Calculate the number density of strontium titanate (SrTiO3), ρ = 5.12 g cm
-3
Divide the density in g/cm^-3 by the number of grams per mole. That will give you mole/cm^3. For the number density, multiply that by Avogadro's number
To calculate the number density of a substance, you need to know its mass density (ρ) and its molar mass (M).
To find the molar mass of strontium titanate (SrTiO3), you need to sum up the atomic masses of all atoms in one molecule of SrTiO3.
The atomic masses of Sr, Ti, and O are approximately 87.62 g/mol, 47.88 g/mol, and 16.00 g/mol, respectively.
SrTiO3 has one atom of Sr, one atom of Ti, and three atoms of O. Therefore, the molar mass of SrTiO3 is:
M = (1 * 87.62 g/mol) + (1 * 47.88 g/mol) + (3 * 16.00 g/mol) = 183.60 g/mol
Given the mass density (ρ) of strontium titanate as 5.12 g/cm^3, we can use the formula for number density (n):
n = ρ / M
n = (5.12 g/cm^3) / (183.60 g/mol)
Note: Convert the units of g/cm^3 to g/mol before performing the division.
To convert the units, we need to multiply the mass density by the reciprocal of the molar volume (Vm). The molar volume is the volume occupied by one mole of a substance, which is the reciprocal of its molar mass.
Vm = 1 / M
Vm = 1 / 183.60 g/mol = 0.0054 mol/g
Now, multiply the mass density by the molar volume:
n = (5.12 g/cm^3) * (0.0054 mol/g) = 0.0276 mol/cm^3
Therefore, the number density of strontium titanate (SrTiO3) is 0.0276 mol/cm^3.