Answer:
0.244 moles
Step-by-step explanation:
We know that if one mole of a substance is present, it has exactly the Avogadro number (NA) of particles.
NA=6.022×1023
Now, the mass of a sample can be given by the sum of the mass of all the particles in it.
So, we can say that the mass of one mole of a compound is equivalent to the mass of all the particles contained in one mole of a substance i.e., 6.022×1023 particles.
The mass of one mole of a substance is known as the molar mass of that substance. Its SI base unit is kg/mol but it is usually expressed in g/mol. It is a bulk property of a substance, not a molecular property.
Now, the molar mass of a sample is given by the mass of the sample substance divided by the number of moles of the substance present in the sample.
M=mn
So, the number of moles in a given sample can be given by
n=mM
Where n is the number of moles,
m is the mass of the substance given (in grams), and
M is the molar mass of the substance (in g/mol).
Now, the molecular mass of one mole of a compound is equal to the sum of atomic masses of all the elements present in the molecule.
So, the molecular mass of one mole of AlCl3 is
MAlCl3=MAl+3×MClMAlCl3=26.981+3×35.453MAlCl3=133.34g/mol
It is given to us that the mass of the sample substance is 32.5 grams.
So, the number of moles of the substance in the sample is
n=32.5g133.34g/moln≅0.244mol
Hence there are approximately 0.244 moles in a sample of 32.5 grams of aluminum chloride (AlCl3).
Note: It must be noted that in 2019, the SI base unit of molar mass was redefined. According to the new definition, the molar mass constant is
Mu=0.99999999965×10−3kg/mol
And not 1×10−3kg/mol.
But since the change is so insignificant, for practical purposes, the molar mass of an element is still considered to be equivalent to the atomic mass of the element.