Question

The molecular mass of\[CuS{O_4}.5{H_2}O\]is:
(Atomic mass of \[Cu\]= 63.5, \[H\] = 1, \[O\] = 16, \[S\] = 32)
A. 233.5 gm/mole
B. 249.5 gm/mole
C. 251.5 gm/mole
D. 247.5 gm/mole

Answer 1

Hint: The molecular mass of a compound is the sum of the masses of each atom present in a molecule of the compound. The mass of each atom is known as its atomic mass.

Complete Step by Step Solution:
The mass of an atom, called the atomic mass, is defined as \[\dfrac{1}{{12}}\] the mass of a single atom of Carbon-12 at rest. Although the SI unit of mass is the kilogram (kg), atomic masses are measured in the non-SI atomic mass unit (amu) or unified mass (u). The atomic mass unit and the kilogram are related as \[1{\rm{ amu = 1}}{\rm{.6605}} \times {\rm{1}}{{\rm{0}}^{ - 27}}{\rm{ kg}}\].

The molecular mass is the mass of a molecule and is calculated as the sum of the masses of all atoms present in a molecule. It is also measured in amu (or u).

Here, we are asked to find out the molecular mass of Copper sulphate pentahydrate (\[CuS{O_4}.5{H_2}O\]) and we are given the following atomic masses:
\[Cu = 63.5{\rm{ }}gm/mole\]
\[H = 1{\rm{ }}gm/mole\]
\[O = 16{\rm{ }}gm/mole\]
\[{\rm{S = 32 gm/mole}}\]
Copper sulphate pentahydrate contains 1 atom of copper, 1 atom of sulphur, 10 atoms of hydrogen and 9 atoms of oxygen. Thus,
\[{\rm{Molecular mass = (Atomic mass of Cu) + (Atomic mass of S) + (10}} \times Atomic{\rm{ mass of H) + (9}} \times Atomic{\rm{ mass of O)}}\]
\[ \Rightarrow Molecular{\rm{ mass = (63}}{\rm{.5 gm/mole) + (32 gm/mole) + (10}} \times {\rm{1 gm/mole) + (9}} \times 16{\rm{ gm/mole)}}\]
\[ \Rightarrow {\rm{Molecular mass = 249}}{\rm{.5 gm/mole}}\]

Thus, option B is correct.

Note: Please note that although atomic and molecular masses are usually expressed in atomic mass units (amu), in the above question and solution, they are expressed in grams per mole (gm/mole or g/mol). This is because, in the above question, the terms “atomic mass” and “molecular mass” are being used to refer to the molar masses of the atom or molecule. Please keep in mind that atomic/molecular mass is distinct from molar mass, although they are related. While the atomic and molecular mass refers to the masses of a single atom or molecule respectively, the molar masses of an atom or molecule refer to the mass of 1 mole of that atom or molecule. Molar masses are expressed in grams per mole.