Question

If the mass of one molecule of water is $18amu$. What is the mass of one mole of water molecules?

Answer 1

Hint – You can start by defining the concept of moles, atomic mass, molecular mass and molar mass. Now use the relation $Molar{\text{ }}mass = Molecular{\text{ }}mass \times {N_A}$(${N_A} =$ Avagadro’s constant) to calculate the mass of one mole of water molecules.

Complete step by step solution:

Before going on to the mathematical calculations, let’s look at the concept of moles, atomic mass and molecular mass and molar mass.
- Mole Concept - So, 1 mole is the amount of a substance that has exactly $6.02214076 \times {10^{23}}$ (also known as Avogadro’s number or Avagadro’s constant) atoms or particles of that substance.
- Concept of Atomic mass – Atomic mass is the mass of an atom described relative to a unit called $amu$(also written as $u$). $1amu$ is defined as $\dfrac{1}{{12}}$ part of the actual mass of a carbon-12 isotope(atomic mass taken as $12amu$). For example - The atomic mass of chlorine($Cl$) and oxygen($O$) is $35.453u$ and $15.999u$ respectively.
- Concept of Molecular mass- Molecular mass is the mass of a single molecule relative to a unit called $amu$ or $u$. In other words molecular mass is the sum of individual atomic masses of all the atoms making up the molecule. For example- Molecular mass of Ethane (${C_2}{H_6}$) is $30.07amu$.
- Concept of molar mass – Molar mass of a given substance is the weight of the substance (in grams) divided by the amount of the substance (in moles). In other words, the molar mass of a substance is the weight of one mole of that substance. Its unit is $g/mol$
- Molar mass is related to molecular mass by the following relation
$Molar{\text{ }}mass = Molecular{\text{ }}mass \times {N_A}$
Here, ${N_A} =$Avagadro’s constant
So for this problem
$\Rightarrow Molar{\text{ }}mass = 18amu \times {N_A}$
$\Rightarrow Molar{\text{ }}mass = 18g/mol$
Hence, the mass of one mole of water is $18g/mol$.

Note – C-12 isotope was taken as the standard reference atomic mass for the$amu$measuring system, because of two reasons. The atom mass of C-12 atom could be measured accurately in comparison to other elements in the periodic table and the weight of carbon-12 atom was between the hydrogen and oxygen atoms used as reference before.