Question

In which case is the number of molecules of water is maximum?
A. \[{10^{ - 3}}mol\] of water
B. \[0.00224L\] of water vapour at \[1atm\] and \[273K\]
C. \[0.18g\] of water
D. \[18ml\] of water

Answer 1

Hint: We need to know and study Avogadro's Number. Avogadro’s number defines the number of units in one mole of any substance. One mole of a substance is defined as the molecular weight of a substance in grams.It is proportionality factor that is used to relate the number of constituent particles in a sample with the amount of substance in that sample.

Complete step by step answer:
From the definition of Avogadro’s number, we know that one mole of a substance contains a number of molecules. Now we calculate the number of molecules for each of the given entities.
\[{10^{ - 3}}mol\] mol of water: \[{10^{ - 3}}mol\] of water will contain a number of molecules, which is equal to \[6.02214076 \times {10^{20}}\] number of water molecules.
 \[0.00224{\text{ }}L\] of water vapour at \[1atm\] and \[273K\] : We first need to find the number of moles of water vapor in \[0.00224L\] of water vapour at \[1atm\] and \[273K\].
\[V = 0.00224L\] , \[P = 1atm\] and \[T = 273K\] .
We know that $PV = nRT$
Or, $n = \dfrac{{PV}}{{RT}}$ = $\dfrac{{1 \times 0.00224}}{{0.0821 \times 273}}$=${10^{ - 4}}moles$
Therefore, ${10^{ - 4}}moles$ of water will contain ${10^{ - 4}}moles$× number of molecules,which is equal to \[6.02214076 \times {10^{19}}\] number of water molecules.
\[0.18g\] of water : Since \[18grams\] of water makes one mole of water(molecular weight of water), therefore \[0.18g\] of water contains \[{10^{ - 2}}moles\] of water. Hence, \[0.18g\] of water will contain a number of molecules, which is equal to \[6.02214076 \times {10^{21}}\] molecules of water.
\[18ml\] of water: \[18ml\] of water is also equal to \[18g\]of water since the density of water is \[1g/ml\] . Therefore \[18g\]of water contains \[1mole\] of water. Hence the number of water molecules in \[18ml\] of water will be equal to Avogadro’s number which is equal to .
Therefore, the maximum number of water molecules is present in \[18ml\] of water.
Hence,the correct option is option (D).

Note:
It must be noted that the Avogadro’s number is calculated based on the charge of electrons. The charge on an electron based on modern experiments is estimated to be \[1.60217653 \times {10^{ - 19}}coulombs\] per electron. Dividing the charge on a mole of electrons by the charge on a single electron the Avogadro's number of \[6.02214154 \times {10^{23}}\] particles per mole is obtained.