Question

Compute the mass fraction of eutectoid ferrite in an iron-carbon alloy that contains 0.50 wt% C. The iron-iron carbide phase diagram is shown in the Animated Figure 9.24.

Answer 1

The mass fraction of eutectoid ferrite in a specific iron-carbon alloy cannot be calculated without the phase diagram. However, a similar calculation for mass percentage of iron in iron(III) oxide (Fe2O3) results in approximately 69.94% iron.

Step-by-step explanation:

To calculate the mass fraction of eutectoid ferrite in an iron-carbon alloy with 0.50 wt% C, you would typically refer to the iron-iron carbide phase diagram. However, since we are not provided with the diagram, we can't complete this specific calculation. Instead, we can discuss the calculation of mass percentage of iron in compounds of iron and oxygen as a similar example.

For instance, to find the mass percentage of iron in iron(III) oxide (Fe₂O₃), we must recognize that there are two moles of iron for every mole of iron(III) oxide. Iron has an atomic weight of 55.85 g/mol, so two moles of iron would weigh 111.7 g. Since one mole of Fe₂O₃ has a mass of 159.69 g (55.85 g/mol × 2 for iron plus 16.00 g/mol × 3 for oxygen), the mass percent of iron can be calculated as (111.7 g / 159.69 g) × 100, which gives approximately 69.94%.

Answer 2

To calculate the mass fraction of eutectoid ferrite in an iron-carbon alloy, you can use the lever rule. This involves determining the distances between phase boundaries on a phase diagram and using them in a formula. The mass fraction of eutectoid ferrite can then be used to calculate the mass fraction of carbon and iron.

Step-by-step explanation:

The mass fraction of eutectoid ferrite in an iron-carbon alloy can be calculated using the lever rule. The lever rule states that the fraction of a phase present in an alloy is equal to the distance of the phase boundary divided by the total distance between the two phase boundaries. In this case, the phase boundaries are the boundaries between eutectoid ferrite and austenite, and between eutectoid ferrite and cementite.

The mass fraction of eutectoid ferrite can be calculated using the following formula:

mass fraction of ferrite = (distance from eutectoid ferrite boundary) / (distance between eutectoid ferrite and austenite boundaries)

You will need to refer to the phase diagram to determine the distances. Once you have the mass fraction of eutectoid ferrite, you can calculate the mass fraction of carbon using the relationship between the two phases. For example, if eutectoid ferrite and cementite have a mass fraction ratio of 1:1, then the mass fraction of carbon would be equal to the mass fraction of ferrite. Finally, you can subtract the mass fraction of carbon from 1 to find the mass fraction of iron.