How many grams of iron can be produced of 156000 calories of heat are absorbed by a large enough sample of iron III oxide
To determine the number of grams of iron that can be produced, we need to first identify the chemical equation for the reaction involved.
The reaction between iron (Fe) and iron(III) oxide (Fe2O3) can be represented as:
2 Fe2O3 + 3 C --> 4 Fe + 3 CO2
From this balanced equation, we can see that 2 moles of Fe2O3 react with 3 moles of carbon (C) to produce 4 moles of Fe.
Next, we need to convert the given heat energy (156,000 calories) into the amount of energy required to produce the desired amount of iron. For this conversion, we need to know the enthalpy change (ΔH) for the reaction.
Let's assume that the enthalpy change for this reaction is ΔH = -824 kJ/mol (negative because it is an exothermic reaction).
We also need to know the molar mass of Fe2O3, which is 159.69 g/mol.
Now, let's calculate the amount of iron (Fe) produced:
1. Convert calories to kilojoules (kJ):
1 cal = 0.004184 kJ
Therefore, 156,000 cal = 651.264 kJ
2. Calculate the moles of Fe produced using the molar enthalpy change (ΔH) value:
Moles = Energy change (kJ) / ΔH (kJ/mol)
Moles = 651.264 kJ / (-824 kJ/mol) = -0.7906 mol (negative sign indicates that it's a product)
3. Use the stoichiometry of the balanced equation to find the moles of Fe2O3 required:
2 moles of Fe2O3 produce 4 moles of Fe
Therefore, 0.7906 mol of Fe corresponds to (0.7906 mol / 2 mol) × 4 mol = 1.582 mol of Fe2O3
4. Convert moles of Fe2O3 to grams:
Mass (g) = Moles × Molar mass (g/mol)
Mass (g) = 1.582 mol × 159.69 g/mol = 252.32 g
Therefore, approximately 252.32 grams of iron can be produced if 156,000 calories of heat are absorbed by a large enough sample of iron(III) oxide (Fe2O3).