an 0.5031 gram sample of iron ore is determined through redox titration using K2Cr2O7. The sample was dissolved in HCl and all the iron was converted to the 2+ state. Titration to the endpoint required 24.34 mL of 0.01887 mol/L K2Cr2O7. Calculate the amount of Fe2O3 as a percent of the original sample.
Fe2O3 ==> 2Fe^3+ and reduce to Fe^2+.
6Fe^2+ + Cr2O7^2- ==> 6Fe^3+ + 2Cr^3+
I balanced only the redox portion of the equation which is sufficient for what we want to do.
mols Cr2O7^2- = M x L = ?
mols Fe = 6 x that (look at the coefficients in the equation above).
g Fe = mols Fe x atomic mass Fe = ?
%Fe = (g Fe/mass sample)*100 = ?
then convert %Fe to %Fe2O3 this way.
%Fe2O3 = %Fe x (molar mass Fe2O3/2*atomic mass Fe) = ?
To calculate the amount of Fe2O3 as a percent of the original sample, we need to determine the amount of iron (Fe) in the sample and then convert it to Fe2O3.
Here are the steps to calculate the amount of Fe2O3:
Step 1: Calculate the number of moles of K2Cr2O7 used in the titration.
We are given the volume (24.34 mL) and concentration (0.01887 mol/L) of K2Cr2O7 used. To calculate the number of moles, we use the formula:
moles of K2Cr2O7 = concentration × volume in liters
Converting the volume to liters:
volume = 24.34 mL = 24.34 mL × (1 L / 1000 mL) = 0.02434 L
Calculating the number of moles:
moles of K2Cr2O7 = 0.01887 mol/L × 0.02434 L = 0.0004582 mol
Step 2: Determine the stoichiometry between K2Cr2O7 and Fe.
From the balanced redox equation, we can determine the stoichiometry between K2Cr2O7 and Fe. The balanced equation for the reaction is:
6 Fe2+ + Cr2O72- + 14 H+ → 6 Fe3+ + 2 Cr3+ + 7 H2O
This equation tells us that for every 1 mol of K2Cr2O7 used, we need 6 moles of Fe2+.
Step 3: Convert moles of K2Cr2O7 to moles of Fe.
Using the stoichiometry, we can convert the number of moles of K2Cr2O7 to moles of Fe:
moles of Fe = moles of K2Cr2O7 × (6 moles of Fe2+ / 1 mole of K2Cr2O7)
moles of Fe = 0.0004582 mol × (6 / 1) = 0.0027492 mol
Step 4: Calculate the mass of Fe in the sample.
The atomic mass of Fe is 55.845 g/mol. Using this, we can calculate the mass of Fe in the sample:
mass of Fe = moles of Fe × atomic mass of Fe
mass of Fe = 0.0027492 mol × 55.845 g/mol = 0.1534 g
Step 5: Calculate the amount of Fe2O3 as a percent of the original sample.
From the balanced equation, the molar ratio between Fe and Fe2O3 is 2:3. This means that for every 2 moles of Fe, we have 3 moles of Fe2O3.
Using this ratio, we can calculate the amount of Fe2O3:
moles of Fe2O3 = moles of Fe × (3 moles of Fe2O3 / 2 moles of Fe)
moles of Fe2O3 = 0.0027492 mol × (3 / 2) = 0.0041238 mol
Finally, to calculate the percent of Fe2O3 in the original sample:
percent of Fe2O3 = (moles of Fe2O3 / original sample weight) × 100
percent of Fe2O3 = (0.0041238 mol / 0.5031 g) × 100
Using the given weight of the sample (0.5031 g):
percent of Fe2O3 = 0.008207 × 100 = 0.8207%
Therefore, the amount of Fe2O3 as a percent of the original sample is approximately 0.8207%.