We know that a molecule is composed of one or many types of atoms which are bonded with each other through chemical bonds. The chemical bonds can be ionic or covalent bond. Hence the molecular weight would be the sum of atomic masses of all constituent atoms in atomic mass units. The constituent atoms can be check in the molecular formula of the given molecule. An atomic mass unit can be defined as 1/12$^{th}$ the weight of the C-12 isotope. It represents as amu or u. 

The molecular weight of a substance represents that how many grams are in one mole of the given substance. In other words, the mass of ne mole of substance is known as molecular weight. The atomic weight of constituent atoms can be check in the Modern Periodic table. In case of molecules with multi-atoms, the number of constituent atoms must be multiply with the atomic weight of them. 

Based on Molecular weight, some of the problems are given below:

Question 1: Calculate the molecular weight of aluminum sulphate. (Given atomic weight of Al = 26.98 amu, S = 32.06 amu and O = 16.00 amu)
Solution:

Molecular formula of aluminum sulphate is $Al_2(SO_4)_3$. Hence we can say that there are 2 atoms of Al, 3 atoms of S and 12 atoms of O in one mole Aluminum sulphate.

Hence total weight of;
Two Al atom; 2 $\times$ 26.98 = 53.96 amu

Three S atoms = 3 $\times$ 32.06 = 96.18 amu

Twelve O atoms = 12 $\times$ 16.00 = 192.00 amu

The molecular weight of Aluminum sulphate would be;
53.96 + 96.18 + 192.00 = 342.14 amu.

Question 2: Calculate the molecular weight of hydrogen peroxide and write the molecular formula of it.
Solution:

The molecular formula of hydrogen peroxide is $H_2O_2$. It states that there are two hydrogen atoms and two oxygen atoms in one molecule of hydrogen peroxide. 

The atomic weight of Hydrogen = 1.0079 amu
Atomic weight of Oxygen atom = 15.9994 amu

Hence molecular weight formula would be;

Molecular weight of $H_2O_2$ = [Mass of H $\times$ 2 ] + [Mass of O $\times$ 2 ]

Molecular weight of $H_2O_2$ = (2 $\times$ 1.0079) + (2 $\times$ 15.9994)

Molecular weight of $H_2O_2$ = 34.0146 amu.