Question

Hemoglobin, the protein responsible for carrying oxygen from the lungs to the body tissues, contains \(0.355\) per cent iron. Hydrolysis of \(100 \mathrm{~g}\) of hemoglobin gives \(1.48 \mathrm{~g}\) of tryptphan; calculate the minimum molecular weight of hemoglobin which is consistent with these results.

Short answer

The minimum molecular weight of hemoglobin that is consistent with the given results is approximately 963.24 g/mol.

Step-by-step solution

Calculate the mass of iron in 100 g of hemoglobin

We know that hemoglobin contains \(0.355\%\) iron, so to find the mass of iron in 100 g of hemoglobin, we calculate: Mass of iron = (Percentage of iron / 100) * Mass of hemoglobin Mass of iron = \((0.355 / 100) * 100 \mathrm{~g}\) Mass of iron = \(0.355 \mathrm{~g}\)

Calculate the number of moles of iron

Now that we have the mass of iron, we need to calculate the number of moles. To do this, we will use the molar mass of iron. The molar mass of iron is approximately 56 g/mol. Moles of iron = Mass of iron / Molar mass of iron Moles of iron = \(0.355 \mathrm{~g} / 56 \mathrm{~g/mol}\) Moles of iron = \(6.339 \times 10^{-3} \mathrm{~mol}\)

Calculate the number of moles of tryptophan

We are given that 100 g of hemoglobin yields 1.48 g of tryptophan. We will first calculate the moles of tryptophan using the molar mass of tryptophan, which is approximately 204 g/mol. Moles of tryptophan = Mass of tryptophan / Molar mass of tryptophan Moles of tryptophan = \(1.48 \mathrm{~g} / 204 \mathrm{~g/mol}\) Moles of tryptophan = \(7.255 \times 10^{-3} \mathrm{~mol}\)

Calculate the molar ratio of iron to tryptophan

Next, we will calculate the molar ratio of iron to tryptophan. Molar ratio = Moles of iron / Moles of tryptophan Molar ratio = \(\frac{6.339 \times 10^{-3} \mathrm{~mol}}{7.255 \times 10^{-3} \mathrm{~mol}}\) Molar ratio = \(0.874\)

Determine the minimum molecular weight of hemoglobin

Knowing the molar ratio of iron to tryptophan (0.874), we can now calculate the minimum molecular weight of hemoglobin. Molecular weight of hemoglobin = (Moles of iron * Molar mass of iron) + (Moles of tryptophan * Molar mass of tryptophan) / Molar ratio Molecular weight of hemoglobin = \(\frac{(6.339 \times 10^{-3} \mathrm{~mol} \times 56 \mathrm{~g/mol}) + (7.255 \times 10^{-3} \mathrm{~mol} \times 204 \mathrm{~g/mol})}{0.874}\) Molecular weight of hemoglobin = \(963.24 \mathrm{~g/mol}\) The minimum molecular weight of hemoglobin that is consistent with the given results is approximately 963.24 g/mol.

Key concepts

Percentage Composition

Percentage composition is crucial in understanding the makeup of compounds and molecules. In the context of hemoglobin, knowing that it contains 0.355% iron allows us to determine how much iron is present in a 100 g sample. Here's a simpler explanation of the process:
To find the percentage composition of iron in hemoglobin, you divide the given percentage by 100 and then multiply by the sample's mass. This reveals the actual mass of iron in that sample of hemoglobin. It's like finding out how much flour is in a cake mix that claims to be 20% flour. If you had 100 grams of the mix, 20 grams would be flour. Similarly, in our 100 gram hemoglobin example, there would be 0.355 grams of iron.

Moles Calculation

In chemistry, the mole is a fundamental unit used to measure the amount of substance. When we calculate moles from mass, we're essentially counting how many particles (like atoms or molecules) we have. Like counting eggs in dozens, we count atoms and molecules in moles.
To find the moles of iron in hemoglobin, we take the mass of iron we just calculated and divide it by iron's molar mass (the weight of one mole of iron atoms). This gives us the actual number of moles of iron in our sample. It's like figuring out the number of egg cartons we have if each carton holds a dozen eggs and we have a total number of eggs.

Molar Mass

Molar mass can be thought of as the weight of one mole of any chemical species (atoms, molecules, ions, etc.). It's measured in grams per mole (g/mol) and is specific to each element or compound. The molar mass acts like the unique 'ID' for different atoms in the realm of chemistry.
In our hemoglobin example, we use the molar mass of iron to not only figure out how many moles we have but also to further explore the relationship between elements and compounds in a molecule. The molar mass is akin to knowing that each egg weighs approximately 60 grams which would allow you to find the total weight if you knew the number of eggs.

Stoichiometry

Stoichiometry is the tool that lets chemists figure out the relationships between reactants and products in a chemical reaction. It's like a recipe that tells you how much of each ingredient you'd need to make a cake.
In this case, we use stoichiometry to find the ratio of moles of iron to moles of tryptophan in hemoglobin. This gives us a 'recipe' for how much iron and tryptophan combine to form hemoglobin. The final step involves using this ratio to calculate the minimum molecular weight of hemoglobin, which is essentially adding up the weights of the ingredients once we know how many of each we have. Think of it as calculating the total weight of the ingredients in a cake to find out how heavy the cake will be before you make it.