Question

How many moles of ${{H}_{2}}O$ contains $2.60\times {{10}^{23}}$ molecules of water?

Answer 1

Hint: The mole is the unit of measurement for the amount of substance in the international system of units. It is defined as exactly $6.022\times {{10}^{28}}$ Particles, which may be atoms, molecules, ions or electrons.

Complete step by step answer:
We know that,
$1mole=6.022\times {{10}^{23}}$ molecules.
To know how many moles in ${{H}_{2}}O$ contain $9.60\times {{10}^{23}}$ molecules of water divided $1$ mole by the given molecules i.e.
$1mole=6.022\times {{10}^{23}}$ molecules.
$r\text{mole}=2.60\times {{10}^{23}}$ molecules
By applying cross multiplication we can calculate the no. of moles.
$2.60\times {{10}^{23}}=x\times 6.022\times {{10}^{23}}$
$x$ mole $=0.432175$ moles.
Therefore, $2.60\times {{10}^{23}}$ molecules of ${{H}_{2}}O$ contain $0.432175$ no. of moles.
The mole is widely used in chemistry as a convenient way to express amounts of reactants and products of chemical reactions.
The mole is essentially a count of particles, usually the particles counted are chemically identical entities, individually distinct.
Avogadro constant is the proportionality factor that reacts to the number of constituent particles in a sample with the amount of substance in that sample. The value of Avogadro constant was chosen so that the mass of one mole of a chemical compound in grams, is numerically equal to the average mass of one molecule of the numerically equal to the average mass of one molecule of the compound in Daltons. Avogadro constant ${{N}_{A}}$ is the proportionality factor that relates the molar mass of a substance to the average of one molecule. The numeric value of the Avogadro constant is called the Avogadro number ${{N}_{ A}}=6.022\times {{10}^{23}}.$

Additional Information:
The mole also be used to measure the amount of atoms, ions electrons or other entities, the concentration of a solution is commonly expressed by its molarity, defined as the amount of dissolved substance in mole per unit volume of solution, for which the unit typically used in mole per liter.
The term gram-molecule (g mol) was formally used for mole of molecules and gram atom for mole of atoms. The history of the mole is intervened with that of molecules mass, atomic mass unit and the Avogadro number. The Avogadro constant ${{N}_{A}}$ is related to other physical constants and properties.
(1) It relates molar gas constant $R$ and the elementary charge $e.$
$R={{K}_{B}}{{N}_{A}}$
(2) It relates the faraday constant $F$ and the elementary charge $e.$
$F=e{{N}_{A}}$
(3) It relates the molar mass constant, ${{M}_{u}}$ atomic mass with ${{m}_{u}}$
${{M}_{u}}={{m}_{u}}{{N}_{A}}$
The Avogadro constant also relates the molar volume of a substance to the average volume normally occupied by one of its particles, when both are expressed in the same unit of valence.

Note: In a solid the constant particles are fixed and bound in a lattice arrangement, yet they may be separable without losing their chemical identity. Thus the solid is composed of a certain number of moles of such particles. In other cases, such as diamond the entire crystal is essentially a single molecule; the mole still needs to express the number of atoms bound together, rather than a count of multiple molecules. The official mole is based on an outdated continuum concept of matter. The mole is not a true metric unit, rather it is a parametric unit, and the amount of substance is a parametric base quantity. The Avogadro constant also relates the molar volume normally occupied by one of its particles, when both are expressed in the same unit of volume. The mass of one mole of any substance is $N$ times the average mass of one of its constituent particles.