Estimate the number of atoms in 7.827 g of iron using the mass of an atomic mass unit (1.661 x 10^-27). The atomic mass of Fe is 55.85 u.
You are ignoring units.
mass of iron is in grams.
atomic mass is in grams.
amu is in kg.
So you have an incompatability in units.
number atoms= massiron/(massofeach atom)
where mass ofeach atom=55.85u*mass/u
so fix the units to be compatable, and you have it.
that is my problem i am not sure how to fix the units. Do I divide the grams by 1000 so i would have 0.007927 grams then multiply by 55.85? Thank you so much for any help.
1*10^23 atoms
To estimate the number of atoms in 7.827 g of iron, we need to follow a series of steps. Let's go through them:
Step 1: Convert the given mass of iron (7.827 g) into atomic mass units (u).
To do this, we need to use the mass of one atomic mass unit (1.661 x 10^-27 kg).
First, convert grams to kilograms:
7.827 g = 0.007827 kg.
Then, divide the mass in kg by the mass of one atomic mass unit:
0.007827 kg / (1.661 x 10^-27 kg/u) = 4.713 x 10^23 u.
Step 2: Determine the number of iron atoms in one atomic mass unit (u).
To do this, we divide the molar mass of iron (55.85 g/mol) by Avogadro's number (6.022 x 10^23 atoms/mol).
55.85 g/mol / (6.022 x 10^23 atoms/mol) = 9.274 x 10^-23 g/atom.
Step 3: Calculate the number of iron atoms.
Multiply the number of atomic mass units from Step 1 by the number of atoms in one atomic mass unit from Step 2:
4.713 x 10^23 u * 9.274 x 10^-23 g/atom = 4.370 x 10^1 atoms.
Therefore, the estimated number of atoms in 7.827 g of iron is approximately 43.7 atoms.