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How many molecules of water are present in 0.25 mole of \[{{\text{H}}_{\text{2}}}{\text{O}}\]?
(A) 6.0 x \[{\text{1}}{{\text{0}}^{{\text{22}}}}\]
(B) 4.5 x \[{\text{1}}{{\text{0}}^{{\text{23}}}}\]
(C) 1.5 x \[{\text{1}}{{\text{0}}^{{\text{23}}}}\]
(D) 18 x \[{\text{1}}{{\text{0}}^{{\text{23}}}}\]

Last updated date: 19th Jul 2024
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Hint: One mole of any substance has Avogadro number of atoms or molecules or ions. Avogadro number, \[{\text{}}{{\text{N}}_{\text{A}}}\]= \[{\text{6}}{\text{.023 x 1}}{{\text{0}}^{{\text{23}}}}\]

Complete step by step answer: It is given that number of moles of water, \[{{\text{H}}_{\text{2}}}{\text{O}}\]= 0.25 moles.
We need to find the number of molecules present.
We know that 1 mole of \[{{\text{H}}_{\text{2}}}{\text{O}}\] contains Avogadro number of molecules.
⟹1 mole = \[{\text{6}}{\text{.023 x 1}}{{\text{0}}^{{\text{23}}}}\] molecules
Therefore 0.25 mole of water has x molecules of \[{{\text{H}}_{\text{2}}}{\text{O}}\].
⟹0.25 mole = x molecules
 ∴ x = \[{\text{6}}{\text{.023 x 1}}{{\text{0}}^{{\text{23}}}}{\text{x 0}}{\text{.25 = 1}}{\text{.51 x 1}}{{\text{0}}^{{\text{23}}}}\] molecules
Hence, 0.25 mole of water has \[{\text{1}}{\text{.51 x 1}}{{\text{0}}^{{\text{23}}}}\] molecules.

So, the correct option is C.

Additional Information: A mole is the SI unit to measure the amount of substance. Avogadro number is defined as the number of atoms present in 12g of carbon-12. The value of Avogadro number is \[{\text{6}}{\text{.023 x 1}}{{\text{0}}^{{\text{23}}}}\] molecules/atoms. It is denoted as \[{\text{}}{{\text{N}}_{\text{A}}}\]. Therefore, the number of moles can also be calculated from Avogadro number.
\[{\text{Number of moles = }}\dfrac{{{\text{Number of particles}}}}{{{\text{Avogadro Number}}}}\]
Here the term particle refers to either atoms or molecules or even it can be used to refer to ions.
It must be noted that the number of moles and molecules are the two different entities.
Water molecule has a molar mass of 18 g calculated from its constituent atoms masses. It is an universally essential compound.

Note: It must be noted that the number of moles and molecules are the two different entities. Avogadro number gives the number of molecules or atoms or ions present in one mole of the substance by which we can easily find the number of molecules in 0.25 mole of \[{{\text{H}}_{\text{2}}}{\text{O}}\].