Final answer:
The composition of the iron-carbon alloy with mass fractions of total ferrite and total cementite as 0.93 and 0.07, respectively, is approximately 99.531% iron and 0.469% carbon.
Step-by-step explanation:
To compute the composition of an iron-carbon alloy in which the mass fractions of total ferrite (alpha-Fe) and total cementite (Fe3C) are 0.93 and 0.07, respectively, we need to understand that ferrite is essentially pure iron while cementite contains a fixed ratio of iron to carbon, specifically 3 atoms of iron to 1 atom of carbon.
Using the Iron-Carbon phase diagram, we know that the composition of cementite by mass is approximately 6.7% carbon and 93.3% iron. Given the mass fraction of cementite in the alloy, we can calculate the mass fraction of carbon in the alloy as follows:
Carbon in cementite = 6.7% of total cementite
Carbon in alloy = 6.7% of 0.07 (cementite mass fraction) = 0.00469 or 0.469%
Since the rest of the alloy is ferrite which does not contain carbon, the mass percentage of carbon in the alloy is thus 0.469%. The remainder of the alloy is iron, so the mass percentage of iron can be calculated by subtracting the mass percentage of carbon from 100%, yielding:
Iron in alloy = 100% - Carbon in alloy = 100% - 0.469% = 99.531%
So, the composition of the iron-carbon alloy is 99.531% iron and 0.469% carbon, approximately, when considering the mass fractions provided.