3 + 2C → 2Fe + 2CO2

Now, the equation is balanced.

To determine the ratio of C to Fe in the reaction, we compare the coefficients of C and Fe on the balanced equation. From the equation, we can see that for every 2 moles of carbon (C), we get 2 moles of iron (Fe). Therefore, the ratio of C to Fe is 1:1.

To balance the equation Fe2O3 + C → Fe + CO2, we need to ensure that the same number of atoms of each element appears on both sides of the equation.

First, let's count the number of atoms for each element:
Fe: There are 2 Fe atoms on the left side and 1 Fe atom on the right side.
O: There are 3 O atoms on the left side and 2 O atoms on the right side.
C: There is 1 C atom on the left side and 1 C atom on the right side.

Starting with Fe, we see that there are 2 Fe atoms on the left side and only 1 Fe atom on the right side. This means we need to balance the number of Fe atoms. To do that, we can put a coefficient of 2 in front of Fe on the right side:

Fe2O3 + C → 2Fe + CO2

Now let's balance the O atoms. There are 3 O atoms on the left side and 2 O atoms on the right side. To balance them, we can put a coefficient of 3/2 in front of CO2:

Fe2O3 + C → 2Fe + (3/2)CO2

To simplify the equation, let's multiply every coefficient by 2 to get rid of the fractions:

2Fe2O3 + 2C → 4Fe + 3CO2

Now the equation is balanced.

To determine the ratio of C to Fe in the reaction, we can compare the coefficients in front of C and Fe. From the balanced equation, we see that the coefficient in front of C is 2, and the coefficient in front of Fe is 4.

Therefore, the ratio of C to Fe in the reaction is 2:4, which simplifies to 1:2.