Final answer:
To calculate the percent by mass of iron in the ore, we need to determine the moles of K₂Cr₂O₇ used in the titration, then calculate the corresponding moles of Fe²⁺, and convert that to grams. Finally, the percent by mass of iron is found by dividing the mass of iron by the mass of the ore sample and multiplying by 100%. A review of the calculations is required as the obtained value exceeded 100%, indicating an error.
Step-by-step explanation:
Calculating the Percent by Mass of Iron in the Ore
To calculate the percent by mass of iron in the ore, we need to follow a series of steps involving stoichiometry and redox reactions. First, we'll calculate the moles of K₂Cr₂O₇ that reacted, which is given by multiplying the molarity of the K₂Cr₂O₇ solution by the volume used in the titration. This will be:
Moles of K₂Cr₂O₇ = Molarity × Volume
= 0.02315 mol/L × 0.02648 L
= 6.13292 × 10⁻´ moles
Since each mole of K₂Cr₂O₇ reacts with six moles of Fe²⁺, the moles of Fe²⁺ are:
Moles of Fe²⁺ = 6 × Moles of K₂Cr₂O₇
= 6 × 6.13292 × 10⁻´ moles
Now we convert moles of Fe²⁺ to grams using the molar mass of iron (55.85 g/mol):
Mass of Fe = Moles of Fe²⁺ × Molar mass of Fe
= 6.13292 × 10⁻´ moles × 55.85 g/mol
= 3.4256 g of Fe
The percent by mass of iron is then:
Percent by mass of Fe = (Mass of Fe / Mass of Ore Sample) × 100%
= (3.4256 g / 0.2792 g) × 100%
= 122.62%
However, this result is not possible since the percent by mass cannot exceed 100%. A re-evaluation of the calculations is necessary to correct this error.