Question

$ 1 $ mole of $ {{H}_{2}}O $ consists of $ 6.022\times {{10}^{23}} $ molecules.
Find the number of molecules present in $ 3 $ moles of water?
What will be the mass of $ 5 $ moles of water?

Answer 1

Hint : The number of moles is the number of particles present in a substance. The particles can include atoms, molecules, ions, electrons, protons and many more. We use different formulas to calculate the number of atoms depending on what is given in the question.

Complete Step By Step Answer:
Number of moles is the number of particles in Avogadro number of a substance.
The particles include atoms, molecules, ions like electrons, protons, neutrons, etc.
Atoms are the smallest unit of a substance.
Two or more atoms combine to form a molecule.
Avogadro’s number is the number of units in one mole of a substance.
The value of Avogadro’s number is $ 6.022\times {{10}^{23}} $ . It can be varied depending upon the given value in question.
(a) $ n=\dfrac{x}{6.022\times {{10}^{23}}} $
where,
n is the number of moles
x is the number of molecules
Therefore,
 $ x=n\times 6.022\times {{10}^{23}} $
Here, $ n=3 $ (given in the question)
Hence,
 $ x=3\times 6.022\times {{10}^{23}} $
 $ x=18.066\times {{10}^{23}} $ molecules.
The number of molecules are $ 18.066\times {{10}^{23}} $ molecules.
(b) $ n=\dfrac{m}{M} $
where,
  n is the number of moles
m is the given mass
M is the molecular mass of the substance
Therefore,
 $ m=n\times M $
We have given the number of moles to be 3
and the molecular mass of water ( $ {{H}_{2}}O $ ) is $ 18 $ gm.
Hence,
 $ \begin{align}
  & m=3\times 18 \\
 & m=54 \\
\end{align} $
Therefore, the required mass is 54gm.

Note :
 $ n=\dfrac{m}{M} $ ( if we know the mass of the substance)
 $ n=\dfrac{x}{6.022\times {{10}^{23}}} $ (if the number of particles are given)
In this way we can calculate the number of moles depending upon the given quantity and also we can calculate the quantity if the number of moles are given.