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.