Question 3.5.4: A soil sample is analyzed to determine the iron content. Fir......
A soil sample is analyzed to determine the iron content. First, the iron is isolated as Fe(NO_{3})_{2}. This compound is then reacted with KMnO4.
5 Fe(NO_{3})_{2} + KMnO_{4} + 8 HNO_{3} → 5 Fe(NO_{3})_{3} + Mn(NO_{3})_{2} + 4 H_{2}O + KNO_{3}
In one experiment, a 12.2-g sample of soil required 1.73 g of KMnO_{4} to react completely with the Fe(NO_{3})_{2}. Determine the percent (by mass) of iron present in the soil sample.
You are asked to calculate the mass percent of iron in a soil sample.
You are given a balanced equation, the mass of solid analyzed, and the mass of one of the reactants used to analyze the sample.
Step 1. Use the mass of KMnO_{4} to determine the amount of Fe(NO_{3})_{2} present in the soil sample.
1.73 g KMnO_{4}\left(\frac{1\text{ mol KMnO}_{4}}{158.0 \text{ g}} \right) \left(\frac{5\text{ mol Fe(NO}_{3}\text{)}_{2}}{1\text{ mol KMnO}_{4}} \right) = 0.0547 mol Fe(NO_{3})_{2}
Step 2. Use the stoichiometry of the chemical formula of Fe(NO_{3})_{2} and the molar mass of Fe to calculate the mass of Fe present in the soil sample.
0.0547 mol Fe(NO_{3})_{2}\left(\frac{1\text{ mol Fe}}{1\text{ mol Fe(NO}_{3})_{2}} \right) \left(\frac{55.85\text{ g}}{1\text{ mol Fe}} \right) = 3.06 g Fe
Step 3. Use the mass of Fe in the soil sample and the mass of the soil sample to calculate the percent by mass of Fe in the soil.
\frac{3.06 \text{ g Fe in soil sample}}{12.2\text{ g soil sample}} \times 100% = 25.1% Fe
Is your answer reasonable? Because the soil sample is not pure, the mass of iron in the soil is less than the mass of the soil sample and the weight percent of iron in the sample is less than 100%.