Question

What is the number of particles present in $ 36g $ of $ {H_2}O $ ?

Answer 1

Hint :The number of moles of a molecule defined as the ratio of given mass of molecule to its molar mass. The number of particles of a molecule is defined as the number of elementary atoms in per mole substance and is equal to the product of the number of moles present and Avogadro’s constant.
 $ N = n \times {N_a} $
Where, $ N $ is the number of particles in the given compound, $ n $ is the number of moles of the compound and $ {N_a} $ is the Avogadro’s constant.

Complete Step By Step Answer:
As per question, the data given is as follows:
Given mass of $ {H_2}O = 36g $
Molar mass of $ {H_2}O = 18\;gmo{l^{ - 1}} $
To calculate number of particles of a compound, we first need to calculate the number of moles present for the given mass of the compound, which is calculated as follows:
Number of moles of $ {H_2}O = \dfrac{{36}}{{18}} $
 $ \Rightarrow n = 2\;{\rm{moles}} $
Hence, the number of moles of water present $ = 2\;{\rm{moles}} $
Now, using the formula for the number of particles i.e., number of particles $ = n \times {N_A} $
Where, $ {N_A} $ is the Avogadro’s constant whose value is equal to $ 6.023 \times {10^{23}} $ .
Substituting values:
Number of particles $ = 2 \times 6.023 \times {10^{23}} $
 $ \Rightarrow 12.046 \times {10^{23}} $
 $ \Rightarrow 1.2 \times {10^{24}} $
Hence, the number of particles present in $ 36g $ of $ {H_2}O = 1.2 \times {10^{24}} $ .

Note :
The number of constituent particles like atoms, ions or molecules in a substance is related with the mass of that substance through a proportionality factor known as Avogadro’s constant. The standard unit i.e., SI unit Avogadro’s number is reciprocal of the unit of mole that is $ mol{e^{ - 1}} $ . As we know that Avogadro’s constant is dimensionless and with the help of Avogadro’s constant, we can also relate the molar volume of a substance to the average volume which is occupied by one particle, when the volumes are in the same units.