Iron crystallizes in a body–centered cubic structure. The volume of one Fe atom is 9.38 x 10–24 cm3, and the density of Fe is 7.874 g/cm3. Find an approximate value for Avogadro’s number.
mass of Fe atom = 56 grams/mol
how many cm^3/mol ?
56 g / 7.874 g/cm^3 = 7.11 cm^3/mol
how many atoms is that?
7.11 cm^3/mol / (9.38*10^-24 cm^3/atom)
= .76*10^24 atoms/mol
= 7.6 *10^23
well, not too bad :)
Damon's method looks MUCH simpler than what I would do but here is mine.
volume Fe atom = 9.38E-24 cc.
V = (4/3)*pi*r^3 and solve for r = radius
r = about 1.31E-8 cm
For a body centered cubic, a = edge length. 4r = a(3)^1/2 and solve for a.
a = about 3.03E-8 cm
volume of unit cell = a^3 = about 2.77E-23 cc.
mass unit cell = volume x density = 2.77E-23 x 7.874 = 2.18E-22
u.c. = unit cell
mass u.c. = 2.18E-22 atoms/unit cell x 55.85/N and solve for N.
That's about 5.1E23 compared to the accepted value of 6.02E23.
To find an approximate value for Avogadro's number, we can use the formula:
Avogadro's number = density × volume of one atom / molar mass
First, we need to find the molar mass of iron (Fe). The atomic mass of iron (atomic number 26) is approximately 55.845 g/mol.
Using the formula, we can calculate Avogadro's number:
Avogadro's number ≈ (density × volume of one atom) / molar mass
Plugging in the values:
Avogadro's number ≈ (7.874 g/cm3 × 9.38 x 10–24 cm3) / 55.845 g/mol
Calculating this expression:
Avogadro's number ≈ 1.33 x 10^23 mol-1
Therefore, an approximate value for Avogadro's number is 1.33 x 10^23 mol-1.
To find an approximate value for Avogadro's number, we can use the given information about the volume of one iron (Fe) atom and the density of iron.
Step 1: Convert the given density from grams per cubic centimeter (g/cm³) to kilograms per cubic meter (kg/m³). This is done by dividing the density by 1000 since there are 1000 grams in a kilogram:
Density of Fe = 7.874 g/cm³ = 7.874/1000 kg/m³ = 0.007874 kg/m³.
Step 2: Calculate the mass of one iron (Fe) atom using its volume and density.
Mass = Density × Volume
Mass of one Fe atom = 0.007874 kg/m³ × 9.38 x 10^(-24) cm³ = 7.374 x 10^(-26) kg.
Step 3: Calculate the approximate number of iron (Fe) atoms in one mole of Fe using the molar mass of Fe.
The molar mass of Fe is approximately 55.845 g/mol.
Number of Fe atoms per mole (Avogadro's number) = (6.022 x 10^23 atoms/mol) / (55.845 g/mol) ≈ 1.080 x 10^22 atoms/g.
Step 4: Calculate the approximate value for Avogadro's number.
Avogadro's number ≈ (Number of Fe atoms per mole) / (Mass of one Fe atom)
Avogadro's number ≈ (1.080 x 10^22 atoms/g) / (7.374 x 10^(-26) kg) ≈ 1.469 x 10^28 atoms/kg.
Therefore, an approximate value for Avogadro's number is 1.469 x 10^28 atoms/kg.