Please someone explain the best way of solving this. A 55 kg woman has 7.5 x 10 to the power of negative 3 moles of hemoglobin (Molar mass=64,456 g/mole) in her blood, how many hemoglobin molecules is that? What is the quantity in grams?
hepl
1 mol has 5.02E23 molecules so 7.5E-3 mols will have
7.5E-3 mols x (6.022E23 molecules/mol) = ? number of molecules.
Then grams = mols x molar mass = ?
To solve this problem, we'll follow these steps:
Step 1: Convert the mass of hemoglobin to grams.
Step 2: Calculate the number of moles of hemoglobin.
Step 3: Use Avogadro's number to determine the number of hemoglobin molecules.
Let's start with Step 1:
Step 1: Convert the mass of hemoglobin to grams.
Given:
Mass of hemoglobin = 7.5 x 10^(-3) moles
Molar mass of hemoglobin = 64,456 g/mole
To convert moles to grams, you can multiply the number of moles by the molar mass.
Mass of hemoglobin in grams = (7.5 x 10^(-3) moles) x (64,456 g/mole)
Mass of hemoglobin in grams = 483.42 grams (rounded to two decimal places)
Now let's move on to Step 2:
Step 2: Calculate the number of moles of hemoglobin.
Given:
Mass of hemoglobin = 483.42 grams
Molar mass of hemoglobin = 64,456 g/mole
To convert grams to moles, divide the mass by the molar mass.
Number of moles of hemoglobin = 483.42 grams / 64,456 g/mole
Number of moles of hemoglobin = 7.5 x 10^(-3) moles (as given in the question)
Finally, let's proceed to Step 3:
Step 3: Use Avogadro's number to determine the number of hemoglobin molecules.
Avogadro's number tells us that there are 6.022 x 10^23 molecules in one mole of any substance.
Number of hemoglobin molecules = Number of moles of hemoglobin x Avogadro's number
Number of hemoglobin molecules = (7.5 x 10^(-3) moles) x (6.022 x 10^23 molecules/mole)
Number of hemoglobin molecules = 4.5165 x 10^21 hemoglobin molecules (rounded to the appropriate significant figures)
So, the 7.5 x 10^(-3) moles of hemoglobin is equivalent to approximately 4.5165 x 10^21 hemoglobin molecules. The mass of this quantity of hemoglobin is 483.42 grams.
To find the number of hemoglobin molecules, you can use Avogadro's number, which states that 1 mole of any substance contains 6.022 x 10^23 particles (atoms, molecules, or ions). So, first, let's calculate the number of moles of hemoglobin:
Number of moles = Mass of hemoglobin / Molar mass
Given that the mass of hemoglobin is 7.5 x 10^-3 moles and the molar mass is 64,456 g/mole, we can substitute these values into the formula:
Number of moles = 7.5 x 10^-3 moles / (64,456 g/mole)
Now, let's solve for the number of moles:
Number of moles = 0.00075 moles
Next, we can use Avogadro's number to convert the moles to the number of hemoglobin molecules:
Number of hemoglobin molecules = Number of moles x Avogadro's number
Number of hemoglobin molecules = 0.00075 moles x 6.022 x 10^23 molecules/mole
Calculating this, we get:
Number of hemoglobin molecules ≈ 4.5165 x 10^20 molecules
To find the quantity in grams, we can use the mass of hemoglobin:
Quantity in grams = Mass of hemoglobin x Number of moles
Quantity in grams = 7.5 x 10^-3 moles x 64,456 g/mole
Calculating this, we get:
Quantity in grams ≈ 483.42 grams
Therefore, the woman has approximately 4.5165 x 10^20 hemoglobin molecules in her blood, and the quantity is approximately 483.42 grams.