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

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.