Question

The number of water molecules present in a drop of water (volume=$0.0018ml$) at room temperature is:
A.$6.023 \times {10^{19}}$
B.$1.084 \times {10^{18}}$
C.$4.84 \times {10^{17}}$
D.$6.023 \times {10^{23}}$

Answer 1

Hint: In this question, we have to calculate the number of entities in a volume of water. Simply use the unitary method to find the answer to this question. \[6.022 \times {10^{23}}\] is Avogadro's number and represents the number of atoms/molecules present in one mole of the substance. We shall use the mole concept to find the number of moles present and hence, the number of molecules.

Formula used: \[{\text{Density = }}\dfrac{{{\text{mass}}}}{{{\text{volume}}}}\]and ${\text{No}}{\text{. of moles = }}\dfrac{{{\text{Given mass}}}}{{{\text{Molar mass}}}}$

Complete step by step answer:
Rearranging the formulas of density, we have:
\[ \Rightarrow {\text{mass = density} \times \text{volume}}\]
Now the density of water =\[1{\text{g/ml}}\]. In the question we have the volume of water =\[0.0018{\text{mL}}\].
Hence, mass of \[0.0018{\text{mL}}\] water =\[1 \times 0.0018 = 0.0018{\text{gm}}\]. Molar mass of water =\[18{\text{gm/mol}}\].
Number of moles in \[0.0018{\text{gm}}\] of water can be calculated using formula for no. of moles = $\dfrac{{0.0018}}{{18}}$ ​\[ = 0.0001\;{\text{mole}}\].
The number of molecules of water in 1 mole = \[6.022 \times {10^{23}}\;{\text{molecules}}\].
Thus number of molecules of water in \[0.0001\;{\text{mole}}\] = \[6.022 \times {10^3} \times 0.0001 = 6.023 \times {10^{19}}\]
Hence, the number of water molecules present in a drop of water (volume = \[0.0018{\text{mL}}\]) at room temperature are \[6.023 \times {10^{19}}\].

Hence, the correct answer is option A.

Note:
The concept that a mole of any substance contains the same number of particles was formed out of research which was conducted by Italian physicist Amedeo Avogadro. Avogadro constant can be defined as the number of molecules, atoms, or ions in one mole of a substance: $6.022 \times {10^{23}}$ per mol. It is derived from the number of atoms of the pure isotope $^{{\text{12}}}{\text{C}}$ in 12 grams of that substance and is the reciprocal of atomic mass in grams. The formulae for the mole concept can be summarized as:
${\text{Number}}{\text{ of moles = }}\dfrac{{{\text{Mass of the Substance in grams}}}}{{{\text{Molar mass of a Substance}}}} = \dfrac{{{\text{Number of Atoms or Molecules}}}}{{6.022 \times {{10}^{23}}}}$.
These formulae can be used to establish relationships between formula mass, the mole, and Avogadro’s number can be applied to compute various quantities that describe the composition of substances and compounds.