# What is the entropy change associated with the chemical reaction that occurs when iron oxide is converted to its metal form?

Fe2O3(s) + 3CO(g) → 2Fe(s) + 3CO2(g)

A. Zero
B. Positive
C. Negative
D. Cannot be determined

I think the answer is b or c.

## To determine the entropy change associated with a chemical reaction, you need to consider the change in entropy of the system before and after the reaction.

First, let's analyze the number of moles and states of each substance involved in the reaction:

Fe2O3(s) + 3CO(g) → 2Fe(s) + 3CO2(g)

From the balanced equation, we can observe:

1) Fe2O3(s) is in the solid state.
2) CO(g) is in the gaseous state.
3) Fe(s) is in the solid state.
4) CO2(g) is in the gaseous state.

The entropy change associated with the reaction can be calculated using the formula:

ΔS = Σ S(products) - Σ S(reactants)

Since the reaction involves multiple substances, we need to calculate the entropy change of each substance and then sum them up.

To calculate the entropy change for each substance, we can use the equation:

ΔS = n * R * ln(V2/V1)

Where:
- ΔS is the change in entropy.
- n is the number of moles.
- R is the ideal gas constant (8.314 J/(mol K)).
- V2 is the final volume.
- V1 is the initial volume.

Now, let's calculate the entropy change for each substance:

1) Fe2O3(s): Since Fe2O3(s) is in the solid state, its change in entropy is negligible. Therefore, its entropy change (ΔS) is approximately equal to zero.

2) CO(g): Use the formula ΔS = n * R * ln(V2/V1). Since the reaction involves 3 moles of CO, the entropy change for CO(g) can be calculated as follows:

ΔS = 3 * R * ln(V2/V1)

3) Fe(s): Similar to Fe2O3(s), Fe(s) is in the solid state, so its entropy change is negligible. Therefore, its entropy change (ΔS) is approximately equal to zero.

4) CO2(g): Use the formula ΔS = n * R * ln(V2/V1). Since the reaction involves 3 moles of CO2, the entropy change for CO2(g) can be calculated as follows:

ΔS = 3 * R * ln(V2/V1)

Finally, sum up the entropy changes for each substance:

Total entropy change (ΔS) = ΔS(CO) + ΔS(CO2)

Now, analyze the calculated value of the total entropy change. If it is positive, the answer is B (Positive). If it is negative, the answer is C (Negative). If the total entropy change is zero, the answer is A (Zero).

It is important to note that without specific values for the volumes of the substances involved, we cannot determine the exact sign (positive or negative) of the entropy change in this reaction. However, based on the nature of the substances and typical reactions, we can assume that the formation of more gaseous molecules (CO2) would generally lead to a positive entropy change.

So, in this case, the answer is most likely B (Positive).

## Why guess?

Work it out.
dHrxn = (n*dHf products) - (n*dHf reactants)