Question

Hemoglobin is \(6.0 \%\) heme \(\left(\mathrm{C}_{34} \mathrm{H}_{32} \mathrm{FeN}_{4} \mathrm{O}_{4}\right)\) by mass. To remove the heme, hemoglobin is treated with acetic acid and \(\mathrm{NaCl},\) which forms hemin \(\left(\mathrm{C}_{34} \mathrm{H}_{32} \mathrm{~N}_{4} \mathrm{O}_{4} \mathrm{FeCl}\right) .\) A blood sample from a crime scene contains \(0.65 \mathrm{~g}\) of hemoglobin. (a) How many grams of heme are in the sample? (b) How many moles of heme? (c) How many grams of Fe? (d) How many grams of hemin could be formed for a forensic chemist to measure?

Short answer

(a) 0.039 g of heme, (b) 6.32 x 10^{-5} moles of heme, (c) 0.00353 g of Fe, (d) 0.0412 g of hemin.

Step-by-step solution

Calculate the mass of heme in the sample

Given that the hemoglobin is 6.0% heme by mass, first calculate the mass of heme in a 0.65 g blood sample. Use the formula: \[ \text{mass of heme} = \text{total mass of hemoglobin} \times \frac{\text{percentage of heme}}{100} \] Substituting the values: \[ \text{mass of heme} = 0.65 \text{ g} \times \frac{6.0}{100} = 0.039 \text{ g} \]

Calculate the moles of heme

To find the moles of heme, use the molar mass of heme (\text{C}_{34}\text{H}_{32}\text{FeN}_{4}\text{O}_{4}). First calculate its molar mass, \[ \text{molar mass of heme} = 34 \times 12.01 + 32 \times 1.01 + 55.85 + 4 \times 14.01 + 4 \times 16.00 = 616.49 \text{ g/mol} \] Use the formula: \[ \text{moles of heme} = \frac{\text{mass of heme}}{\text{molar mass of heme}} \] Substituting the values: \[ \text{moles of heme} = \frac{0.039 \text{ g}}{616.49 \text{ g/mol}} \text{ mol} = 6.32 \times 10^{-5} \text{ mol} \]

Calculate the mass of Iron (Fe)

Use the number of moles of heme to find the mass of iron in the sample. Since there is one atom of Fe per molecule of heme: \[ \text{mass of Fe} = \text{moles of heme} \times \text{molar mass of Fe} \] Substituting the values: \[ \text{mass of Fe} = 6.32 \times 10^{-5} \text{ mol} \times 55.85 \text{ g/mol} = 0.00353 \text{ g} \]

Calculate the mass of hemin that can be formed

To find the mass of hemin (\text{C}_{34}\text{H}_{32}\text{FeN}_{4}\text{O}_{4}\text{FeCl}) that can be formed, use the molar mass of hemin. The molar mass is \[ \text{molar mass of hemin} = 616.49 \text{ g/mol} + 35.45 = 651.94 \text{ g/mol} \] Use the formula: \[ \text{mass of hemin} = \text{moles of heme} \times \text{molar mass of hemin} \] Substituting the values: \[ \text{mass of hemin} = 6.32 \times 10^{-5} \text{ mol} \times 651.94 \text{g/mol} = 0.0412 \text{ g} \]

Key concepts

mass percentage

Mass percentage helps us understand how much of a specific substance is present in a mixture or compound. In our problem, we see that hemoglobin is 6.0% heme by mass. This tells us that in every 100 grams of hemoglobin, there are 6 grams of heme.
To find the mass of heme in a specific sample, use the formula: mass of heme = total mass of hemoglobin × (percentage of heme / 100) In this case, for a 0.65 g blood sample: mass of heme = 0.65 g × (6.0 / 100) = 0.039 g.
This calculation lets us know how much heme is contained in the given hemoglobin sample.

molar mass calculation

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). To solve our exercise, we need the molar mass of heme (C_{34}H_{32}FeN_{4}O_{4}).
Use the atomic masses of the elements: -Carbon (C): 12.01 g/mol-Hydrogen (H): 1.01 g/mol-Iron (Fe): 55.85 g/mol-Nitrogen (N): 14.01 g/mol-Oxygen (O): 16.00 g/mol.
Calculate the molar mass of heme: molar mass of heme = (34 × 12.01) + (32 × 1.01) + 55.85 + (4 × 14.01) + (4 × 16.00) = 616.49 g/mol.
This information is crucial as it allows us to convert between mass and moles when dealing with chemical calculations.

stoichiometry

Stoichiometry involves using balanced chemical equations to determine the relationships between reactants and products. Here, it helps us convert between moles of heme and moles of iron or hemin formed. Since heme has one iron (Fe) atom per molecule, the moles of heme equals the moles of iron. For a forensic chemist, using stoichiometry ensures precision in their measurements and calculations. For example, to find the mass of iron from the moles of heme, use the formula: mass of Fe = moles of heme × molar mass of Fe given the moles of heme = 6.32 × 10^{-5} mol and molar mass of Fe = 55.85 g/mol: mass of Fe = 6.32 × 10^{-5} mol × 55.85 g/mol = 0.00353 g.

forensic chemistry

Forensic chemistry applies chemical principles to solve crimes. In our problem, the forensic chemist analyzes hemoglobin to measure hemin, a substance that forms when hemoglobin is treated with acetic acid and NaCl.
This process can help determine the presence and amount of hemoglobin in a sample.
By calculating the mass of hemin produced, investigators can estimate the original hemoglobin content. This data is vital for forensic chemists in crime scene investigations, helping them gather evidence through chemical analysis. For instance, to find the mass of hemin formed, use moles of heme and molar mass of hemin:mass of hemin = moles of heme × molar mass of hemin. Here, moles of heme = 6.32 × 10^{-5} mol and molar mass of hemin = 651.94 g/mol: mass of hemin = 6.32 × 10^{-5} mol × 651.94 g/mol = 0.0412 g.
Understanding these chemical principles aids forensic chemists in accurate measurements, crucial for criminal investigations.